Colombian Physics Olympiads

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Colombian Physics Olympiad Problems

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Colombian Olympiad Physics Training Problems Problem 1-1 A hinge construction comprises three diamonds whose side lengths are in the proportions 3:2:1. Vertex A 3 is shifted in the horizontal direction with velocity V constant. Determine the velocities of the vertices A 1, A 2, B 2 at all angles of the building are straight.

Problem 1-2 In a movie screen shows the movement of a car. The radius of the front wheels of the car is r = 0.35 m and the rear R of r = 1.5. The front wheels have N 1 = 6 radios. The camera filming the film moves at a speed of 24 frames per second. a) Considering that the wheels of the car move without slipping, determine the minimum speed at which the car must be moved to the front wheels appear to rotate in the screen. b) What is the minimum number of radios N 2 which must be to the rear wheels while the front also appear to not rotate? For the next question considering that the number of spokes of the front and rear wheels is N 1 = N 2 = 6. c) How fast is the car moving from left to right, to a spectator will appear that the spokes of the wheels rotate in a counter clockwise? Problem 1-3 Two tanks are moving on a horizontal ground so that approximate along the same line with constant speed as shown. Each tank fires a shot at the same time in the same vertical plane of the other tank. The speed of each projectile with respect to the tank is u 1 and u 2 and the respective angles with the horizontal 1 2. Both shot tanks impinging upon. a) Find the relative speed of the tanks. b) Find the condition required for u 1, u 2 and 1, 2. Neglecting air resistance constant and assume the value of the acceleration of gravity). What if the above condition is not satisfied?

Problem 1-4 To measure the wind velocity distribution as a function of the height, is rolled up balloon ascends so that constant velocity. When the balloon is released, the dependency was measured elevation angle to the horizon balloon as a function of time as shown in Fig. Assuming that the wind speed at the ground surface is zero and the distance from the observer to the left point where the balloon is L = 1 km, determine the height of the balloon after 7 minutes of being released and the wind speed so high.

Problem 2-1 Determine the force exerted on the wall of a wedge to slip her true body of mass m. The angle of the wedge base The coefficient of friction between the body and the surface of the wedge is between the wedge and the ground. Problem 2-2 A solid is placed on a rough plane and inclined an angle to horizon. One inextensible cord is attached to the solid and its other end passing through a hole made in the plane. Initially, the rope is horizontal and is then pulled slowly until the solid reaches the half circumference having described hole. Find the coefficient of friction and the solid body plane.

Problem 2-3 A cable is placed on a cylinder so that part of it lies on a table and lying on the flat part. After the cable is released it begins to move without friction. Find the speed of the cable after it has established a uniform motion. The height of the table is equal to h.

Problem 2-4 Mass m A wedge is supported on a block of mass M and a stationary wall as shown in Fig. Find the acceleration of each of the blocks. Neglect friction.

Problem 2-5 Determine the accelerations of the bodies of masses m 1, m 2 and m 3 mechanical system of FIG. Is negligible friction between all surfaces in contact.

Problem 2-6 At the end of a table of length L and mass M is located a small block of mass m. The table can move without friction on a horizontal surface. The coefficient of kinetic friction between the body and the table is What minimum speed V is necessary to communicate at once to the table so that it drops the block?

Problem 2-7 For a thread shaped path and of rectangular cross section made on the internal surface of a hollow cylinder and slides a cube infinity. The inner radius of the cylinder is R basis. The thread pitch is h. The coefficient of friction is l. Find the maximum speed (speed limit) reached by the ulna. The dimensions of the cube and the thread profile are much smaller than R.

Problem 2-8 A rope is tied at one end to the lateral surface of a cylinder of radius r at its base and is wound around this k times (k is an integer). A mass m is connected to the other end of the rope and a speed communicates directed along the radius of the cylinder as shown in Fig. How long the rope is wrapped around the cylinder again. The cylinder is located on a smooth horizontal surface.

Problem 2-9 A small metal sphere mass m is skewered on a vertical metal ring of radius R so that it can slide without friction. The ball is connected to a massless spring which has one end fixed to the upper ring. The ball is displaced to point P or so POA = 60 ° and then released. If m = 1kg, k = 50 N / m, R = 50 cm and the natural length of the spring is 50 cm find: a) The conditions to be satisfied by the quantities given above so that when the ball is released from the point P or it reaches the point B. b) The equilibrium positions of the ball along the ring. Point B Is stable equilibrium position?

Problem 2-10 Two bodies of mass m 1 and m 2 are connected by an inextensible string passing over a pulley. The planes in which the bodies are formed with angles the horizontal and The body of the right is higher than the left

a distance h. After a time t starting the movement both bodies are at the same height. The coefficient of friction between the bodies and surfaces is To determine the relationship between the mass of bodies.

Problem 2-11 In the system of the figure, the block of mass M can move without friction. At baseline the suspended body mass m of yarn is separated from an angle the vertical and released. What is the mass of the body, if the angle forms with the vertical thread does not change when moving the system?

Problem 2-12 Two small bodies of masses m 1 and m 2 are joined by an elastic spring constant k. This system is on a smooth horizontal surface. At one point the bodies are released. The bodies begin to oscillate along a straight line. a) What is the period of the oscillations? b) How does each body position relative to the center of mass as a function of time? c) How does the distance between bodies with time? Problem 2-13 A body mass m is placed on another mass M, which is suspended from a spring elastic constant k, fig.9. At first spring body depends only mass M, then both bodies are loosened. Find the maximum force exerted by M on m.

Problem 3-1

A bucket of mass m lies on a horizontal surface. How high strength and low angle relative to the horizon than is necessary to pull the bucket by its upper edge to overturn without slippage, if the friction coefficient is equal to Problem 3-2 A thin sheet of paper is pressed toward the table by a homogeneous mass m bar whose upper end is fastened in an articulated manner. The angle between the bar and the sheet the coefficient of friction between them is There is friction between the table and paper. What minimum horizontal force must be applied to the blade out?

Problem 3-3 A solid cylinder of radius R is supported by two blocks of the same height as shown in Fig. A block is stationary and the other moves with speed V to the left. How the cylinder pressed force on the stationary block at the time when the two blocks are separated by a distance ? Consider that at the initial time the blocks were very close to each other, there is friction between the block and the cylinder.

Problem 3-4 A straight rod, uniform, homogeneous mass m and length L is placed on a horizontal table with its mass center horizontal distance perpendicular to the edge as shown in Fig. The rod is released from rest in its horizontal position and starts to rotate on the edge of the table. If the coefficient of static friction to the initiation of the movement between the bar and the table is μ, find the angle with the horizontal bar starting reached before sliding.

Problem 3-5 A homogeneous uniform circular cylinder rests on the edge of a horizontal step. The cylinder rolls out onto the stage with a negligible initial velocity without slipping. Find the angle that the cylinder rotates before leaving step and the angular velocity of the cylinder after it has rotated. Suppose that the effects of air resistance can be neglected.

Problem 3-6 A homogeneous light stick length L is originally placed horizontally. This is supported so that it can rotate freely around its center in a vertical plane. A spider falls with a vertical speed v o and lands located midway between the center of the bottom and the top. The mass m of the spider is equal to the mass of the stick. Immediately after landing the spider begins to run along this so that the angular velocity of the stick remains constant. Determine the largest value of v or so that when the spider reaches the end of the stick it is vertical. It is assumed that the spider is apparent from the stick when it is in vertical position. Draw a diagram of the path followed by the spider. (Moment of inertia of a bar of length L with respect to a perpendicular axis and passing 2/12). through its center, R = mL Problem 3-7 A homogeneous sphere, solid of radius R and mass m is dropped. Its center of mass is at rest, but the sphere is rotating about a horizontal axis barycentric angular velocity o. The lowest point of the sphere is at a height h from the ground as shown in Fig. When the field is released and hits the floor it bounces a fraction of its original height. The ball and the floor are made of materials such that the deformation of the impact both are considered negligible. Assume that the coefficient of kinetic friction between the ball and the floor is It is assumed that the air resistance is negligible and that the time of impact is very small but finite. (Moment of 2/5). inertia of the sphere about an axis passing through its center, R = 2Mr 1. Assuming that the sphere moves during the impact. Find: a) The rebound tangent angle b) The horizontal distance traveled by the center of mass after the first impact and after the second impact. c) The minimum possible value of

o.

2. Assume now that the slide ceases before the end of the time interval of impact. Reply back questions a) and b). 3. Taking into account the cases 1 and 2 to graph as versus

o.

Problem 4-1 The system of figure consists of two masses m and M together by a light rod of length L. The coefficient of friction between the rod and the edge of the step is μ. There is friction between the mass mand the wall. Find an expression relating the quantities m, M, L and so that the rod remains in equilibrium on the step.

Problem 4-2 Two wedges equal in shape of isosceles triangles, each of mass m 2 and the vertical angle equal are placed one after the other with their bases on a horizontal plane rough. The edges of the wedges are in contact. A mass m smooth sphere of radius r 1 and is positioned between the wedges so that the system is in equilibrium. Prove that there is balance is met:

where is the coefficient of friction and a is the length of each wedge base. Problem 4-3

Two identical blocks parallelepiped (dimensions a, b and c) are arranged as shown in Fig. The mass of the blocks is m and the coefficient of friction between them and the floor is Finding the possible values of the angle so that the system remains in the equilibrium position shown.

Problem 4-4 Three identical cylinders are positioned as shown in Fig. The coefficient of friction between the cylinders is 1 and between the cylinders and the floor is 2. Find the condition to be satisfied 1 and 2 sothat the system remains in balance.

Problem 4-5 Four smooth and equal spheres are placed at the bottom of a hemisphere of radius a. The radius of each sphere is b. A fifth sphere of the same radius and density is placed on them under what conditions there is a balance? There is no contact friction between the bodies. Problem 4-6 Three identical inelastic cords are fixed equidistant from each other a ring of radius r and similarly to a ring of radius 2r. The cords pass through a third ring of radius r as shown in Fig. The ring 1 is fixed in a horizontal plane and the whole system is in equilibrium. Find the distance between the centers of the rings 2 and 3. All rings are made of the same wire.

Problem 4-7

Pliers consist of two identical rigid parts fastened with a pivot at point O. What is the force exerted on the pivot if the edges of the clips are pressed with a force F? Assume there is no friction in the pivot.

Problem 4-8 A rope of length L =

R / 2 is placed on the surface of a fixed cylinder of radius R, with one end located in the upper part thereof as shown in Fig. Find

the acceleration of the cord as soon as it is released. Neglect friction

Problem 4-9 A rope of length L and M is suspended mass of the ends of the points O and O 'of a horizontal roof as shown in the figure below. If the distance from the ceiling to the lowest point of the string is H what is the tension in the rope at the lowest point of this?

Problem 4-10 A small cube of mass m is placed on an incline as shown in Fig. The angle of inclination of the plane is the cube is

= 2tan

and the coefficient of friction between the plane and

Determine the minimum horizontal force required to move the bucket.

Problem 4-11 A light bar length d is secured to the lower ends of two spring constants k 1 and k 2 respectively as shown in Fig. At a distance x from one of them in vertical direction throw applying a slight force F. What spring constant is observed?. Graphing the results

Problem 5-1 A body of mass m 1 = 0.1 kg is suspended from a long wire. He is bound in turn one light string of length L = 0.2 m with one small sphere of mass m 2 = 0.05 kg suspended at the other end as shown in Fig. In the small sphere below is communicated with a very short stroke velocity v or horizontally. What value v or the bodies would be found on the same horizontal?

Problem 5-2 A boy slowly ascends a mountain covered with snow and pulling a sled by a rope as shown in Fig. The rope is always parallel to the tangent at any point on the mountain where the child is located. The mountain top is at a height h and a distance L from its base. What made the boy work to bring the sled to the top of the mountain. The mass of the sled is m and the coefficient of friction μ on snow is.

Problem 5-3 Resting against a system that is on a smooth horizontal surface and consisting of two bodies of mass m, coupled by a spring with spring constant k, the speed V collides true body mass thereof. The collision is elastic. Determine the maximum elongation of the spring.

Problem 5-4

In a thermally insulated flat tube are infinite mass m with two pistons, between which there are n mols of monatomic gas at temperature T o. At the initial instant their velocities are directed in the same direction and is equal to V and pV, where p is a constant. To what maximum temperature will heat the gas? The plungers do not conduct heat. Neglect the mass of gas compared to the mass of the pistons.

Training Problems

Problem 5-5 In the figure shown how high will a sandbag of mass m 2 launched with the help of a very thin board of mass m and length L, if on the other end of the table from the height H drops a sack of mass m 1 ?

Training Problems

Problem 5-6 Two identical balls are linked through a light rope of length L and placed on a table as shown in Fig. Determine the height of the table so that the two balls reach the ground falling at the same time, if the ball is initially at the right edge of the table and about to fall. The friction between the table and the balls like between the string and the edge of the table are neglected.

Problem 5-7 In the initial state the centers of two masses M and spheres with radii R 10 are separated a distance R as indicated below. In one load is distributed evenly + Q and-Q in the second. The first area is connected to a remote wall with a thread which supports a maximum tension T. The second area is released at one time. Determine the velocity of the spheres after colliding if the collision is quite inelastic. The loads are not redistributed.

Problem 5-8 A conductor bar length L and mass m of two rigid bars hanging conductive also negligible mass and length h which are hooked on a horizontal axis. The system is in a vertical homogeneous magnetic field intensity B. A current pulse I or passes through the bar for a short time interval Determine the maximum inclination of the suspension bar relative to the vertical.

Problem 5-9 A satellite moves in a circular orbit of radius R around the earth R = 2 R t (R t = radius of the earth). At one point, the satellite is launched from a ship to a distant planet. The spacecraft is launched tangentially to the circular orbit in the direction of movement of the satellite. As a result, the satellite is in an elliptical orbit that passes close to the earth at a point that is opposite to the launch site of spacecraft. What is the relationship between the mass of the spacecraft and the satellite before launch? How much time elapsed from when the ship is launched until the satellite reaches the opposite point of its orbit? A narrow tube of constant cross-section forms a square of side L, and is in a vertical plane. The tube is filled with two liquids - miscible equal volume and density of 1 and 2. At first, denser liquid occupying the upper tube. At some instant the liquids are set into motion. Find the maximum speed. No friction. The acceleration of gravity is g.

Problem 5-11 A spacecraft in flight explodes into three equal portions. A portion continues along the original line of flight. The other two shoot out in directions forming an angle of 60 ° with the original path. The energy released in the explosion is twice larger than the kinetic energy possessed probe precisely at the time of the explosion. Determine the kinetic energy of each fragment immediately after the explosion. Problem 5-12 Two blocks of equal masses m are joined through an elastic spring constant k, as indicated below. The upper block is lowered so as to compress the spring a distance x or and then released. What is the maximum height of the center of mass of the system after releasing the upper block?

Problem 5-13 In a thermally insulated flat tube are infinite two pistons with mass m and M, between which there is a monatomic gas occupying a volume V or P or pressure. The plungers are freed. Estimate the maximum speeds of the pistons. Underestimate gas mass compared to the mass of the pistons.

Problem 5-14 The piston of mass M, which encloses the volume V or a monatomic gas pressure P or and temperature T or moves at speed u. Determining the temperature and gas volume during maximum compression.The system is thermally insulated. Neglecting the heat capacities of the plunger and the container.

Problem 5-15 On one end of a straw length L and m is mass of mass M a grasshopper. The straw is flat on a horizontal table. What minimum speed must the grasshopper jump to reach the other end of the straw? Problem 5-16 Three bodies of equal mass m are interconnected by a length strings as shown in Fig. Each of the bodies has the same charge q. If one of the threads is cut what is the maximum speed acquired by each of the masses?

Problem 5-17

Two identical particle velocities u and v, and form angles with the joining line, and the distance L from each other as shown in Fig. The charge on each particle is q. Determine the mass of the particles, it is known that the minimum distance which is equal to a close.

Problem 5-18 A meteor moving towards a planet of mass M (along a line through the center of the planet), hitting a spinning artificial satellite by a circular orbit of radius R around the planet. The mass of the satellite is ten times greater than the mass of the meteor. As a result of the crash the meteorite is embedded in the satellite, which in turn passes into a new orbit the planet whose minimum distance is R / 2. Determine the speed or the meteorite before the crash. Problem 5-19 Two identical disks, mass m and radius R, slide on a frictionless ice rink and go to meet with parallel velocities v 1 and v 2, while rotating with angular velocity 1 and 2 in opposite directions. When hitting the edges are glued and their centers are separated by a distance equal to the diameter of both disks. Determine the linear and angular velocities after the collision set.

Problem 6-1 A homogeneous rod, cylindrical, thin and of length L, which is rotatable about an axis O at one end, is introduced slowly into water as indicated in the figure. The density of the rod is less than that of water o can stay upright stick to a certain value of x, it will show as x 1. If x is smaller than x 1, a minor perturbation of the rod is inclined as shown in Figure b. If the axis of rotation remains in the water immersing the rod assumes a position as shown in figure c.

a) Determine the

dependence versus x.

b) Determine the value of x 1. c) Construct a function of x, with-L R T) is: (1.1 6) the minus sign indicates that it is an attractive force, ie a force pulling the particle towards Earth. By Therefore we can calculate Potential Energy of equation (1.15) as (1.17 ) substituting Equation (1.16) into equation (1.17) and integrating *:

(1.18) * See Appendix at the end of this calculator solucionario. The minus sign indicates that the potential energy is negative for any infinite distance, ie, the potential energy is zero at infinity and decreases with decreasing separation distance.This corresponds to the fact that the gravitational force exerted on the particle by Earth Attraction is. Escape Velocity Now we can find the gravitational potential energy of a particle of mass m on the surface Earth using equation (1.18): (1.19) where R T is the radius Earth , M T is its mass. The amount of work required, equation (1.15), to move the body from the surface of Earth to infinity is, using equation (1.19): (1.20) Taking the following data:

(1.21) we can calculate: (1.22) If a projectile which is situated on the surface of Earth we give you more energy than this, then, neglecting the resistance of the atmosphere, would escape Earth never to return. As this happens, its kinetic energy decreases while its potential energy increases, but their speed is never reduced to zero. The speed Escape v 0, so that the projectile does not return to Earth Is given by (1.2 3) of which we can solve equation v 0:

2.

If we consider the planet Earth as a spherical conductor of 6400 Km Radio capacitance is: a) 0.00712 C b) 0.0712 F c) 0.000712 F d) 0.00000712 C e) ______ Help: Solution

3.

From the relation found C = 0.000712 F When 1.00 g of water, which occupies a volume of 1.00 cc, boiling at atmospheric pressure, becomes steam at 1671 cc. The heat of vaporization of water is 539 cal / g at 1atm. Change in internal energy of the system is: a) 2000 cal b) 45,788 cal c) lime 0.0333 d) 498 cal e) 17 cal f) ______ Help: 1 cal = 4186 J Solution Heat of vaporization C V C is the heat required for a unit mass of substance m pass from the liquid to gaseous state holding constant Temperature and Pressure. This is say (3.1) Pressure Pressure is one way to describe Force acting on a fluid. Is defined as the magnitude of Normal Force per unit area. (3.2) Work From equation (1.4) of this solucionario

, We can write (3.

3) then (3.4) if p is a constant

(3.5) 1st Act Thermodynamics If a system state changes from an initial equilibrium i to a final equilibrium state f in a defined way, if the heat absorbed by the system C, the work is done by the system and the change in T Energy inner system is  E I then: (3.6) Now if we replace the equations (3.1) and (3.5) in equation (3.6) we get: (3.7) In our case V 2 is the volume of vapor V 1 is the volume of liquid Replacing data:

4.

The fact that this amount is positive means that the internal energy of the system increases during the process. That is the 539 [cal] needed to boil 1 [g] Water 41 [cal]invested in external work of expansion and 498 [cal] as internal energy are added to the system. Consider a solid cylinder of radius R and mass M, which rolls without sliding down an inclined plane, the inertia of the cylinder is . The velocity of its center of mass when the cylinder reaches the lower part of the plane is: a) b) _________ Solution

c)

d)

e)

f)

This is a problem of rotational dynamics. Consider the following: Rigid Body Body where the constituting particles always maintained the same position each. If a rigid body rotates with an angular velocity  in each particle of the rotation body has a certain amount of kinetic energy. A particle of mass m, which is at a distance r from the rotation axis moves in a circle of radius r with an angular speed  around this axis and has a linear speed given by (4.1)

Therefore its kinetic energy this is (4.2) The kinetic energy Total body is the sum of the kinetic energies of each of its constituent particles. If the body is rigid then all particles have the same angular velocity  but each particle may have a different radius r. Therefore Kinetic Energy Total Revolving rigid body is:

(4. 3)

where n indicates the total number of masses which form the system. Rotational Inertia Rotational inertia, denoted by I, plays the same role in rotational motion that performed by Mass M in the transnational movement. Is defined as

(4.4) Note that Rotational Inertia a body depends on the particular axis which is rotating, as well as body shape and the way it is distributed mass. Substituting equation (4.4) in equation (4.3) we obtain Kinetic Energy Rotation E CR:

(4.5) Center of Mass In physics always treat objects as if they were mere particles have mass but not size. Since the translational motion of each particle undergoes the same displacement body which then any movement of a particle represents the movement of the entire body. Even when the body turn to move or vibrate one point in the body called center of mass that moves in the same way you would a particle subject to the same forces.

Position the center of mass of a set of masses that lie on a line or in a plane or in space is given by:

Now consider the problem posed considering Act Conservation Energy : Initially the cylinder is at rest at a height h above the floor leaning against the upper end of the inclined plane (Figure 4.1)

When rolling down the inclined plane loses the cylinder equal to a potential energy (4.6 ) In its motion the cylinder must earn a kinetic energy equal to (4.7) where

v  Linear speed of the Center of Mass   Angular speed around the center of mass

Hence Conservation of Energy we have: (4.8)

we also know that: equation (4.8):

and

. Then substituting in

(4.9) v clearing where we finally obtain that:

* Appendix Calculation. Calculation Differential calculus is an important mathematical tool for the analysis of physical systems. It's not complicated, just use some familiar ideas (eg   and applies them to a small world (eg d, o), infinitely small, or in the words of calculation: infinitesimal. Let your main ideas: Euclidean plane Locus represented by:

Variable changing, which varies, is denoted by x The change that must be considered is the following

Delta:

is a symbol used to denote a difference between a target value

and an initial value, for example

Differential: d is equal to the delta is a delta just super small, infinitely small, infinitesimal. Summation is a mathematical symbol used to denote sum, for example is used to denote the sum of all students college or the amount of bricks with which he has built a house, etc. Integral: Or is a mathematical symbol used to denote sum (like ), Which is used only to denote for example the sum of the number of atoms of oxygen in a room, or the number of drops of water having an ocean, etc. Function Is a relationship between the elements (dots) set x to the elements (points) and assembly. We use the symbol to denote a function. For example in the Euclidean plane a function can be positive:

If we take two points on the x axis, these will correspond to other points on the y axis:

We as:

know

that Delta ,

x and Delta

and are

defined

These Deltas can be represented in the Euclidean plane:

Media Ratio Is defined as the average ratio

that in physics is precisely half the speed.

Limit If we let eg Delta x becomes very but very small, making each horizontal line is but not touching: What we get finally is a point we denote by dx. Obviously at this point corresponds dy point:

Now that the notation has been made is a limit. The threshold applied to the mean ratio or average speed

So d remains

only very small. And

It is known as the instantaneous velocity. And these last two equations define what is referred to as derivative calculation. Viewing FIGURE C.4 Question is: How many points dx between x 1 and x 2? ... Many do not? And what happens if we add? You agree that we obtain Sure! Of course you do. What you have to realize is known as the fundamental theorem of calculus:

Well ... Other useful rules are (without proof, but we hope you've motivated you enough to investigate more about the physics and calculus):

where k is a constant.

REVIEW 3rd of Secondary (20072002) Notes: Read the review and consultation if you have questions. DO NOT put your personal data or the question paper or leaves your solutions!, We will give you a form for that. The conceptual part is worth 40% and 60% practical part. Have a time of 2 hours.

1. 2. 3. 4.

1.

2.

Conceptual part In the street the whole day a cold drizzle falls. In the kitchen is laid much laundry. Do clothes dry faster if you open the window? Because the paper kite tail is placed? As can determine the density of any stone using a dynamometer and water containers? Maximum pressure that can be measured using two U mercury manometer connected in series by a short tube if each of them allows to measure pressure Pa. m? Practical part A hexagonal pencil was pushed along the horizontal plane as shown in Figure 1 With what values of the friction coefficient between the stylus and the stylus slide plane for the roll plane without?

Figure 2 was made from the photograph taken from the tails of smoke trailing advancing two locomotives for railroad rectilinear path with speeds and

. The directions of

movement of trains are marked with arrows. Find the wind speed.

3.

Three bodies with masses m 1, m 2 and m 3 can slide along the frictionless horizontal line (figure 3). Where m 1 >> m 2 and m 3 >> m 2. Determine the maximum speeds of the bodies ends at baseline if they were at rest, while the body was half the speed v. The clashes are considered quite elastic.

SOLUTIONS Conceptual part 1.

Both on the streets and in the kitchen with the window closed the steam is saturated.

But Street temperature is lower than in the premises. Consequently, the steam pressure in the street is lower than in the room. So when you open the window of the kitchen steam will come out of it on the street, due to which the steam is in the kitchen is always unsaturated. The clothes will dry faster. 2. Thanks to the different length of the wires going from main line to points comet paper, the latter is stable with respect to rotation around the axis OO 'and O 1 O 1'. The tail of the comet facilitate stability of paper regarding the rotation around the vertical axis O 2 O 2 '.

3.

 To determine the density of the stone is essential to know its mass m and volume V:

. Using the dynamometer can determine the value of the body weight in air P 1 and P 2 in the water. The difference between these values is equal to the force Archimedes acting on the stone water (Archimedes force which acts upon the stone in the air can be underestimated). Knowing the density of water determine the volume dela stone:

,

and density:

4. The manometer mercury U-shaped (Figure 4a) measures the soprepresión , Or indicates how much pressure p at the elbow Left gauge is greater than the atmospheric pressure p 0. The limitation on the range of the pressure values to be measured imposed by the length of the manometer tubes. You can not measure the overpressure greater that with which the mercury reaches the edge of the right side (according to Figure 4a). The limit value of the overpressure measured to the gauge in question is equal to m.

In the case of series connection of two pressure gauges (figure 4b) the overpressure left elbow gauge 1 is greater than

in

Because the pressure p 2 in the elbow

Left gauge 2 is greater than atmospheric in the magnitude thereby . The compressed air in the left elbow gauge 2 occupies the volume

where S is the sectional area of the tubes. First this air volume occupied

right elbow gauge one and the same volume in the left elbow and pressure gauge 2 This air was equal to the Atmospheric (p 0). Assuming isothermal compressed air can be applied is the law of Boyle - Mariotte:

where . Multiplying the numerator and denominator on the right side of this equation by

where

As

Then

, We get

Pa.

Practical part 1. In moving the stylus up side two forces act: the normal reaction force plane N and the friction force F (Figure 1sol). Because the stylus is not displaced in the vertical direction then Friction can annotate Consider the time "critical" when the stylus touches the plane at point A. For the pen not

. For the magnitude of the force

returns the resultant of all the forces must pass through the center of mass of the pencil. Accordingly, for the center of mass must pass the resultant R of the forces N and F. If the coefficient friction force is large and R passes under the center of mass, the pencil will spin. Thus the condition that the pen is not turning shall be recorded as follows: or is obtained where finally .

2.

The plume released by the locomotive at point A at time t will be run by

the wind at point C. Thereby

. Where

is the wind speed (Figure 2a.). But after a time t the locomotive will be located at point B. The progress of the train is equal to , Where is the speed of the train. It is noteworthy that the plume is oriented along Vector , Or what for that matter, along the vector .

Now it's easy to find the wind speed. We draw on an arbitrary scale the vector

. Then from the origin O of

vector we draw from the same scale the vector . The ends of the vectors and we draw straight lines parallel to corresponding columns of smoke (Figure 2b.) At the point M of intersection of these lines with the point O enlasamos. In precisely selected scale OM vector is the wind speed. In effect, the OM-vector v 1 is oriented along plume dela

dragging the first locomotive, while the OM-vector v 2, along the plume of the second. As measured by length of the vector rule module OM will find the wind speed. Equals 3.

.

Collisions of the mass m 2 body with mass bodies m 1 and m 3 continue until the speed becomes the same

less than the speed of one of the bodies (M 1 or M 3). But since m 1 >> m 2 and m 3 >> m 2, momentum and energy of the body mass m 2 is much smaller than the momentum and energy of these bodies of masses m 1 and m 3. Consequently, noting the law conservation of energy and momentum can not take into account the energy and momentum of the body of mass m 2 cease after collision Denoting v 3 v 1 and the velocities of the bodies of masses m 1 and m 3 after cease collisions can be noted:

Solving these equations together and considering >> m 1 m 2 and m 3 >> m 2 found:

and

.

REVIEW 4th of Secondary (20072002) Notes: Read the review and consultation if you have questions. DO NOT put your personal data or the question paper or leaves your solutions!, We will give you a form for that. The conceptual part is worth 40% and 60% practical part. Have a time of 2 hours.

1.

Conceptual part Determine the density of an unknown liquid. You can use: option 1: two vessels with

one liquid glass tube 80 to 100 cm. long, rulers, rubber tubes, funnels. option 2: liquid to be analyzed, graduated cylinder, liquid with known density dynamometer. 2. In a plane mirror is an image of a candle. What will happen to this if between the mirror and the candle is placed parallel plate glass? 3. In the street the whole day a cold drizzle falls. In the kitchen is laid much laundry. Do clothes dry faster if you open the window? 4. In a vase with water that rotates around its axis (figure 1) is released to a ball that floats Awash. What part of the area will be located the ball?

Practical part 1. The foam cube with a mass M = 100 g. is situated on a horizontal support (Figure 2). The hub height is h = 10 cm. Below the cube is pierced by a bullet that flies

vertically and whose mass is m = 10 gr. The speed of the bullet entry in the bucket is

,

to the output

2.

. Toddle onto the cube or not?

From the South Pole and the North Pole of the Earth simultaneously take off two rockets with equal

Initial velocities directed horizontally. Within the time

rockets were

at the maximum distance from one another. Determine the maximum distance between the rockets. The acceleration of fall on Earth is considered known. The radius of the Earth is 3.

.

In the space between the walls of the ampoule in a pressure flask was established

to

ambient temperature. Appreciating the time during which the content in the tea thermos be cooled from 90

 0

C to 70 0 C  The surface of the blister is

specific heat capacity of water is

. The heat capacity is 1 liter. The , The universal gas constant is

. Not taking into account the heat leakage through the cap. SOLUTIONS Conceptual part 1. By immersing the same in two different liquids load forces acting on Archimedes the same is determined as follows: , where

and

(1)

are the densities of the liquids, one of which is unknown.

Values F 1 and F 2 can be determined by the difference of the indications of the dynamometer which is suspended load in cases when the latter is in the air and in the liquid: ,

(2)

where P Dynamometer is the indication when the load was in the air, P 1 and P 2 the indications dynamometer, when the load is in the density liquids known and unknown. From equations (1) and (2) we find the unknown density of the liquid:

2.

In tracing the course of a few rays is easy to be convinced that, after entering the candle

and the mirror is disposed parallel flat plate glass, the image of the candle will approach the mirror. 3.

See sec Third solutions.

4.

Since the ball floats to flower the water, the density of the material itself is lower than the density

Water . Suppose that the ball is located at a distance R from the axis of a rotating vessel. If the density of the ball is equal to the density of water, it would be an invariable distance axis of rotation. The centripetal acceleration may be communicated to the resulting ball force and gravity forces of the surrounding water pressure. In this resulting module would equal where

is the angular speed of rotation of the container V, the volume of the pellet.

The pellet density Arranged in the same point from the surrounding water acts a Like force the ball now communicates acceleration

This acceleration is greater than that needed for rotation by the circle of radius R. Accordingly, the equilibrium position of the ball is located in the axis of the container. Practical part 1. The cube can jump if the magnitude of the force F, which acts on the same part of the bullet, is greater than the magnitude of the force of gravity

. Let us find this force. For this

examine the bullet. In the same from the bucket acts a force equal in magnitude, but opposite in direction to the force of gravity m g. The speed of the bullet passing through the hub, varies insignificant variation is equal to 5 m / s, which is only 5% of the speed of the bullet to penetrate into the bucket. Therefore we can consider that no force F depends on the speed of the bullet and is constant. The momentum of the bullet passing through the hub, to effect changes in the bullet action of two forces: the force of gravity and the force friction. If the time in which the bullet passes through the whole cube, is denoted by , then (1). Time not hard to find him. Since the forces acting on the hub are constant, the acceleration is constant also Bullet and therefore the speed of the bullet changes linearly with time. Therefore the average speed of movement of the bullet in the cube is equal to . Accordingly, the bullet passes through the hub in time . Substituting this value

in Eq. (1) we find: .

As

is small, the value of

is much smaller than the pulse variation

Bullet and can be neglected. The force F was greater than the strength of the gravity acting on the hub. So skip the bucket. 2. Rockets move by ellipses. The takeoff point corresponds to the distance minimum from the center of the earth, while the point of the orbit that is encime Earth point diametrically opposite to the apogee of the orbit. At these points the rocket velocity is perpendicular to the line drawn from the center of the Earth to orbit. L denote the length of the major axis of the orbit. Then the maximum distance s between rockets will equal

. The period T of the rocket flight orbit equals

to . If the flight period for the circular orbit of radius R t is denoted by T 1, then according to Kepler's third law

where

. Because centripetal acceleration of the satellite moving the circular orbit radius R p is equal to g, then .

Therefore

. Thus

. . 3. Denote temperature T 1 and T 2 tea room temperature. Wall bumping warm air molecules acquire contained in the ampoule kinetic energy

. But upon contacting the cold wall kinetic energy

of the molecules reach equal

Thus the molecule transfers energy .

The number of collisions of the molecules with the walls of surface S at time equals (1) where n is the concentration of molecules and , The mean velocity projection module of the molecules on the X axis perpendicular to the wall. To make the assessment that you can take: The mean square velocity v is determined by the formula

where M is the molar mass of the gas and T, the average temperature in the vial. Since the values of T 1 and T 2 are coming we can take: . From the main equation of the kinetic theory of gases we obtain . Rewriting the formula (1):

meaning that at time

energy is transferred (2).

For

content in the tea thermos cools from the temperature until the temperature energy must be transferred .

Substituting this expression for W in the formula (2), we find the time necessary to cool the tea:

.

REGIONAL PEACE

1st Secondary 1)

Conceptual part List several repetitive phenomena that occur in nature and that could serve as reasonable weather patterns.

2) a.

You can combine two vectors of different magnitude to give a zero resultant?

b.

They can do three vectors?

3)

List several scalar quantities.

4)

Is time a vector? Why?

1)

Practical part Express your height in miles. In your answer using only prefixes.

A plane travels 876.5 [km] in a straight line at an angle of 37.5  to the North

2)

East. How much the plane has traveled both to the North and to the East, from its starting point? . Help: 3)

Two trucks carrying sand. One of these, B, has a small hole in its base through which the sand is falling to the floor. They have taken the following mass versus time for both trucks: Data # Time [min] A forklift Mass [kg] Cart B mass [kg] 1 0.0 8.75 8.75 2 1.0 8.76 7.77 3 2.0 8.75 6.74 4 3.0 8.77 5.76 5 4.0 8.75 4.75 6 5.0 8.75 3.76 7 6.0 8.74 2.73 a) Plot: 

The mass versus time for the truck to



The mass versus time for the truck B

b) Because if A mass is constant we have different data? The number of seconds in a year can be replaced conveniently by   10. What is the

4)

percentage error of this figure?. Take  = 3.141592653 June 8, 2003

REGIONAL PEACE

2nd of Secondary Conceptual part 1) b.

2)

If a  b = 0, does it follow that a and b are perpendicular to each other?

c.

If a  = 0, Should be parallel to and b?

d.

Can a dot product between vectors be a negative amount? List several scalar and vector quantities.

3) 4)

What experimental evidence exists to assume that the speed of sound is the same for all wavelengths? What is it that causes mirages? Do you have something to do with the fact that the refractive

1)

index of air is not constant but changes to its density? Draw rays explaining the phenomenon. Practical part A cylindrical vessel containing water has a radius of 2 cm. In 2 hours the water level low 1 mm. Estimate in grams per second, the evaporation rate at which water is evaporating.

2)

The lowest tone that can detect the human ear as sound is about 20 [Hz] and the highest is about 20000 [Hz]. What is the wavelength of each of them in the air?. The speed of sound in air is 331.3 [ms -1]. Indicates a wavelength where the wavelength and amplitude.

3)

What should be the height of a vertical mirror, so that a person 6 feet tall to be able to observe the entire image?. Assume that your eyes are 4 inches below the top is its head

4)

Has been taken following the motion of a body: Data # Time [s] Position [m] Speed [ms -1]

Acceleration [ms 2]

1 2 3 4 5 6

0.0 1.0 2.0 2.5 3.5 4.0

1.0 3.7 4.8 5.0 3.9 1.4

4.0 1.8 0.7 0.0 -3.0 -6.2

-3.8 -1.2 -1.0 -1.9 -4.9 -7.3

Plot: 

the position versus time



the speed versus time



acceleration versus time. June 8, 2003

REGIONAL PEACE

3rd of Secondary SOLUTIONS 1)

Conceptual part What is the difference between mass and weight? Much do you weigh?

2)

Everyone knows that when you look in a mirror is an inversion of the left and right. The right hand seems to be a left, left eye seems to be one law, etc.. Is it possible to design a mirror system that would allow to observe an image as the way in which people normally observed? If possible, draw a picture with some typical ray showing that this is true.

3) 4)

Explain: Archimedes Principle, equations of continuity and Bernoulli, As you may know the distance that has been struck by lightning from where you find yourself? Practical part

1) a.

Using the definition of scalar product a  b = (a) (b) cos  and that a  b = a x b x + a and b and b z + z obtaining the angle between the vectors: a = 3 i + 3 j - 3 k and b = 2 i + 3 k

b. 2)

Plot the vectors a = 3 i + 3 j + 3 k, and b = 2 i + 3 k and the vector product a  He drops a stone from the top of a building. The sound of the stone to hit the ground is

heard 6.5 s later. If the speed of sound is 1120 ft s -1 Calculate the height of the building.

3)

(Venturi tube) analytically determining the fluid velocity, density  known, it travels through the tube shown in the figure, where MP1 and MP2 are two pressure gauges. A 1 and A 2 are the areas perpendicular to the flow in regions 1 and 2 respectively.

Finally with data:  = 1 g / cc, p 1 = 1000 N m -2 , P 2 = 800 N m -2, A 1 = 40 cm 2, A 2 = 22 cm 2, calculate v 1 June 8, 2003

REGIONAL PEACE

4th of Secondary 1) 2) 3)

Conceptual part Explain the Steiner theorem, also known as the parallel axis theorem. Explain that the dynamic lifting force is the force acting on a body because of its motion through a fluid. Comment: 1st and 2nd law of thermodynamics, entropy, reversible and irreversible processes, isothermal processes and adiabatic.

4)

Explain what the Doppler effect.

1)

Practical part A disc of 0.5 [m] radius and 20 [kg] of mass can rotate freely about a fixed horizontal axis passing through its center. Applies a force F of 9.8 [N] pulling a cord coiled around the edge of the disc.Find the angular acceleration of the disk and its angular velocity after 2 [s]. Finding the reaction force also exists in the brackets which support the axis of the disc.

2)

A semiquantitative definition of electric flux is: us that: q sphere vectors

3)

. And Gauss's law tells

. Write the electric field of a point charge q taking Gaussian surface as a of

radius r. Help: and

The

total

area

of

a

sphere

is

r 2 and

the

have the same direction.

A boat in motion produces surface waves on a calm lake. The boat runs 12 oscillations in 20 [s]; each oscillation produces a wave crest. The crest of the wave takes 6 [s] to reach the distant shore 12 [m]. Calculate the wavelength of surface waves.

4)

Three capacitors of 1.5  F], 2  F] and 3  F] are connected in a) series, b) are parallel and applies a potential difference of 20 [V]. Determine in each case i) the capacitance of the system, ii) loading and the potential difference of each capacitor, iii) energy of the system.

REGIONAL PEACE

1st Secondary SOLUTIONS 1)

Conceptual part List several repetitive phenomena that occur in nature and that could serve as reasonable weather patterns.

Sun The time when the moon becomes full, the beginning of a season, solar cycles, the movement of the stars, etc.. 2) a.

You can combine two vectors of different magnitude to give a zero resultant?

Sun b.

They can do three vectors?

Sun 3) 4)

1) 2)

No If

List several scalar quantities. Sun - mass, time, density, volume, temperature, electric current, etc.. Is time a vector? Why? Sun - No, that the management and direction of a vector has no restriction on its orientation. Practical part Express your height in miles. In your answer using only prefixes. Sun - If you measure 1.67 meters then say you write 1.67 milli Kilo meters. A plane travels 876.5 [km] in a straight line at an angle of 37.5  to the North East. How much the plane has traveled both to the North and to the East, from its starting point? . Help:

Sun -

Eastbound:

876.5 cos (52.5  = 533.6 [km]

Northbound

876.5 sin (52.5  = 695.4 [km]

Since 90  - 37.5  = 52.5  angle that is taken with respect to the horizontal. 3)

Two trucks carrying sand. One of these, B, has a small hole in its base through which the sand is falling to the floor. They have taken the following mass versus time for both trucks: Data # Time [min] A forklift Mass [kg] Cart B mass [kg] 1 0.0 8.75 8.75 2 1.0 8.76 7.77 3 2.0 8.75 6.74 4 3.0 8.77 5.76 5 4.0 8.75 4.75 6 5.0 8.75 3.76 7 6.0 8.74 2.73 a) Plot: 

The mass versus time for the truck to



The mass versus time for the truck B

b) Because if A mass is constant we have different data? Sun - Because when we take measurements random errors always exist, why not find a single result if not several. But note that the difference between them (mass of Cart A) is not great. These differences are known as natural statistical fluctuations. The number of seconds in a year can be replaced conveniently by   10. What is the

4)

percentage error of this figure?. Take  = 3.141592653 Sun -   10 = 31415926.53 In a year of 365 days or 8760 hours are 31,536,000 seconds. Therefore the error percentage is 0.38% Remember And This is a rough estimate because in a year when there are actually 365.2 days. June 8, 2003

REGIONAL PEACE

2nd of Secondary SOLUTIONS Conceptual part 5) a.

If a  b = 0, does it follow that a and b are perpendicular to each other?

Sun - Yes, since by definition a  b = (a) (b) cos  as cos  = 0 if and only if  = 90  then a and b are perpendicular. b.

If a  = 0, Should be parallel to and b?

Sun - Yes, since by definition a  = (a) (b) sin  u and as sin  = 0 if and only if  = 0  then a and b are parallel. c.

Can a dot product between vectors be a negative amount?

Sun - Yes, you can. Which can not be negative is the magnitude of a vector. 6)

List several scalar and vector quantities. Sun -

7)

8)

Scalar: mass, time, density, volume, temperature, electric current, etc.. Vectors: Strength, Speed, Acceleration, Magnetic Fields, Electric, Gravity; Momentum, Torque, What experimental evidence exists to assume that the speed of sound is the same for all wavelengths? Sun - Any piece of music, which is a collection of different wavelengths of sound waves, could never be heard as we do if the speed was different for certain wavelengths, as certain notes come to us much later or earlier than the other, you think? Would hear at the wrong without understanding anything. What is it that causes mirages? Do you have something to do with the fact that the refractive index of air is not constant but changes to its density? Draw rays explaining the phenomenon. Sun - They did have a lot to do. The refractive index is sensitive to temperature changes. The mirages usually happen in deserts or on paved roads in a region very hot places exceeding 40  C, so ground-level air is hot and have lower density than the cooler air rises

5)

creating a series of strata or layers of different temperature levels. A layer of cold air, another of hot air and cold another produce a lens which bends the light rays and makes an image appear which can not be. Practical part A cylindrical vessel containing water has a radius of 2 cm. In 2 hours the water level low 1 mm. Estimate in grams per second, the evaporation rate at which water is evaporating. [Cc s -1]. 1cc water = 1 g of water. 1 [mm]

Sun - The volume of water that falls is = 0.1 [cm]. Therefore 6)

[G s -1]

The lowest tone that can detect the human ear as sound is about 20 [Hz] and the highest is about 20000 [Hz]. What is the wavelength of each of them in the air?. The speed of sound in air is 331.3 [ms -1]. Indicates a wavelength where the wavelength and amplitude. Sol - As [mm]

and

[Ms -1] then the wavelengths are 16,565 [m] and 16,565

7)

What should be the height of a vertical mirror, so that a person 6 feet tall to be able to observe the entire image?. Assume that your eyes are 4 inches below the top is its head Sun - The figure shows the trajectories of rays that leave the top of the head of the individual and his toes. These rays chosen so that enter the eye after reflection, affect the vertical mirror in points a and b respectively. The mirror needs to occupy only that region between these two points. Projecting rays reaching the eye towards the place where they form the mirror image is that this should have half the height of the individual, ie 3 feet. Note that this height is independent of the distance at which is the person in the mirror.

8)

Has been taken following the motion of a body: Data # Time [s] Position [m] Speed [ms -1]

Acceleration [ms 2]

1 2 3 4 5 6

0.0 1.0 2.0 2.5 3.5 4.0

1.0 3.7 4.8 5.0 3.9 1.4

Plot: 

the position versus time



the speed versus time



acceleration versus time.

4.0 1.8 0.7 0.0 -3.0 -6.2

-3.8 -1.2 -1.0 -1.9 -4.9 -7.3

June 8, 2003

REGIONAL PEACE

3rd of Secondary SOLUTIONS 1)

Conceptual part What is the difference between mass and weight? Much do you weigh? Sun - The mass is a scalar, its units are [kg], the weight is a vector, is a force therefore is measured in Newtons [N]. If you say you have a mass of 66 [kg] weights then 66 [kg]  [ms -2] = 645.15 [N]. 9775 [ms -2] is gravity in La Paz. 9.81 [ms -2] is the gravity at sea level. 1.67 [ms -2] is the gravity on the moon. How much would you weigh on the moon?

2)

Everyone knows that when you look in a mirror is an inversion of the left and right. The right hand seems to be a left, left eye seems to be one law, etc.. Is it possible to design a mirror system that would allow to observe an image as the way in which people normally observed? If possible, draw a picture with some typical ray showing that this is true. Sun - If possible, be requires two mirrors that are joined at an angle of 90  between

3)

them. Each image in a mirror will be reflected in the other mirror as to achieve reverse what we usually see as a result finding the desired image. Explain: Archimedes Principle, equations of continuity and Bernoulli,

Sol - A body wholly or partly immersed in a fluid is pushed upward by a force that equals the weight of the fluid displaced by said body (Archimedes). The principle that expresses the conservation of mass in a fluid movement is known as the

Where is the fluid density, is the area through which the fluid at a given time and is the fluid velocity. That the product of these three quantities remain constant is a fancy way of saying that the mass does not change in the fluid. continuity equation:

The principle that expresses the conservation of energy in the movement of a fluid is known as

4)

Bernoulli's equation:

Where

and

and

the height at which the fluid moves,

is the pressure,

the severity

continue to express the density and

velocity of fluid. The first term is the kinetic energy per unit volume [J m -3], the second and third terms express the potential energy per unit volume [N m -2 = J m -3] due to internal forces (pressure) and external forces respectively. Therefore the total energy per unit volume remains constant. As you may know the distance that has been struck by lightning from where you find yourself? Sun - First "see" the beam. Light travels at a speed of approximately

[Ms -1] so we

can say that lightning emits light reaches us instantly. Then we have the time

that comes to

us in the "sound" of the beam. The speed of sound in air is worth

[Ms -1]. Then

using the relationship

the distance found. Practical part

1) a.

Using the definition of scalar product a  b = (a) (b) cos  and that a  b = a x b x + a and b and b z + z obtaining the angle between the vectors: a = 3 i + 3 j - 3 k and b = 2 i + 3 k

 

Sun - The angle will b. Sun -

2)

Plot the vectors a = 3 i + 3 j + 3 k, and b = 2 i + 3 k and the vector product a  a  = 9i - 3 j - 6 k, which must be stressed is that both a and b form a

plane

in space which is perpendicular to the vector to  the graph is easily accomplished by locating the points in space (3,3,3), (2,0,2) and (9, -3, -6 ) indicating the end of each vector starting at the origin (0,0,0). He drops a stone from the top of a building. The sound of the stone to hit the ground is heard 6.5 s later. If the speed of sound is 1120 ft s -1 Calculate the height of the building. Sun - The total displacement covered by the stone and the sound is:

where g = -32.2 [ft / s 2] also

then

[S]

where

solution: 3)

cleared

[S]. Finally

staying

only

with

the

positive

[Feet].

(Venturi tube) analytically determining the fluid velocity, density  known, it travels through the tube shown in the figure, where MP1 and MP2 are two pressure gauges. A 1 and A 2 are the areas perpendicular to the flow in regions 1 and 2 respectively.

Finally with data:  = 1 g / cc, p 1 = 1000 N m -2 , P 2 = 800 N m -2, A 1 = 40 cm 2, A 2 = 22 cm 2, calculate v 1 Sun - From the continuity equation:

(A) And the Bernoulli equation when the system is in a horizontal position: (B)

If we replace (A) in (B) and then solve for

we obtain:

Replacing the data provided we find that:

13.16 [ms -1]

4)

Verify that when a wave hits a certain angle and passes through half limited by flat faces parallel, the direction of propagation of the beam emerging is parallel to the incident beam. Sun Consider the following figure:

Using the law of refraction or Snell's law we find: Similarly:

n 1 sin  i) = n 2 sin  t)

n 2 sin  = n 2 sin 

Now within the medium 2 is true also that  i = 

t.

Combining these equations is reached  t =  i, which is what we wanted to prove. June 8, 2003

REGIONAL PEACE CONTEST II

4th of Secondary SOLUTIONS 5)

6)

7)

Conceptual part Explain the Steiner theorem, also known as the parallel axis theorem. Sun - The parallel axis theorem is given by the relationship: , Where I is the inertia around the axis of rotation arbitrary I cm is the rotational inertia parallel axis passing through the center of mass, M is the total mass of the object and h is the perpendicular distance between the axes. The two axes are parallel. The moments of inertia with respect to the parallel axes relate in this simple way. Explain that the dynamic lifting force is the force acting on a body because of its motion through a fluid. Sun - These bodies are the wings of an airplane or a helicopter propellers. The streamlines of air around the wing of an aircraft for example cause the air speed above the wing has a greater magnitude than the air velocity below this, which means that the pressure above the wing is less than pressure below which must occur if there is to be a push upward. Comment: 1st and 2nd law of thermodynamics, entropy, reversible and irreversible processes, isothermal processes and adiabatic. Sun All thermodynamic system in an equilibrium state has a state variable, called the internal energy of the system is such that its change

where

Energy is added to

is the energy supplied by the system when performing work. (1st Law) the system by heat transfer and

It is impossible for a cycler not produce another effect that continuously transfer heat from one body to another at a higher temperature than this. It is also possible to reformulate the 2nd law in terms of entropy: A natural process that begins in an equilibrium state and ends in another place at the direction that causes the entropy of the system and its environment increases. Entropy is a thermodynamic variable that measures the disorder. If a change occurs very slowly so that at each moment the system is in an equilibrium position then the process is reversible. And if the system away from its equilibrium state then the process is irreversible. When there is a change in system pressure or volume but the temperature is kept constant is spoken of an isothermal process. When there are non-heat exchange between the system and the environment comes to an adiabatic process. An adiabatic process can be reversible or irreversible. 8)

Explain what the Doppler effect. When a person hears a sound is moving toward the stationary source that produces it, the frequency of the sound heard is greater than when at rest. If the person is moving away from the stationary source, less frequently heard when this than when at rest. Similarly is the

5)

equivalent when both source and person move away from or towards. This effect applies to all waves in general. Practical part A disc of 0.5 [m] radius and 20 [kg] of mass can rotate freely about a fixed horizontal axis passing through its center. Applies a force F of 9.8 [N] pulling a cord coiled around the edge of

the disc.Find the angular acceleration of the disk and its angular velocity after 2 [s]. Finding the reaction force also exists in the brackets which support the axis of the disc. Sun 6)

A semiquantitative definition of electric flux is: us that: q sphere

7)

. Write the electric field of a point charge q taking Gaussian surface as a of

vectors

. And Gauss's law tells

radius r. Help: and

The

total

area

of

a

sphere

r 2 and

is

the

have the same direction.

A boat in motion produces surface waves on a calm lake. The boat runs 12 oscillations in 20 [s]; each oscillation produces a wave crest. The crest of the wave takes 6 [s] to reach the distant shore 12 [m]. Calculate the wavelength of surface waves.

8)

Three capacitors of 1.5  F], 2  F] and 3  F] are connected in a) series, b) are parallel and applies a potential difference of 20 [V]. Determine in each case i) the capacitance of the system, ii) loading and the potential difference of each capacitor, iii) energy of the system.

REGIONAL PEACE

3rd of Secondary SOLUTIONS 1)

Conceptual part What is the difference between mass and weight? Much do you weigh? Sun - The mass is a scalar, its units are [kg], the weight is a vector, is a force therefore is measured in Newtons [N]. If you say you have a mass of 66 [kg] weights then 66 [kg]  [ms -2] = 645.15 [N]. 9775 [ms -2] is gravity in La Paz. 9.81 [ms -2] is the gravity at sea level. 1.67 [ms -2] is the gravity on the moon. How much would you weigh on the moon?

2)

Everyone knows that when you look in a mirror is an inversion of the left and right. The right hand seems to be a left, left eye seems to be one law, etc.. Is it possible to design a mirror system that would allow to observe an image as the way in which people normally observed? If possible, draw a picture with some typical ray showing that this is true. Sun - If possible, be requires two mirrors that are joined at an angle of 90  between

3)

them. Each image in a mirror will be reflected in the other mirror as to achieve reverse what we usually see as a result finding the desired image. Explain: Archimedes Principle, equations of continuity and Bernoulli, Sol - A body wholly or partly immersed in a fluid is pushed upward by a force that equals the weight of the fluid displaced by said body (Archimedes). The principle that expresses the conservation of mass in a fluid movement is known as the

Where is the fluid density, is the area through which the fluid at a given time and is the fluid velocity. That the product of these three quantities remain constant is a fancy way of saying that the mass does not change in the fluid. continuity equation:

The principle that expresses the conservation of energy in the movement of a fluid is known as Bernoulli's equation:

Where

and

and

the height at which the fluid moves,

is the pressure,

the severity

continue to express the density and

velocity of fluid. The first term is the kinetic energy per unit volume [J m -3], the second and third terms express the potential energy per unit volume [N m -2 = J m -3] due to internal forces

4)

(pressure) and external forces respectively. Therefore the total energy per unit volume remains constant. As you may know the distance that has been struck by lightning from where you find yourself? Sun - First "see" the beam. Light travels at a speed of approximately

[Ms -1] so we

can say that lightning emits light reaches us instantly. Then we have the time

that comes to

us in the "sound" of the beam. The speed of sound in air is worth

[Ms -1]. Then

using the relationship

the distance found. Practical part

1) a.

Using the definition of scalar product a  b = (a) (b) cos  and that a  b = a x b x + a and b and b z + z obtaining the angle between the vectors: a = 3 i + 3 j - 3 k and b = 2 i + 3 k

 

Sun - The angle will b.

Plot the vectors a = 3 i + 3 j + 3 k, and b = 2 i + 3 k and the vector product a 

Sun -

2)

a  = 9i - 3 j - 6 k, which must be stressed is that both a and b form a

plane

in space which is perpendicular to the vector to  the graph is easily accomplished by locating the points in space (3,3,3), (2,0,2) and (9, -3, -6 ) indicating the end of each vector starting at the origin (0,0,0). He drops a stone from the top of a building. The sound of the stone to hit the ground is heard 6.5 s later. If the speed of sound is 1120 ft s -1 Calculate the height of the building. Sun - The total displacement covered by the stone and the sound is:

where g = -32.2 [ft / s 2] also

[S]

then

where

solution: 3)

[S]. Finally

cleared

staying

only

with

the

positive

[Feet].

(Venturi tube) analytically determining the fluid velocity, density  known, it travels through the tube shown in the figure, where MP1 and MP2 are two pressure gauges. A 1 and A 2 are the areas perpendicular to the flow in regions 1 and 2 respectively.

Finally with data:  = 1 g / cc, p 1 = 1000 N m -2 , P 2 = 800 N m -2, A 1 = 40 cm 2, A 2 = 22 cm 2, calculate v 1 Sun - From the continuity equation:

(A) And the Bernoulli equation when the system is in a horizontal position: (B)

If we replace (A) in (B) and then solve for

we obtain:

Replacing the data provided we find that:

13.16 [ms -1]

4)

Verify that when a wave hits a certain angle and passes through half limited by flat faces parallel, the direction of propagation of the beam emerging is parallel to the incident beam. Sun Consider the following figure:

Using the law of refraction or Snell's law we find: Similarly:

n 1 sin  i) = n 2 sin  t)

n 2 sin  = n 2 sin 

Now within the medium 2 is true also that  i = 

t.

Combining these equations is reached  t =  i, which is what we wanted to prove. June 8, 2003

REGIONAL PEACE CONTEST II

4th of Secondary SOLUTIONS 5)

Conceptual part Explain the Steiner theorem, also known as the parallel axis theorem. Sun - The parallel axis theorem is given by the relationship: , Where I is the inertia around the axis of rotation arbitrary I cm is the rotational inertia parallel axis passing through the center of mass, M is the total mass of the object and h is the perpendicular distance

6)

7)

between the axes. The two axes are parallel. The moments of inertia with respect to the parallel axes relate in this simple way. Explain that the dynamic lifting force is the force acting on a body because of its motion through a fluid. Sun - These bodies are the wings of an airplane or a helicopter propellers. The streamlines of air around the wing of an aircraft for example cause the air speed above the wing has a greater magnitude than the air velocity below this, which means that the pressure above the wing is less than pressure below which must occur if there is to be a push upward. Comment: 1st and 2nd law of thermodynamics, entropy, reversible and irreversible processes, isothermal processes and adiabatic. Sun All thermodynamic system in an equilibrium state has a state variable, called the internal energy of the system is such that its change

where

Energy is added to

is the energy supplied by the system when performing work. (1st Law) the system by heat transfer and

It is impossible for a cycler not produce another effect that continuously transfer heat from one body to another at a higher temperature than this. It is also possible to reformulate the 2nd law in terms of entropy: A natural process that begins in an equilibrium state and ends in another place at the direction that causes the entropy of the system and its environment increases. Entropy is a thermodynamic variable that measures the disorder. If a change occurs very slowly so that at each moment the system is in an equilibrium position then the process is reversible. And if the system away from its equilibrium state then the process is irreversible. When there is a change in system pressure or volume but the temperature is kept constant is spoken of an isothermal process. When there are non-heat exchange between the system and the environment comes to an adiabatic process. An adiabatic process can be reversible or irreversible. 8)

Explain what the Doppler effect. When a person hears a sound is moving toward the stationary source that produces it, the frequency of the sound heard is greater than when at rest. If the person is moving away from the stationary source, less frequently heard when this than when at rest. Similarly is the

5)

equivalent when both source and person move away from or towards. This effect applies to all waves in general. Practical part A disc of 0.5 [m] radius and 20 [kg] of mass can rotate freely about a fixed horizontal axis passing through its center. Applies a force F of 9.8 [N] pulling a cord coiled around the edge of the disc.Find the angular acceleration of the disk and its angular velocity after 2 [s]. Finding the reaction force also exists in the brackets which support the axis of the disc. Sun -

6)

A semiquantitative definition of electric flux is: us that: q sphere vectors

7)

. And Gauss's law tells

. Write the electric field of a point charge q taking Gaussian surface as a of

radius r. Help: and

The

total

area

of

a

sphere

is

r 2 and

the

have the same direction.

A boat in motion produces surface waves on a calm lake. The boat runs 12 oscillations in 20 [s]; each oscillation produces a wave crest. The crest of the wave takes 6 [s] to reach the distant shore 12 [m]. Calculate the wavelength of surface waves.

Three capacitors of 1.5  F], 2  F] and 3  F] are connected in a) series, b) are parallel

8)

and applies a potential difference of 20 [V]. Determine in each case i) the capacitance of the system, ii) loading and the potential difference of each capacitor, iii) energy of the system.

REGIONAL PEACE

3rd of Secondary SOLUTIONS 1)

Conceptual part What is the difference between mass and weight? Much do you weigh? Sun - The mass is a scalar, its units are [kg], the weight is a vector, is a force therefore is measured in Newtons [N]. If you say you have a mass of 66 [kg] weights then 66 [kg]  [ms -2] = 645.15 [N]. 9775 [ms -2] is gravity in La Paz. 9.81 [ms -2] is the gravity at sea level. 1.67 [ms -2] is the gravity on the moon. How much would you weigh on the moon?

2)

Everyone knows that when you look in a mirror is an inversion of the left and right. The right hand seems to be a left, left eye seems to be one law, etc.. Is it possible to design a mirror system that would allow to observe an image as the way in which people normally observed? If possible, draw a picture with some typical ray showing that this is true. Sun - If possible, be requires two mirrors that are joined at an angle of 90  between

3)

them. Each image in a mirror will be reflected in the other mirror as to achieve reverse what we usually see as a result finding the desired image. Explain: Archimedes Principle, equations of continuity and Bernoulli, Sol - A body wholly or partly immersed in a fluid is pushed upward by a force that equals the weight of the fluid displaced by said body (Archimedes). The principle that expresses the conservation of mass in a fluid movement is known as the

Where is the fluid density, is the area through which the fluid at a given time and is the fluid velocity. That the product of these three quantities remain constant is a fancy way of saying that the mass does not change in the fluid. continuity equation:

The principle that expresses the conservation of energy in the movement of a fluid is known as

4)

Bernoulli's equation:

Where

and

and

the height at which the fluid moves,

is the pressure,

the severity

continue to express the density and

velocity of fluid. The first term is the kinetic energy per unit volume [J m -3], the second and third terms express the potential energy per unit volume [N m -2 = J m -3] due to internal forces (pressure) and external forces respectively. Therefore the total energy per unit volume remains constant. As you may know the distance that has been struck by lightning from where you find yourself? Sun - First "see" the beam. Light travels at a speed of approximately

[Ms -1] so we

can say that lightning emits light reaches us instantly. Then we have the time

that comes to

us in the "sound" of the beam. The speed of sound in air is worth

[Ms -1]. Then

using the relationship

the distance found. Practical part

1) a.

Using the definition of scalar product a  b = (a) (b) cos  and that

a  b = a x b x + a and b and b z + z obtaining the angle between the vectors: a = 3 i + 3 j - 3 k and b = 2 i + 3 k

 

Sun - The angle will b.

Plot the vectors a = 3 i + 3 j + 3 k, and b = 2 i + 3 k and the vector product a 

Sun -

2)

a  = 9i - 3 j - 6 k, which must be stressed is that both a and b form a

plane

in space which is perpendicular to the vector to  the graph is easily accomplished by locating the points in space (3,3,3), (2,0,2) and (9, -3, -6 ) indicating the end of each vector starting at the origin (0,0,0). He drops a stone from the top of a building. The sound of the stone to hit the ground is heard 6.5 s later. If the speed of sound is 1120 ft s -1 Calculate the height of the building. Sun - The total displacement covered by the stone and the sound is:

where g = -32.2 [ft / s 2] also

[S]

then

where

solution: 3)

[S]. Finally

cleared

staying

only

with

the

positive

[Feet].

(Venturi tube) analytically determining the fluid velocity, density  known, it travels through the tube shown in the figure, where MP1 and MP2 are two pressure gauges. A 1 and A 2 are the areas perpendicular to the flow in regions 1 and 2 respectively.

Finally with data:  = 1 g / cc, p 1 = 1000 N m -2 , P 2 = 800 N m -2, A 1 = 40 cm 2, A 2 = 22 cm 2, calculate v 1 Sun - From the continuity equation:

(A) And the Bernoulli equation when the system is in a horizontal position: (B)

If we replace (A) in (B) and then solve for

we obtain:

Replacing the data provided we find that:

13.16 [ms -1]

4)

Verify that when a wave hits a certain angle and passes through half limited by flat faces parallel, the direction of propagation of the beam emerging is parallel to the incident beam. Sun Consider the following figure:

Using the law of refraction or Snell's law we find: Similarly:

n 1 sin  i) = n 2 sin  t)

n 2 sin  = n 2 sin 

Now within the medium 2 is true also that  i = 

t.

Combining these equations is reached  t =  i, which is what we wanted to prove. June 8, 2003

REGIONAL PEACE CONTEST II

4th of Secondary SOLUTIONS 5)

6)

7)

Conceptual part Explain the Steiner theorem, also known as the parallel axis theorem. Sun - The parallel axis theorem is given by the relationship: , Where I is the inertia around the axis of rotation arbitrary I cm is the rotational inertia parallel axis passing through the center of mass, M is the total mass of the object and h is the perpendicular distance between the axes. The two axes are parallel. The moments of inertia with respect to the parallel axes relate in this simple way. Explain that the dynamic lifting force is the force acting on a body because of its motion through a fluid. Sun - These bodies are the wings of an airplane or a helicopter propellers. The streamlines of air around the wing of an aircraft for example cause the air speed above the wing has a greater magnitude than the air velocity below this, which means that the pressure above the wing is less than pressure below which must occur if there is to be a push upward. Comment: 1st and 2nd law of thermodynamics, entropy, reversible and irreversible processes, isothermal processes and adiabatic. Sun -

All thermodynamic system in an equilibrium state has a state variable, called the internal energy of the system is such that its change

where

Energy is added to

is the energy supplied by the system when performing work. (1st Law) the system by heat transfer and

It is impossible for a cycler not produce another effect that continuously transfer heat from one body to another at a higher temperature than this. It is also possible to reformulate the 2nd law in terms of entropy: A natural process that begins in an equilibrium state and ends in another place at the direction that causes the entropy of the system and its environment increases. Entropy is a thermodynamic variable that measures the disorder. If a change occurs very slowly so that at each moment the system is in an equilibrium position then the process is reversible. And if the system away from its equilibrium state then the process is irreversible. When there is a change in system pressure or volume but the temperature is kept constant is spoken of an isothermal process. When there are non-heat exchange between the system and the environment comes to an adiabatic process. An adiabatic process can be reversible or irreversible. 8)

Explain what the Doppler effect. When a person hears a sound is moving toward the stationary source that produces it, the frequency of the sound heard is greater than when at rest. If the person is moving away from the stationary source, less frequently heard when this than when at rest. Similarly is the

5)

equivalent when both source and person move away from or towards. This effect applies to all waves in general. Practical part A disc of 0.5 [m] radius and 20 [kg] of mass can rotate freely about a fixed horizontal axis passing through its center. Applies a force F of 9.8 [N] pulling a cord coiled around the edge of the disc.Find the angular acceleration of the disk and its angular velocity after 2 [s]. Finding the reaction force also exists in the brackets which support the axis of the disc. Sun -

6)

A semiquantitative definition of electric flux is: us that: q sphere vectors

7)

. And Gauss's law tells

. Write the electric field of a point charge q taking Gaussian surface as a of

radius r. Help: and

The

total

area

of

a

sphere

is

r 2 and

the

have the same direction.

A boat in motion produces surface waves on a calm lake. The boat runs 12 oscillations in 20 [s]; each oscillation produces a wave crest. The crest of the wave takes 6 [s] to reach the distant shore 12 [m]. Calculate the wavelength of surface waves.

8)

Three capacitors of 1.5  F], 2  F] and 3  F] are connected in a) series, b) are parallel and applies a potential difference of 20 [V]. Determine in each case i) the capacitance of the system, ii) loading and the potential difference of each capacitor, iii) energy of the system.

REGIONAL PEACE

3rd of Secondary SOLUTIONS 1)

Conceptual part What is the difference between mass and weight? Much do you weigh? Sun - The mass is a scalar, its units are [kg], the weight is a vector, is a force therefore is measured in Newtons [N]. If you say you have a mass of 66 [kg] weights then 66 [kg]  [ms -2] = 645.15 [N].

9775 [ms -2] is gravity in La Paz. 9.81 [ms -2] is the gravity at sea level. 1.67 [ms -2] is the gravity on the moon. How much would you weigh on the moon? 2)

Everyone knows that when you look in a mirror is an inversion of the left and right. The right hand seems to be a left, left eye seems to be one law, etc.. Is it possible to design a mirror system that would allow to observe an image as the way in which people normally observed? If possible, draw a picture with some typical ray showing that this is true. Sun - If possible, be requires two mirrors that are joined at an angle of 90  between

3)

them. Each image in a mirror will be reflected in the other mirror as to achieve reverse what we usually see as a result finding the desired image. Explain: Archimedes Principle, equations of continuity and Bernoulli, Sol - A body wholly or partly immersed in a fluid is pushed upward by a force that equals the weight of the fluid displaced by said body (Archimedes). The principle that expresses the conservation of mass in a fluid movement is known as the

Where is the fluid density, is the area through which the fluid at a given time and is the fluid velocity. That the product of these three quantities remain constant is a fancy way of saying that the mass does not change in the fluid. continuity equation:

The principle that expresses the conservation of energy in the movement of a fluid is known as

4)

Bernoulli's equation:

Where

and

and

the height at which the fluid moves,

is the pressure,

the severity

continue to express the density and

velocity of fluid. The first term is the kinetic energy per unit volume [J m -3], the second and third terms express the potential energy per unit volume [N m -2 = J m -3] due to internal forces (pressure) and external forces respectively. Therefore the total energy per unit volume remains constant. As you may know the distance that has been struck by lightning from where you find yourself? Sun - First "see" the beam. Light travels at a speed of approximately

[Ms -1] so we

can say that lightning emits light reaches us instantly. Then we have the time

that comes to

us in the "sound" of the beam. The speed of sound in air is worth

[Ms -1]. Then

using the relationship

the distance found. Practical part

1) a.

Using the definition of scalar product a  b = (a) (b) cos  and that a  b = a x b x + a and b and b z + z obtaining the angle between the vectors: a = 3 i + 3 j - 3 k and b = 2 i + 3 k

Sun - The angle will b. Sun -

 

Plot the vectors a = 3 i + 3 j + 3 k, and b = 2 i + 3 k and the vector product a  a  = 9i - 3 j - 6 k, which must be stressed is that both a and b form a

plane

in space which is perpendicular to the vector to  the graph is easily accomplished by locating the points in space (3,3,3), (2,0,2) and (9, -3, -6 ) indicating the end of each vector starting at the origin (0,0,0).

2)

He drops a stone from the top of a building. The sound of the stone to hit the ground is heard 6.5 s later. If the speed of sound is 1120 ft s -1 Calculate the height of the building. Sun - The total displacement covered by the stone and the sound is:

where g = -32.2 [ft / s 2] also

[S]

then

where

solution: 3)

cleared

[S]. Finally

staying

only

with

the

positive

[Feet].

(Venturi tube) analytically determining the fluid velocity, density  known, it travels through the tube shown in the figure, where MP1 and MP2 are two pressure gauges. A 1 and A 2 are the areas perpendicular to the flow in regions 1 and 2 respectively.

Finally with data:  = 1 g / cc, p 1 = 1000 N m -2 , P 2 = 800 N m -2, A 1 = 40 cm 2, A 2 = 22 cm 2, calculate v 1 Sun - From the continuity equation:

(A) And the Bernoulli equation when the system is in a horizontal position: (B)

If we replace (A) in (B) and then solve for Replacing the data provided we find that: 4)

we obtain: 13.16 [ms -1]

Verify that when a wave hits a certain angle and passes through half limited by flat faces parallel, the direction of propagation of the beam emerging is parallel to the incident beam. Sun Consider the following figure:

Using the law of refraction or Snell's law we find: Similarly:

n 1 sin  i) = n 2 sin  t)

n 2 sin  = n 2 sin 

Now within the medium 2 is true also that  i = 

t.

Combining these equations is reached  t =  i, which is what we wanted to prove. June 8, 2003

REGIONAL PEACE CONTEST II

4th of Secondary SOLUTIONS 5)

6)

7)

Conceptual part Explain the Steiner theorem, also known as the parallel axis theorem. Sun - The parallel axis theorem is given by the relationship: , Where I is the inertia around the axis of rotation arbitrary I cm is the rotational inertia parallel axis passing through the center of mass, M is the total mass of the object and h is the perpendicular distance between the axes. The two axes are parallel. The moments of inertia with respect to the parallel axes relate in this simple way. Explain that the dynamic lifting force is the force acting on a body because of its motion through a fluid. Sun - These bodies are the wings of an airplane or a helicopter propellers. The streamlines of air around the wing of an aircraft for example cause the air speed above the wing has a greater magnitude than the air velocity below this, which means that the pressure above the wing is less than pressure below which must occur if there is to be a push upward. Comment: 1st and 2nd law of thermodynamics, entropy, reversible and irreversible processes, isothermal processes and adiabatic. Sun All thermodynamic system in an equilibrium state has a state variable, called the internal energy of the system is such that its change

where

Energy is added to

is the energy supplied by the system when performing work. (1st Law) the system by heat transfer and

It is impossible for a cycler not produce another effect that continuously transfer heat from one body to another at a higher temperature than this. It is also possible to reformulate the 2nd law in terms of entropy: A natural process that begins in an equilibrium state and ends in another place at the direction that causes the entropy of the system and its environment increases. Entropy is a thermodynamic variable that measures the disorder.

If a change occurs very slowly so that at each moment the system is in an equilibrium position then the process is reversible. And if the system away from its equilibrium state then the process is irreversible. When there is a change in system pressure or volume but the temperature is kept constant is spoken of an isothermal process. When there are non-heat exchange between the system and the environment comes to an adiabatic process. An adiabatic process can be reversible or irreversible. 8)

Explain what the Doppler effect. When a person hears a sound is moving toward the stationary source that produces it, the frequency of the sound heard is greater than when at rest. If the person is moving away from the stationary source, less frequently heard when this than when at rest. Similarly is the

5)

equivalent when both source and person move away from or towards. This effect applies to all waves in general. Practical part A disc of 0.5 [m] radius and 20 [kg] of mass can rotate freely about a fixed horizontal axis passing through its center. Applies a force F of 9.8 [N] pulling a cord coiled around the edge of the disc.Find the angular acceleration of the disk and its angular velocity after 2 [s]. Finding the reaction force also exists in the brackets which support the axis of the disc. Sun -

6)

A semiquantitative definition of electric flux is: us that: q sphere vectors

7)

. And Gauss's law tells

. Write the electric field of a point charge q taking Gaussian surface as a of

radius r. Help: and

The

total

area

of

a

sphere

is

r 2 and

the

have the same direction.

A boat in motion produces surface waves on a calm lake. The boat runs 12 oscillations in 20 [s]; each oscillation produces a wave crest. The crest of the wave takes 6 [s] to reach the distant shore 12 [m]. Calculate the wavelength of surface waves.

8)

Three capacitors of 1.5  F], 2  F] and 3  F] are connected in a) series, b) are parallel and applies a potential difference of 20 [V]. Determine in each case i) the capacitance of the system, ii) loading and the potential difference of each capacitor, iii) energy of the system.