P2

PROJECTILE MOTION CALCULATIONS: Force, Motion & Energy Question 1: What do you call an object that is moving in two dimensions?  A projectile is an object that moves in two dimensions. Question 2: What is the unit for maximum height?  Height is measured in meters, m. Question 3: What is the value of the acceleration due to gravity?  The value of acceleration due to gravity is 9.8 m/s 2 or approximately 10 m/s2. Question 4: A projectile is fired with an initial horizontal velocity of u 0from a cannon that lies on the top of 2 m high ground. If the value of the velocity, once the projectile reaches the ground, is 10 m/s, calculate the value of its initial velocity. Assume that the value of the acceleration of gravity is g = 10 m/s2. 

The correct answer is that the value of the initial velocity is 7.75 m/sec. Our given quantities are the final velocity, the height from where the projectile was fired from and, of course the value of the acceleration. Therefore, by making use of equation (6) we get that:

Question 5: A projectile is fired with an initial horizontal velocity of v 0 = 10 m/s from a cannon that lies on a height of 5 m. Determine the horizontal distance of the motion. Assume that the value of the acceleration of gravity is g = 10 m/s 2. 

The correct answer is the distance x that the projectile will cover shall be 10 m. For the x axis we know that there are no forces exerted on the object, thus: x = v0 x t Moreover, for the y axis, the total distance traveled by the object until it reaches the ground shall be: Therefore, if we substitute the expression for the time into the expression for the x distance we get:

Question 6: A projectile is released on a height of 10 m with a velocity of v 0= 10 m/s that forms an angle of 30o with the horizontal. Assuming that the time needed for the projectile to hit the ground is 2 s and that the vertical component of velocity is 5 m/s. At that time, what is the velocity of the projectile? Assume that the value of the acceleration of gravity is g = 10 m/sec2. 

The correct answer is that the final magnitude of the velocity, once the projectile reaches the ground, shall be 9.95 m/sec. We know the values of the initial velocity and angle. Therefore, we can find the expression for each constituent of the velocity (vx and vy) by:

Question 7: An object is fired from the ground with a horizontal component of the initial velocity of v 0,x=10 m/s and vertical component of the velocity, v0,y=20 m/s. The object reaches a height of 5 m and then spans a distance until it reaches the ground. How much time does it take for the projectile in order to reach the height? Assume that the value of the acceleration of gravity is g = 10 m/s 2. 

The correct answer is that t=2.4 sec. The velocity forms an angle with the horizontal level, thus, we need to analyze the velocity into its constituent vectors for x and y. However, we also know that the final y displacement is h. Since we want to find the time that took the object to reach h:

Question 8: An object is fired from the ground with an initial velocity of 10 m/s that forms an angle of 30 o with the horizontal level and follows a parabolic trajectory as shown in the figure above. The object reaches a height h and then spans a distance x until it reaches the ground. How much distance did the projectile span just before reaching the ground? Assume that the value of the acceleration of gravity is g = 10 m/s 2.

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The correct answer is 8.7 m. We need to follow the steps of the previous exercise in order to, initially, find the time that the projectile took before landing to the ground. Consequently, we need to implement the simple equation v x=xt in order to find the total distance covered.

Question 9: A firework is thrown into the air with an initial velocity of 70 m/s at an angle of 60 o from the horizontal level. At some height h, the shell (firework) will explode in order to provide the attendants with a spectacular view. At what height did the shell explode? Assume that the value of the acceleration of gravity is g = 10 m/s 2. 

The correct answer is 185.44 m. This can be found by making use of eq. 3. Keep in mind that when we deal with maximum height, this will automatically mean that the vertical velocity (v y) is equal to zero.

Question 10: A football player is ready to hit a free kick. Since our player is extremely good with geometry, he has already calculated that he needs to shoot the ball at an angle 35o with an initial velocity of v0 so that the ball will go over the wall and meet the back of the net. What should the initial velocity of the ball be if the target is 35 m away? Assume that the value of the acceleration of gravity is g = 10 m/s 2. 

The correct answer is 20.06 m/sec. We need to find the initial velocity v0 and we know the initial angle and the distance x. Moreover, we know that the initial and final y are zero. Therefore, we can make use of eq. 2 for both x and y in order to get two expressions for the initial velocity and time (we do not know the value of time).

LAW OF CONSERVATION OF MOMENTUM: Force, Motion & Energy Question 1: Which of the following statements describes momentum? 

Translational or linear momentum, or just momentum of the body, is defined as a product of body's mass and velocity. p = mv

Question 2: Momentum, as well as velocity, is what type of quantity?  Momentum is a vector quantity as it is the product of the scalar quantity, mass and a vector quantity, velocity. Question 3: What is the unit for momentum?  The unit for momentum is kg∙m/s. Question 4: What word can best describe the total momentum in an isolated system? 

In an isolated system, the total amount of momentum is constant. This is the law of conservation of momentum.See your results Question 5: Calculate the momentum of a car, which has a mass of 1000 kg and moves with a velocity of 20 m/s. 

P=mv P=(1000kg) (20m/s) P=20000kg x m/s

Question 6: The total momentum of two objects before collision is 350 kgm/s. What will be their total momentum after collision? 

The law of conservation of momentum states that the total momentum before and after a collision is constant.

Question 7:

Two objects with a total mass of 20 kg has an initial momentum of 100 kg∙m/s. If the masses stick together after the collision, what is the final velocity of the masses? 

100kg x m/s

Question 8: Two billiard balls with mass 1.0 kg each are travelling towards each other. The first one is moving at a velocity of 3 m/s, while the other one moves at a velocity of -2m/s. After the collision, one billiard ball moves to the left at a speed of 2 m/s. What is the speed of the other ball? 

3m/s

Question 9: A 2.0-kg chunk of putty moving at 5.0 m/s collides with and sticks to a 8.0-kg bowling ball that is initially at rest. The bowling ball with its putty passenger will then be set in motion with what speed? 

1m/s

Question 10: A 125 kg car moving at 12 m/s hits a 200 kg car moving at -13m/s. If the first car bounces back at -12.5 m/s what is the velocity of the second car after the collision? 

2.3m/s

IMPULSE: Force, Motion & Energy Question 1: How is impulse calculated?  A change in momentum is impulse and it is expressed as F∆t = ∆p. This shows that to calculate impulse, F is multiplied by the time interval. Impulse is the change in momentum. In symbol, F∆t = ∆p. Question 2: Which of the following is the unit of impulse?  Impulse is the product of force and the time interval, F ∆t. If F is in Newton and ∆t is in seconds, the unit of impulse is Ns. Question 3: Which determines the momentum a moving body?  Momentum is the product of mass and velocity. Question 4: Which of the following statements is true about an object with constant mass but its momentum is changing? 

Mass and velocity determines the change in momentum. If any one of them changes, momentum also changes.

Question 5: What is the purpose of an airbag in an automobile? 

Upon collision, the airbag is inflated. The inflated bag provides a protective cushion to the driver and the passengers. It increases the impact time, thus, reducing the impact force on the passengers.

Question 6: What is the momentum of a large bus compared to that of a small car traveling at the same speed? 

Mass and velocity affect momentum. Since the velocities are the same but the mass of the bus is greater than the car, the bus will have greater momentum.

Question 7: A baseball bat comes in contact with a baseball in 0.001 s. If the force of contact is 5000 N, what is the impulse of the interaction? 

5Ns

Question 8: Jenny was texting on her phone when she drove into South's busy parking lot last Friday morning. She bumped the rear-ended of a car in the parking lot. Jenny's 1300-kg car was moving at 11 m/s and stopped in 0.14 seconds. Determine the force experienced by Jenny's car. 

7857N

Question 9: NASA has been testing on using air bags to soften the landings of crew exploration vehicles (CEV) on land. What stopping time will be required in order to safely stop a 8000 kg CEV moving at 10 m/s with an average force of 500 kN? 

0.16s

Question 10: While playing basketball, James lost his balance after making a lay-up and colliding with the padded wall behind the basket. His 60kg body decelerated from 6 m/s to 0 m/s in 0.16 seconds. What is the impact force on James's body?

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2250N