Applications of Laws of Motion

Applications of Laws of Motion

Due: 7:00pm on Monday, October 1, 2012

Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy

A message from your instructor...

For Items 2, 9, 10, 11, 15, 16 and 17, please submit your answers online, and also submit written work showing how

you solved these problems. Put your written solutions in the homework box on the second floor of the Physics

Building by the same due date and time as for the online assignment.

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?

Express the tension in terms of and .

You did not open hints for this part.

ANSWER:

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Applications of Laws of Motion http://session.masteringphysics.com/myct/assignmentPrintView?displa...

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Part B

Given , the tension in the string, calculate , the magnitude of the vertical acceleration of the block of mass

.

Express the acceleration magnitude in terms of , , and .


ANSWER:

Part C

Given the magnitude of the acceleration of the block of mass , find , the magnitude of the horizontal

acceleration of the block of mass .

Express in terms of .


ANSWER:

Part D

Using the result of Part C in the formula for that you previously obtained in Part A, express

as a function of .

Express your answer in terms of and .

ANSWER:

Part E

Having solved the previous parts, you have all the pieces needed to calculate , the magnitude of the

acceleration of the block of mass . Write an expression for .

Express the acceleration magnitude in terms of , , and .


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ANSWER:


Submit written work for the following problem.

Problem 5.92

Two blocks connected by a cord passing over a small, frictionless pulley rest on frictionless planes (the figure ).

Part A

Which way will the system move when the blocks are released from rest?

ANSWER:

Correct

Part B

What is the acceleration of the blocks?

ANSWER:

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the blocks will slide to the left

the blocks will slide to the right


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Try Again; 5 attempts remaining

Part C

What is the tension in the cord?

ANSWER:

Try Again; 5 attempts remaining

Contact Forces Introduced

Learning Goal:

To introduce contact forces (normal and friction forces) and to understand that, except for friction forces under

certain circumstances, these forces must be determined from: net Force = ma.

Two solid objects cannot occupy the same space at the same time. Indeed, when the objects touch, they exert

repulsive normal forces on each other, as well as frictional forces that resist their slipping relative to each other.

These contact forces arise from a complex interplay between the electrostatic forces between the electrons and ions

in the objects and the laws of quantum mechanics. As two surfaces are pushed together these forces increase

exponentially over an atomic distance scale, easily becoming strong enough to distort the bulk material in the

objects if they approach too close. In everyday experience, contact forces are limited by the deformation or

acceleration of the objects, rather than by the fundamental interatomic forces. Hence, we can conclude the

following:

The magnitude of contact forces is determined by , that is, by the other forces on, and acceleration of,

the contacting bodies. The only exception is that the frictional forces cannot exceed (although they can be

smaller than this or even zero).

Normal and friction forces

Two types of contact forces operate in typical mechanics problems, the normal and frictional forces, usually

designated by and (or , or something similar) respectively. These are the components of the overall contact

force: perpendicular to and parallel to the plane of contact.

Kinetic friction when surfaces slide

When one surface is sliding past the other, experiments show three things about the friction force (denoted ):

The frictional force opposes the relative motion at the point of contact,1.

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is proportional to the normal force, and2.

the ratio of the magnitude of the frictional force to that of the normal force is fairly constant over a wide

range of speeds.

3.

The constant of proportionality is called the coefficient of kinetic friction, often designated . As long as the sliding

continues, the frictional force is then

(valid when the surfaces slide by each other).

Static friction when surfaces don't slide

When there is no relative motion of the surfaces, the frictional force can assume any value from zero up to a

maximum , where is the coefficient of static friction. Invariably, is larger than , in agreement with the

observation that when a force is large enough that something breaks loose and starts to slide, it often accelerates.

The frictional force for surfaces with no relative motion is therefore

(valid when the contacting surfaces have no relative motion).

The actual magnitude and direction of the static friction force are such that it (together with other forces on the

object) causes the object to remain motionless with respect to the contacting surface as long as the static friction

force required does not exceed

. The equation is valid only when the surfaces are on the verge of sliding.

Part A

When two objects slide by one another, which of the following statements about the force of friction between

them, is true?

ANSWER:

The frictional force is always equal to .

The frictional force is always less than .

The frictional force is determined by other forces on the objects so it can be either equal to or less

than .


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Part B

When two objects are in contact with no relative motion, which of the following statements about the frictional

force between them, is true?

ANSWER:

Part C

When a board with a box on it is slowly tilted to larger and larger angle, common experience shows that the box

will at some point "break loose" and start to accelerate down the board.

The box begins to slide once the component of gravity acting parallel to the board equals the force of static

friction. Which of the following is the most general explanation for why the box accelerates down the board?

ANSWER:

Part D

Consider a problem in which a car of mass is on a road tilted at an angle . The normal force

Select the best answer.

ANSWER:

The frictional force is always equal to .

The frictional force is always less than .

The frictional force is determined by other forces on the objects so it can be either equal to or less

than .

The force of kinetic friction is smaller than that of static friction, but remains the same.

Once the box is moving, is smaller than the force of static friction but larger than the force of

kinetic friction.

Once the box is moving, is larger than the force of static friction.

When the box is stationary, equals the force of static friction, but once the box starts moving, the

sliding reduces the normal force, which in turn reduces the friction.

is found using


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Comparing Friction Forces with Gravity Conceptual Question

A large crate filled with physics laboratory equipment must be moved up an incline onto a truck.

Part A

The crate is at rest on the incline. What can you say about the force of friction acting on the crate?


ANSWER:

Part B

A physicist attempts to push the crate up the incline. The physicist senses that if he applies slightly more force

the crate will move up the incline but cannot muster enough strength to get the motion started. What can you

say now about the force of friction acting on the crate?

ANSWER:

Part C

The frictional force points up the incline.

The frictional force points down the incline.

The frictional force is zero.

The frictional force points up the incline.

The frictional force points down the incline.

The frictional force is zero.


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The first physicist gets a second physicist to help. They both push on the crate, parallel to the surface of the

incline, and it moves at constant speed up the incline. How does the force exerted by the two physicists on the

crate compare with the force of friction on the crate?


ANSWER:

PSS 5.2 Newton’s Second Law: Dynamics of Particles

Learning Goal:

To practice Problem-Solving Strategy 5.2 Newton’s Second Law: Dynamics of Particles.

You want to move a heavy box with mass 30.0 across a carpeted floor. You pull hard on one of the edges of the

box at an angle 30 above the horizontal with a force of magnitude 240 , causing the box to move horizontally.

The force of friction between the moving box and the floor has magnitude 41.5 . What is the box's acceleration

just after it begins to move?

Problem-Solving Strategy: Newton’s second law—Dynamics of particles

IDENTIFY the relevant concepts:

Identify the target variable—usually an acceleration or a force. If the target variable is velocity, time, or distance, you

will use Newton's second law to find the acceleration and then use kinematics to find the target variable.

SET UP the problem using the following steps:

Draw a simple sketch of the situation. Identify one or more moving bodies to which you’ll apply

Newton’s second law.

1.

For each body you identified, draw a free-body diagram that shows all the forces acting on the body.2.

Label each force with an algebraic symbol for the force’s magnitude.3.

Choose your x and y coordinate axes for each body, and show them in that body's free-body diagram.4.

If more than one body is involved, there may be relationships among their motions; for example, they

may be connected by a rope. Express any such relationships as equations relating the accelerations

of the various bodies.

5.

EXECUTE the solution as follows:

For each object, determine the components of the forces along each of the object’s coordinate axes.1.

For each object, write a separate equation for each component of Newton’s second law,

and .

2.

Make a list of all the known and unknown quantities. In your list, identify the target variable or

variables.

3.

Check that you have as many equations as there are unknowns. If you have too few equations, go

back to Step 5 of “Set up the problem".

4.

Do the easy part—the math! Solve the equations to find the target variable(s).5.

is less than

equals

is greater than

.


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EVALUATE your answer:

Does your answer have the correct units? Does it have the correct algebraic sign? When possible, consider

particular values or extreme cases of quantities and compare the results with your intuitive expectations. Ask, “Does

this result make sense?”

IDENTIFY the relevant concepts

The target variable in this problem is the acceleration of the box. Since you know the magnitudes and directions of

all of the forces, you can use Newton's second law to find the acceleration.

SET UP the problem using the following steps

Part A

The figure shows the situation described. Which of

the following describes the best coordinate system?

You should generally align the positive x axis with the

direction in which your object of interest is

accelerating.

ANSWER:

Part B

This question will be shown after you complete previous question(s).

EXECUTE the solution as follows

Part C

Positive x axis to the left, positive y axis upward

Positive x axis to the right, positive y axis downward

Positive x axis to the left, positive y axis downward

Positive x axis to the right, positive y axis upward


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EVALUATE your answer

Part D


Pushing Too Hard

A baggage handler at an airport applies a constant horizontal force with magnitude to push a box, of mass ,

across a rough horizontal surface with a very small constant acceleration .

Part A

The baggage handler now pushes a second box, identical to the first, so that it accelerates at a rate of . How

does the magnitude of the force that the handler applies to this box compare to the magnitude of the force

applied to the first box?


ANSWER:


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Part B

Now assume that the baggage handler pushes a third box of mass so that it accelerates at a rate of .

How does the magnitude of the force that the

handler applies to this box compare to the magnitude

of the force applied to the first box?


ANSWER:


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Board Pulled Out from under a Box

A small box of mass is sitting on a board of mass and length . The board rests on a frictionless horizontal

surface. The coefficient of static friction between the

board and the box is . The coefficient of kinetic friction

between the board and the box is, as usual, less than .

Throughout the problem, use for the magnitude of the

acceleration due to gravity. In the hints, use for the

magnitude of the friction force between the board and the

box.

Part A

Find , the constant force with the least magnitude that must be applied to the board in order to pull the

board out from under the the box (which will then fall off of the opposite end of the board).

Express your answer in terms of some or all of the variables , , , , and . Do not include in

your answer.


ANSWER:

Enhanced EOC: Exercise 5.39

A large crate with mass rests on a horizontal floor. The static and kinetic coefficients of friction between the crate

and the floor are and , respectively. A woman pushes downward on the crate at an angle below the

horizontal with a force .

You may want to review ( pages 146 - 154) .

For help with math skills, you may want to review:

Vector Components

Limits Involving Infinity

For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of

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Minimizing kinetic friction.

Part A

What is the magnitude of the force vector required to keep the crate moving at constant velocity?

Express your answer in terms of , , , and .


ANSWER:

Part B

If is greater than some critical value, the woman cannot start the crate moving no matter how hard she

pushes. Calculate this critical value of .

Express your answer in terms of .


ANSWER:



Exercise 5.30

Some sliding rocks approach the base of a hill with a speed of 14.0 . The hill rises at 39.0 above the horizontal

and has coefficients of kinetic and static friction of 0.420 and 0.620, respectively, with these rocks. Start each part of

your solution to this problem with a free-body diagram.

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Part A

Find the acceleration of the rocks as they slide up the hill.

ANSWER:

Part B

Once a rock reaches its highest point, will it stay there or slide down the hill?

ANSWER:

Part C

If it slides down, find its acceleration on the way down, else enter 0.

ANSWER:



Problem 5.71

A block with mass is placed on an inclined plane with slope angle and is connected to a second hanging

block that has mass by a cord passing over a small, frictionless pulley. The coefficient of static friction is and

the coefficient of kinetic friction is .

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stay there

slide down the hill


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Part A

Find the mass for which block moves up the plane at constant speed once it has been set in motion.

Express your answer in terms of , , , , and .

ANSWER:

Part B

Find the mass for which block moves down the plane at constant speed once it has been set in motion.


ANSWER:

Part C

Find the smallest value of when the blocks will remain at rest if they are released from rest.


ANSWER:



Problem 5.84

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Part A

If the coefficient of static friction between a table and a uniform massive rope is , what fraction of the rope

can hang over the edge of the table without the rope sliding?

Express your answer in terms of .

ANSWER:

A Mass on a Turntable: Conceptual

A small metal cylinder rests on a circular turntable that is

rotating at a constant rate, as illustrated in the diagram.

Part A

Which of the following sets of vectors best describes the velocity, acceleration, and net force acting on the

cylinder at the point indicated in the diagram?


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ANSWER:

Part B

Let be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is

moved to a new location from the center of the turntable. Which of the following statements accurately

describe the motion of the cylinder at the new location?

Check all that apply.


ANSWER:

± 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 .

a

b

c

d

e

The speed of the cylinder has decreased.

The speed of the cylinder has increased.

The magnitude of the acceleration of the cylinder has decreased.

The magnitude of the acceleration of the cylinder has increased.

The speed and the acceleration of the cylinder have not changed.


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Part A

What is the woman's mass?

Express your answer in kilograms.


ANSWER:

± Banked Frictionless Curve, and Flat Curve with Friction

A car of mass = 1100 traveling at 50.0 enters a banked turn covered with ice. The road is banked at

an angle , and there is no friction between the road and the car's tires. . Use = 9.80 throughout this

problem.

Part A

What is the radius of the turn if = 20.0 (assuming the car continues in uniform circular motion around the

turn)?

Express your answer in meters.


ANSWER:

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Part B




Exercise 5.47

In another version of the "Giant Swing", the seat is connected to two cables as shown in the figure , one of which is

horizontal. The seat swings in a horizontal circle at a rate

of 32.0 .

Part A

If the seat weighs 284 and a 900- person is sitting in it, find the tension in the horizontal cable.

ANSWER:

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Part B

If the seat weighs 284 and a 900- person is sitting in it, find the tension in the inclined cable.

ANSWER:



Problem 5.115

On the ride "Spindletop" at the amusement park Six Flags Over Texas, people stood against the inner wall of a

hollow vertical cylinder with radius 2.5 . The cylinder started to rotate, and when it reached a constant rotation

rate of 0.60 , the floor on which people were standing dropped about 0.5 . The people remained pinned

against the wall.

Part A

Draw a force diagram for a person on this ride, after the floor has dropped. (Assume the vertical axis of the

cylinder to be at the left.)

Draw the force vectors with their tails at the dot. The orientation of your vectors will be graded. The

exact length of your vectors will not be graded but the relative length of one to the other will be graded.

ANSWER:

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Part B

What minimum coefficient of static friction is required if the person on the ride is not to slide downward to the

new position of the floor?

Express your answer using two significant figures.

ANSWER:

Part C

Does your answer in part B depend on the mass of the passenger? (Note: When the ride is over, the cylinder is

slowly brought to rest. As it slows down, people slide down the walls to the floor.)

ANSWER:



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yes

no


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Problem 5.118

A physics major is working to pay his college tuition by performing in a traveling carnival. He rides a motorcycle

inside a hollow transparent plastic sphere. After gaining sufficient speed, he travels in a vertical circle with a radius

of 12.2 . The physics major has a mass of 66.0 , and his motorcycle has a mass of 40.0 .

Part A

What minimum speed must he have at the top of the circle if the tires of the motorcycle are not to lose contact

with the sphere?

ANSWER:

Part B

At the bottom of the circle his speed is twice the value calculated in part A. What is the magnitude of the normal

force exerted on the motorcycle by the sphere at this point?

ANSWER:

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?


ANSWER:

Part B

No; the sky diver falls at constant speed.

Yes and her acceleration is directed upward.

Yes and her acceleration is directed downward.


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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?

Express your answer in newtons.


ANSWER:

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 is about 0.250 .

Using this value for , what is the terminal speed of the sky diver?

Express you answer in meters per second.


ANSWER:

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?


ANSWER:

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No; the sky diver keeps falling at constant speed.

Yes and her acceleration is directed downward.

Yes and her acceleration is directed upward.


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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?

Express your answer in newtons.


ANSWER:

Part F

What is the terminal speed of the sky diver when the parachute is opened?

Express your answer in meters per second.


ANSWER:

Score Summary:

Your score on this assignment is 0%.

You received 0 out of a possible total of 165 points.

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