CH 03 HW - Chapter 3 Physics Homework for Mastering PDF

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Chapter 3 Physics Homework for Mastering
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CH 03 HW Due: 3:00pm on Wednesday, September 18, 2019 You will receive no credit for items you complete after the assignment is due. Grading Policy

A World-Class Sprinter World-class sprinters can accelerate out of the starting blocks with an acceleration that is nearly horizontal and has magnitude

.

Part A How much horizontal force

must a sprinter of mass 64

exert on the starting blocks to produce this acceleration?

Express your answer in newtons using two significant figures.

Hint 1. Newton's 2nd law of motion According to Newton's 2nd law of motion, if a net external force of the body times the acceleration of the body:

acts on a body, the body accelerates, and the net force is equal to the mass .

ANSWER: = 960

Correct

Part B Which body exerts the force that propels the sprinter, the blocks or the sprinter?

Hint 1. How to approach the question To start moving forward, sprinters push backward on the starting blocks with their feet. Newton's 3rd law tells you that the blocks exert a force on the sprinter of the same magnitude, but opposite in direction.

ANSWER: the blocks the sprinter

Correct To start moving forward, sprinters push backward on the starting blocks with their feet. As a reaction, the blocks push forward on their feet with a force of the same magnitude. This external force accelerates the sprinter forward.

Free-Body Diagrams Learning Goal: To gain practice drawing free-body diagrams Whenever you face a problem involving forces, always start with a free-body diagram. To draw a free-body diagram use the following steps: 1. Isolate the object of interest. It is customary to represent the object of interest as a point in your diagram. 2. Identify all the forces acting on the object and their directions. Do not include forces acting on other objects in the problem. Also, do not include quantities, such as velocities and accelerations, that are not forces. 3. Draw the vectors for each force acting on your object of interest. When possible, the length of the force vectors you draw should represent the relative magnitudes of the forces acting on the object.

In most problems, after you have drawn the free-body diagrams, you will explicitly label your coordinate axes and directions. Always make the object of interest the origin of your coordinate system. Then you will need to divide the forces into x and y components, sum the x and y forces, and apply Newton's first or second law. In this problem you will only draw the free-body diagram. Suppose that you are asked to solve the following problem: Chadwick is pushing a piano across a level floor (see the figure). The piano can slide across the floor without friction. If Chadwick applies a horizontal force to the piano, what is the piano's acceleration? To solve this problem you should start by drawing a free-body diagram.

Part A Determine the object of interest for the situation described in the problem introduction.

Hint 1. How to approach the problem You should first think about the question you are trying to answer: What is the acceleration of the piano? The object of interest in this situation will be the object whose acceleration you are asked to find.

ANSWER:

the floor. For this situation you should draw a free-body diagram for

Chadwick. the piano.

Correct

Part B Identify the forces acting on the object of interest. From the list below, select the forces that act on the piano. Check all that apply. ANSWER: acceleration of the piano gravitational force acting on the piano (piano's weight) speed of the piano gravitational force acting on Chadwick (Chadwick's weight) force of the floor on the piano (normal force) force of the piano on the floor force of Chadwick on the piano force of the piano pushing on Chadwick

Correct

Now that you have identified the forces acting on the piano, you should draw the free-body diagram. Draw the length of your vectors to represent the relative magnitudes of the forces, but you don't need to worry about the exact scale. You won't have the exact value of all of the forces until you finish solving the problem. To maximize your learning, you should draw the diagram yourself before looking at the choices in the next part. You are on your honor to do so.

Part C Select the choice that best matches the free-body diagram you have drawn for the piano.

Hint 1. Determine the directions and relative magnitudes of the forces Which of the following statements best describes the correct directions and relative magnitudes of the forces involved? ANSWER: The normal force and weight are both upward and the pushing force is horizontal. The normal force and weight are both downward and the pushing force is horizontal. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force has a greater magnitude than the weight. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force and weight have the same magnitude. The normal force is upward, the weight is downward, and the pushing force is horizontal. The normal force has a smaller magnitude than the weight.

ANSWER:

Correct If you were actually going to solve this problem rather than just draw the free-body diagram, you would need to define the coordinate system. Choose the position of the piano as the origin. In this case it is simplest to let the y axis point vertically upward and the x axis point horizontally to the right, in the direction of the acceleration.

Chadwick now needs to push the piano up a ramp and into a moving van. The piano slides up the ramp without friction. Is Chadwick strong enough to push the piano up the ramp alone or must he get help? To solve this problem you should start by drawing a free-body diagram.

Part D Determine the object of interest for this situation. ANSWER:

the ramp. For this situation, you should draw a free-body diagram for

Chadwick. the piano.

Correct

Now draw the free-body diagram of the piano in this new situation. Follow the same sequence of steps that you followed for the first situation. Assume that Chadwick pushes in a direction parallel to the inclined plane. Again, draw your diagram before you look at the choices below.

Part E Which diagram accurately represents the free-body diagram for the piano? ANSWER:

Correct In working problems like this one that involve an incline, it is most often easiest to select a coordinate system that is not vertical and horizontal. Instead, choose the x axis so that it is parallel to the incline and choose the y axis so that it is perpendicular to the incline.

Newton's 1st Law Learning Goal: To understand Newton's 1st law. Newton's Principia states this first law of motion: An object subject to no net force maintains its state of motion, either at rest or at constant speed in a right line. This law may be restated as follows: If the sum of all forces acting on an object is zero, then the acceleration of that object is zero. Mathematically this is just a special case of the 2nd law of motion,

, when

. When studying Newtonian mechanics, it is best to remember the 1st law in two ways:

1. If the net force (i.e., sum of all forces) acting on an object is zero, the object will keep moving with constant velocity (which may be zero). 2. If an object is moving with constant velocity, that is, with zero acceleration, then the net force acting on that object must be zero. Complete the following sentences to see if you can apply these ideas.

Part A If a car is moving to the left with constant velocity, one can conclude that ANSWER: there must be no forces applied to the car. the net force applied to the car is directed to the left. the net force applied to the car is zero. there is exactly one force applied to the car.

Correct

Part B An object cannot remain at rest unless ANSWER: there are no forces at all acting on it. the net force acting on it is zero. the net force acting on it is constant. there is only one force acting on it.

Correct

Part C An object will have constant acceleration if Select the most general response.

Hint 1. More help from Newton To solve this, you have to apply Newton's 2nd law,

.

ANSWER:

there are no forces at all acting on it. the net force acting on it is zero. the net force acting on it is constant in magnitude and direction. there is only one force acting on it.

Correct

Stopping on Snow Light, dry snow is called powder. Skiing on a powder day is different than skiing on a day when the snow is wet and heavy. When you slow down on dry snow the maximum (negative) acceleration caused by the snow acting on your skis is about two-fifths as much as that of stopping on wet snow.

Part A For a given initial velocity, how does the time

it takes to stop on dry snow differ from the time

it takes to stop on wet snow?

Hint 1. How to approach the problem To solve this problem you must use proportional reasoning to find a relation between acceleration

and time .

Find the simplest equation that contains these variables and other known quantities from the problem. Write this equation twice, once to describe and and again to relate and . You need to write each equation so that all the constants are on one side and your variables are on the other. Since your variable is in this problem, you want to write your equations in the form . To finish the problem you need compare the two cases presented in the problem. For this question you should find the ratio . Hint 2. Find which equation to use In this problem you are told that the initial velocities are the same on both types of snow and that the skier is coming to a stop. You are also given information that relates the two accelerations. Which equation is the best to use to find out information about the time necessary to stop? ANSWER:

Hint 3. Relating the stopping time on dry snow to the time on wet snow In the follow-up to Hint 2, the relationship was established. Since

and

are the same on both types of snow we can conclude that

. Use this equation with what is known about the accelerations to find the relationship between

ANSWER:

and

.

Correct This solution illustrates that time is inversely proportional to acceleration. This should make sense; the greater the acceleration, the less time is required to come to a stop from any given initial speed.

Part B For a given initial velocity, how does the stopping distance

on dry snow differ from the stopping distance

on wet snow?

Hint 1. Find which equation to use In this problem you are told that the initial velocities are the same on both types of snow and that the skier is coming to a stop. You are also given information that relates the two accelerations. Which equation is the best (simplest) to use to find information about the stopping distance? ANSWER:

Hint 2. Relating the stopping distance on dry snow to the distance on wet snow In the follow-up to the previous hint, the relationship

was established. We can assume that

in both cases, allowing us to conclude that

. Use this equation with what is known about the accelerations to find the relationship between

and

.

ANSWER:

Correct This solution illustrates that stopping distance is inversely proportional to acceleration. This should make sense; the greater the acceleration, the less time and distance is required to come to a stop from any given initial speed.

Forces on Blocks in an Elevator Conceptual Question Two blocks are stacked on top of each other on the floor of an elevator. For each of the following situations, select the correct relationship between the magnitudes of the two forces given. You will be asked two questions about each of three situations. Each situation is described above the first in the pair of questions. Do not assume anything about a given situation except for what is given in the description for that particular situation.

First situation The elevator is moving downward at a constant speed.

Part A

Hint 1. Comparing forces that act on the same object When comparing forces that act on the same object, draw a free-body diagram of the object being acted on. Then, determine the acceleration of the object. By Newton's 2nd law, the net force must be proportional to the object's acceleration. Hint 2. Draw a free-body diagram for the top block Complete the free-body diagram for the top block by drawing the force on the top block due to the earth. This force should act at the center of the block. ANSWER:

No elements selected

Select the elements from the list and add them to the canvas setting the appropriate attributes.

ANSWER: greater than equal to The magnitude of the force of the bottom block on the top block is

less than unknown compared to

block.

the magnitude of the force of the earth on the top

Correct

Part B

Hint 1. Comparing forces that do not act on the same object If two forces do not act on the same object, they will not appear on the same free-body diagram. Therefore, Newton's 2nd law cannot be used to determine the relative sizes of these forces. Certain forces can, however, be compared using Newton's 3rd law. Hint 2. Newton's 3rd law Newton's 3rd law states that when two objects exert forces on each other, these forces are always equal in magnitude and opposite in direction. Thus, if you are sitting in a chair, the force the chair exerts upward on you is exactly the same as the force you exert downward on the chair, regardless of whether you are at rest in the chair, or have you feet up on your desk, or are in the process of getting up out of the chair, or in the process of landing in the chair after jumping from a great height, ... it does not matter!

ANSWER:

greater than equal to The magnitude of the force of the bottom block on top block is

less than

the magnitude of the force of the top block on bottom

unknown compared to block.

Correct

Second situation The elevator is moving downward at an increasing speed.

Part C

Hint 1. Determining acceleration If the elevator is moving downward at an increasing speed, what is the direction of the elevator's acceleration? ANSWER:

upward zero downward unknown

ANSWER:

greater than equal to The magnitude of the force of the bottom block on the top block is

less than unknown compared to

block.

the magnitude of the force of the earth on the top

Correct

Part D

Hint 1. Newton's 3rd law in accelerating elevator Newton's 3rd law holds that forces come in pairs of equal magnitude and opposite direction in all cases. Thus, the acceleration of the elevator should not affect the relative magnitude of two forces that form a 3rd law pair.

ANSWER: greater than equal to The magnitude of the force of the bottom block on the top block is

less than

the magnitude of the force of the top block on the

unknown compared to bottom block.

Correct

Third situation The elevator is moving upward.

Part E

Hint 1. Determining acceleration If the elevator is moving upward, what is the direction of the elevator's acceleration? ANSWER: upward zero downward unknown

ANSWER: greater than equal to The magnitude of the force of the bottom block on the top block is

less than

the magnitude of the force of the earth on the top

unknown compared to block.

Correct Even though the elevator is moving upwards, you do not know in which direction it is accelerating, or indeed whether the elevator is accelerating at all!

Part F ANSWER: greater than equal to The magnitude of the force of the bottom block on the top block is

less than

the magnitude of the force of the top block on the

unknown compared to bottom block.

Correct

Relating Graphs and Free-Body Diagrams Two forces are exerted on an object of mass on the object.

in the x direction as illustrated in the free-body diagram shown in . Assume that these are the only forces acting

Part A Which of the curves labeled A to D on the graph below could be a plot of

, the velocity of the object in the x direction as a function of time?

Hint 1. How to approach the problem Analyze the free-body diagram to determine whether there is a net force acting on the object along the x axis. If the object is experiencing a net force, then its velocity must be changing in that direction. Hint 2. Relate force, acceleration, and velocity If a constant nonzero net force is applied to an object, what will the object's acceleration and velocity be?

Hint 1. Relating force and acceleration

Recall that Newton's 2nd law applied in the x direction gives

where

is the mass of the object and

Because the object's mass is constant,

, is the acceleration of the object along the x axis. is proportional to

. This means that if

increases,

must also increase.

Hint 2. Relating acceleration and velocity The average acceleration

of an object along the x direction is defined as the rate of change of velocity, ,

where time

occurs after time

.

It may also help to recall that, on a graph of velocity versus time, the slope of the velocity curve is the average acceleration.

ANSWER: Both acceleration and velocity will be constant. Acceleration will not be constant and velocity will change at a nonconstant rate. Acceleration will be constant and velocity will change at a constant rate. Acceleration will be constant and velocity will change at a nonconstant rate.

Correct Keep in mind that on a graph of velocity versus time, the slope of the velocity curve is the average acceleration. Therefore a linearly changing velocity implies a constant acceleration.

ANSWER: A B C D

Correct The net force on the object in the x direction indicates that the object is accelerating in the x direction. But accelerating doesn't necessarily mean speeding up. As depicted by curve B, at the time the net force was applied to the object, the object had already been moving with nonzero velocity in the +x direction. The effect of the acceleration in the x direction on the object was to 1. slow down the object, 2. bring the object to an instantaneous stop (which occurs when line B intersects the horizontal t axis), and 3. speed up the object in the x direction.

Part B Which of the curves labeled A to D on the graph below could be a plot of

, the position of the object along the x axis as a function of time?

Hint 1. How to approach the problem The average velocity

of an object along the x direction is defined as the rate of change of position, ,

where time occurs after time . On a graph of position versus time, the slope of the position curve is the average velocity. Determine what kind of position graph will yield the average velocity found in Part A.