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Assignment 2: Newton's Laws of Motion Due: 2:00am on Saturday, September 11, 2010 Note: To understand how points are awarded, read your instructor's Grading Policy. [Switch to Standard Assignment View]

Pulling Three Blocks Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force . The magnitude of the tension in the string between blocks B and C is = 3.00 . Assume that each block has mass = 0.400

.

Part A What is the magnitude Hint A.1

of the force?

Find the acceleration of block B Hint not displayed

Hint A.2

Find the acceleration of all three blocks Hint not displayed

Express your answer numerically in newtons. ANSWER:

= 4.50 Correct

Part B What is the tension Hint B.1

in the string between block A and block B?

How to approach the question Hint not displayed

Express your answer numerically in newtons ANSWER:

= 1.50

=

Correct

A Ride on the Ferris Wheel A woman rides on a Ferris wheel of radius 16

that maintains the same speed throughout its motion.

To better understand physics, she takes along a digital bathroom scale (with memory) and sits on it. When she gets off the ride, she uploads the scale readings to a computer and creates a graph of scale reading versus time. Note that the graph has a minimum value of 510 and a maximum value of 666

.

Part A What is the woman's mass? Hint A.1

How to approach the problem Hint not displayed

Hint A.2

Find the extreme points on the circular path Hint not displayed

Hint A.3

Find the acceleration of the woman Hint not displayed

Hint A.4

Mass and weight Hint not displayed

Express your answer in kilograms. ANSWER:

= 60 Correct

The Window Washer A window washer of mass

is sitting on a platform suspended by a system of cables and pulleys as

shown . He is pulling on the cable with a force of magnitude . The cables and pulleys are ideal

magnitude

. The cables and pulleys are ideal

(massless and frictionless), and the platform has negligible mass.

Part A Find the magnitude of the minimum force Hint A.1

that allows the window washer to move upward.

Find a simple expression for the tension Hint not displayed

Hint A.2

Upward forces on window washer Hint not displayed

Hint A.3

All forces on window washer Hint not displayed

Hint A.4

What about the platform? Hint not displayed

Express your answer in terms of the mass

and the magnitude of the acceleration due to

gravity . ANSWER: =

Correct

Skydiving A sky diver of mass 80.0

(including parachute) jumps off a plane and begins her descent.

Throughout this problem use 9.80

for the magnitude of the acceleration due to gravity.

Part A At the beginning of her fall, does the sky diver have an acceleration? Hint A.1

Free fall Hint not displayed

Hint not displayed ANSWER:

No; the sky diver falls at constant speed. Yes and her acceleration is directed upward. Yes and her acceleration is directed downward. Correct

This applet shows the sky diver (not to scale) with her position, speed, and acceleration graphed as functions of time. You can see how her acceleration drops to zero over time, giving constant speed after a long time. Part B At some point during her free fall, the sky diver reaches her terminal speed. What is the magnitude of the drag force due to air resistance that acts on the sky diver when she has reached terminal speed? Hint B.1

Dynamic equilibrium Hint not displayed

Express your answer in newtons. ANSWER:

= 784 Correct

Part C For an object falling through air at a high speed , the drag force acting on it due to air resistance can be expressed as , where the coefficient

depends on the shape and size of the falling object and on the density of air.

For a human body, the numerical value for Using this value for Hint C.1

is about 0.250

, what is the terminal speed

.

of the sky diver?

Terminal speed Hint not displayed

Express you answer in meters per second. ANSWER:

= 56.0 Correct

Recreational sky divers can control their terminal speed to some extent by changing their body posture. When oriented in a headfirst dive, a sky diver can reach speeds of about 54 meters per second (120 miles per hour). For maximum drag and stability, sky divers often will orient themselves "belly-first." In this position, their terminal speed is typically around 45 meters per second (100 miles per hour).

Part D When the sky diver descends to a certain height from the ground, she deploys her parachute to ensure a safe landing. (Usually the parachute is deployed when the sky diver reaches an altitude of about 900 --3000 .) Immediately after deploying the parachute, does the skydiver have a nonzero acceleration? Hint D.1

How to approach the problem Hint not displayed

ANSWER:

No; the sky diver keeps falling at constant speed. Yes and her acceleration is directed downward. Yes and her acceleration is directed upward. Correct

Part E When the parachute is fully open, the effective drag coefficient of the sky diver plus parachute increases to 60.0 . What is the drag force acting on the sky diver immediately after she has opened the parachute? Hint E.1

How to approach the problem Hint not displayed

Hint E.2

Find the speed of the sky diver when the parachute is deployed Hint not displayed

Express your answer in newtons. ANSWER:

= 1.88×105 Correct

Part F What is the terminal speed Hint F.1

of the sky diver when the parachute is opened?

How to approach the problem Hint not displayed

Express your answer in meters per second. ANSWER:

= 3.61 Correct

A typical "student" parachute for recreational skydiving has a drag coefficient that gives a terminal speed for landing of about 2 meters per second (5 miles per hour). If this seems slow based on video or real-life sky divers you have seen, that may be because the sky divers you saw were using high-performance parachutes; these offer the sky divers more maneuverability in the air but

using high-performance parachutes; these offer the sky divers more maneuverability in the air but increase the terminal speed up to 4 meters per second (10 miles per hour).

Block on an Incline Adjacent to a Wall A wedge with an inclination of angle

rests next to a wall. A block of mass

is sliding down the plane,

as shown. There is no friction between the wedge and the block or between the wedge and the horizontal surface.

Part A Find the magnitude, Hint A.1

, of the sum of all forces acting on the block.

Direction of the net force on the block Hint not displayed

Hint A.2

Determine the forces acting on the block Hint not displayed

Hint A.3

Find the magnitude of the force acting along the direction of motion Hint not displayed

Express

in terms of

ANSWER:

and

, along with any necessary constants.

=

Correct

Part B Find the magnitude, Hint B.1

, of the force that the wall exerts on the wedge.

The force between the wall and the wedge Hint not displayed

Hint B.2

Find the normal force between the block and the wedge

Hint not displayed Hint B.3

Find the horizontal component of the normal force Hint not displayed

Express

in terms of

ANSWER:

and

, along with any necessary constants.

=

Correct Your answer to Part B could be expressed as either form, we see that as

gets very small or as

or

approaches 90 degrees (

. In either radians), the contact

force between the wall and the wedge goes to zero. This is what we should expect; in the first limit ( small), the block is accelerating very slowly, and all horizontal forces are small. In the second limit (

about 90 degrees), the block simply falls vertically and exerts no horizontal force

on the wedge.

Velocity from Force Diagram Ranking Task Below are birds-eye views of six identical toy cars moving to the right at 2

. Various forces act on the

cars with magnitudes and directions indicated below. All forces act in the horizontal plane and are either parallel or at 45 or 90 degrees to the car's motion. Part A Rank these cars on the basis of their speed a short time after the forces are applied. Hint A.1

How to approach the problem Hint not displayed

Hint A.2

Summing force vectors Hint not displayed

Rank from largest to smallest. To rank items as equivalent, overlap them. ANSWER:

View Correct

Mass on Turntable

Mass on Turntable A small metal cylinder rests on a circular turntable that is rotating at a constant speed as illustrated in the diagram . The small metal cylinder has a mass of 0.20 , the coefficient of static friction between the cylinder and the turntable is 0.080, and the cylinder is located 0.15 from the center of the turntable. Take the magnitude of the acceleration due to gravity to be 9.81 .

Part A What is the maximum speed

that the cylinder can move along its circular path without slipping

off the turntable? Hint A.1

Centripetal acceleration Hint not displayed

Hint A.2

Determine the force causing acceleration Hint not displayed

Hint A.3

Find the maximum possible friction force Hint not displayed

Hint A.4

Newton's 2nd law Hint not displayed

Express your answer numerically in meters per second to two significant figures. ANSWER:

= 0.34 Correct

Two Blocks and Two Pulleys A block of mass

is attached to a massless, ideal string. This string wraps around a massless pulley

and then wraps around a second pulley that is attached to a block of mass

that is free to slide on a

frictionless table. The string is firmly anchored to a wall and the whole system is frictionless. Use the coordinate system indicated in the figure when solving this problem.

Part A Assuming that

is the magnitude of the horizontal acceleration of the block of mass

, what is

,

the tension in the string? Hint A.1

Which physical principle to use Hint not displayed

Hint A.2

Force diagram for the block of mass Hint not displayed

Express the tension in terms of

and

.

ANSWER: =

Correct

Part B Given

, the tension in the string, calculate

of mass Hint B.1

, the magnitude of the vertical acceleration of the block

.

Which physical principle to use Hint not displayed

Hint B.2

Force diagram for the block of mass Hint not displayed

Express the acceleration magnitude ANSWER: =

Correct

Part C

in terms of

,

, and

.

Given the magnitude

of the acceleration of the block of mass

horizontal acceleration of the block of mass Hint C.1

, find

, the magnitude of the

.

Method 1: String constraint (uses calculus) Hint not displayed

Hint C.2

Method 2: Intuition (does not involve calculus) Hint not displayed

Express

in terms of

.

ANSWER: =

Correct

Part D Using the result of Part C in the formula for as a function of

that you previously obtained in Part A, express

.

Express your answer in terms of

and

.

ANSWER: =

Correct

Part E Having solved the previous parts, you have all the pieces needed to calculate acceleration of the block of mass Hint E.1

. Write an expression for

.

How to approach this problem Hint not displayed

Express the acceleration magnitude

in terms of

,

, and

ANSWER: =

Correct

Hanging Chandelier A chandelier with mass

is attached to the

ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated in the figure, which uses a humbler depiction), the

.

, the magnitude of the

workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension and makes an angle of with the ceiling. and makes an angle of

Cable 2 has tension with the ceiling.

Part A Find an expression for

, the tension in cable 1, that does not depend on

.

Find the sum of forces in the x direction

Hint A.1

Hint not displayed Find the sum of forces in the y direction

Hint A.2

Hint not displayed Putting it all together

Hint A.3

Hint not displayed Express your answer in terms of some or all of the variables

,

, and

, as well as the

magnitude of the acceleration due to gravity . ANSWER: =

Correct

At the Test Track You want to test the grip of the tires on your new race car. You decide to take the race car to a small test track to experimentally determine the coefficient of friction. The racetrack consists of a flat, circular road with a radius of 45 . The applet shows the result of driving the car around the track at various speeds. Part A What is Hint A.1

, the coefficient of static friction between the tires and the track?

How to approach the problem Hint not displayed

Hint A.2

Use the applet to find the speed Hint not displayed

Hint A.3

Find an expression for

Find an expression for Hint not displayed Express your answer to two significant figures. ANSWER:

= 0.91 Correct

Score Summary: Your score on this assignment is 100%. You received 40 out of a possible total of 40 points.

View more...
Pulling Three Blocks Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force . The magnitude of the tension in the string between blocks B and C is = 3.00 . Assume that each block has mass = 0.400

.

Part A What is the magnitude Hint A.1

of the force?

Find the acceleration of block B Hint not displayed

Hint A.2

Find the acceleration of all three blocks Hint not displayed

Express your answer numerically in newtons. ANSWER:

= 4.50 Correct

Part B What is the tension Hint B.1

in the string between block A and block B?

How to approach the question Hint not displayed

Express your answer numerically in newtons ANSWER:

= 1.50

=

Correct

A Ride on the Ferris Wheel A woman rides on a Ferris wheel of radius 16

that maintains the same speed throughout its motion.

To better understand physics, she takes along a digital bathroom scale (with memory) and sits on it. When she gets off the ride, she uploads the scale readings to a computer and creates a graph of scale reading versus time. Note that the graph has a minimum value of 510 and a maximum value of 666

.

Part A What is the woman's mass? Hint A.1

How to approach the problem Hint not displayed

Hint A.2

Find the extreme points on the circular path Hint not displayed

Hint A.3

Find the acceleration of the woman Hint not displayed

Hint A.4

Mass and weight Hint not displayed

Express your answer in kilograms. ANSWER:

= 60 Correct

The Window Washer A window washer of mass

is sitting on a platform suspended by a system of cables and pulleys as

shown . He is pulling on the cable with a force of magnitude . The cables and pulleys are ideal

magnitude

. The cables and pulleys are ideal

(massless and frictionless), and the platform has negligible mass.

Part A Find the magnitude of the minimum force Hint A.1

that allows the window washer to move upward.

Find a simple expression for the tension Hint not displayed

Hint A.2

Upward forces on window washer Hint not displayed

Hint A.3

All forces on window washer Hint not displayed

Hint A.4

What about the platform? Hint not displayed

Express your answer in terms of the mass

and the magnitude of the acceleration due to

gravity . ANSWER: =

Correct

Skydiving A sky diver of mass 80.0

(including parachute) jumps off a plane and begins her descent.

Throughout this problem use 9.80

for the magnitude of the acceleration due to gravity.

Part A At the beginning of her fall, does the sky diver have an acceleration? Hint A.1

Free fall Hint not displayed

Hint not displayed ANSWER:

No; the sky diver falls at constant speed. Yes and her acceleration is directed upward. Yes and her acceleration is directed downward. Correct

This applet shows the sky diver (not to scale) with her position, speed, and acceleration graphed as functions of time. You can see how her acceleration drops to zero over time, giving constant speed after a long time. Part B At some point during her free fall, the sky diver reaches her terminal speed. What is the magnitude of the drag force due to air resistance that acts on the sky diver when she has reached terminal speed? Hint B.1

Dynamic equilibrium Hint not displayed

Express your answer in newtons. ANSWER:

= 784 Correct

Part C For an object falling through air at a high speed , the drag force acting on it due to air resistance can be expressed as , where the coefficient

depends on the shape and size of the falling object and on the density of air.

For a human body, the numerical value for Using this value for Hint C.1

is about 0.250

, what is the terminal speed

.

of the sky diver?

Terminal speed Hint not displayed

Express you answer in meters per second. ANSWER:

= 56.0 Correct

Recreational sky divers can control their terminal speed to some extent by changing their body posture. When oriented in a headfirst dive, a sky diver can reach speeds of about 54 meters per second (120 miles per hour). For maximum drag and stability, sky divers often will orient themselves "belly-first." In this position, their terminal speed is typically around 45 meters per second (100 miles per hour).

Part D When the sky diver descends to a certain height from the ground, she deploys her parachute to ensure a safe landing. (Usually the parachute is deployed when the sky diver reaches an altitude of about 900 --3000 .) Immediately after deploying the parachute, does the skydiver have a nonzero acceleration? Hint D.1

How to approach the problem Hint not displayed

ANSWER:

No; the sky diver keeps falling at constant speed. Yes and her acceleration is directed downward. Yes and her acceleration is directed upward. Correct

Part E When the parachute is fully open, the effective drag coefficient of the sky diver plus parachute increases to 60.0 . What is the drag force acting on the sky diver immediately after she has opened the parachute? Hint E.1

How to approach the problem Hint not displayed

Hint E.2

Find the speed of the sky diver when the parachute is deployed Hint not displayed

Express your answer in newtons. ANSWER:

= 1.88×105 Correct

Part F What is the terminal speed Hint F.1

of the sky diver when the parachute is opened?

How to approach the problem Hint not displayed

Express your answer in meters per second. ANSWER:

= 3.61 Correct

A typical "student" parachute for recreational skydiving has a drag coefficient that gives a terminal speed for landing of about 2 meters per second (5 miles per hour). If this seems slow based on video or real-life sky divers you have seen, that may be because the sky divers you saw were using high-performance parachutes; these offer the sky divers more maneuverability in the air but

using high-performance parachutes; these offer the sky divers more maneuverability in the air but increase the terminal speed up to 4 meters per second (10 miles per hour).

Block on an Incline Adjacent to a Wall A wedge with an inclination of angle

rests next to a wall. A block of mass

is sliding down the plane,

as shown. There is no friction between the wedge and the block or between the wedge and the horizontal surface.

Part A Find the magnitude, Hint A.1

, of the sum of all forces acting on the block.

Direction of the net force on the block Hint not displayed

Hint A.2

Determine the forces acting on the block Hint not displayed

Hint A.3

Find the magnitude of the force acting along the direction of motion Hint not displayed

Express

in terms of

ANSWER:

and

, along with any necessary constants.

=

Correct

Part B Find the magnitude, Hint B.1

, of the force that the wall exerts on the wedge.

The force between the wall and the wedge Hint not displayed

Hint B.2

Find the normal force between the block and the wedge

Hint not displayed Hint B.3

Find the horizontal component of the normal force Hint not displayed

Express

in terms of

ANSWER:

and

, along with any necessary constants.

=

Correct Your answer to Part B could be expressed as either form, we see that as

gets very small or as

or

approaches 90 degrees (

. In either radians), the contact

force between the wall and the wedge goes to zero. This is what we should expect; in the first limit ( small), the block is accelerating very slowly, and all horizontal forces are small. In the second limit (

about 90 degrees), the block simply falls vertically and exerts no horizontal force

on the wedge.

Velocity from Force Diagram Ranking Task Below are birds-eye views of six identical toy cars moving to the right at 2

. Various forces act on the

cars with magnitudes and directions indicated below. All forces act in the horizontal plane and are either parallel or at 45 or 90 degrees to the car's motion. Part A Rank these cars on the basis of their speed a short time after the forces are applied. Hint A.1

How to approach the problem Hint not displayed

Hint A.2

Summing force vectors Hint not displayed

Rank from largest to smallest. To rank items as equivalent, overlap them. ANSWER:

View Correct

Mass on Turntable

Mass on Turntable A small metal cylinder rests on a circular turntable that is rotating at a constant speed as illustrated in the diagram . The small metal cylinder has a mass of 0.20 , the coefficient of static friction between the cylinder and the turntable is 0.080, and the cylinder is located 0.15 from the center of the turntable. Take the magnitude of the acceleration due to gravity to be 9.81 .

Part A What is the maximum speed

that the cylinder can move along its circular path without slipping

off the turntable? Hint A.1

Centripetal acceleration Hint not displayed

Hint A.2

Determine the force causing acceleration Hint not displayed

Hint A.3

Find the maximum possible friction force Hint not displayed

Hint A.4

Newton's 2nd law Hint not displayed

Express your answer numerically in meters per second to two significant figures. ANSWER:

= 0.34 Correct

Two Blocks and Two Pulleys A block of mass

is attached to a massless, ideal string. This string wraps around a massless pulley

and then wraps around a second pulley that is attached to a block of mass

that is free to slide on a

frictionless table. The string is firmly anchored to a wall and the whole system is frictionless. Use the coordinate system indicated in the figure when solving this problem.

Part A Assuming that

is the magnitude of the horizontal acceleration of the block of mass

, what is

,

the tension in the string? Hint A.1

Which physical principle to use Hint not displayed

Hint A.2

Force diagram for the block of mass Hint not displayed

Express the tension in terms of

and

.

ANSWER: =

Correct

Part B Given

, the tension in the string, calculate

of mass Hint B.1

, the magnitude of the vertical acceleration of the block

.

Which physical principle to use Hint not displayed

Hint B.2

Force diagram for the block of mass Hint not displayed

Express the acceleration magnitude ANSWER: =

Correct

Part C

in terms of

,

, and

.

Given the magnitude

of the acceleration of the block of mass

horizontal acceleration of the block of mass Hint C.1

, find

, the magnitude of the

.

Method 1: String constraint (uses calculus) Hint not displayed

Hint C.2

Method 2: Intuition (does not involve calculus) Hint not displayed

Express

in terms of

.

ANSWER: =

Correct

Part D Using the result of Part C in the formula for as a function of

that you previously obtained in Part A, express

.

Express your answer in terms of

and

.

ANSWER: =

Correct

Part E Having solved the previous parts, you have all the pieces needed to calculate acceleration of the block of mass Hint E.1

. Write an expression for

.

How to approach this problem Hint not displayed

Express the acceleration magnitude

in terms of

,

, and

ANSWER: =

Correct

Hanging Chandelier A chandelier with mass

is attached to the

ceiling of a large concert hall by two cables. Because the ceiling is covered with intricate architectural decorations (not indicated in the figure, which uses a humbler depiction), the

.

, the magnitude of the

workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension and makes an angle of with the ceiling. and makes an angle of

Cable 2 has tension with the ceiling.

Part A Find an expression for

, the tension in cable 1, that does not depend on

.

Find the sum of forces in the x direction

Hint A.1

Hint not displayed Find the sum of forces in the y direction

Hint A.2

Hint not displayed Putting it all together

Hint A.3

Hint not displayed Express your answer in terms of some or all of the variables

,

, and

, as well as the

magnitude of the acceleration due to gravity . ANSWER: =

Correct

At the Test Track You want to test the grip of the tires on your new race car. You decide to take the race car to a small test track to experimentally determine the coefficient of friction. The racetrack consists of a flat, circular road with a radius of 45 . The applet shows the result of driving the car around the track at various speeds. Part A What is Hint A.1

, the coefficient of static friction between the tires and the track?

How to approach the problem Hint not displayed

Hint A.2

Use the applet to find the speed Hint not displayed

Hint A.3

Find an expression for

Find an expression for Hint not displayed Express your answer to two significant figures. ANSWER:

= 0.91 Correct

Score Summary: Your score on this assignment is 100%. You received 40 out of a possible total of 40 points.

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