Mastering physics homework 2 answers

11/10/2014 HW_Week2

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HW_Week2

Due: 11:59pm on Friday, September 12, 2014

You will receive no credit for items you complete after the assignment is due. Grading Policy

Speed of a Bullet

A bullet is shot through two cardboard disks attached a distance apart to a shaft turning with a rotational period , as

shown.

Part A

Derive a formula for the bullet speed in terms of , , and a measured angle between the position of the hole in

the first disk and that of the hole in the second. If required, use , not its numeric equivalent. Both of the holes lie at

the same radial distance from the shaft. measures the angular displacement between the two holes; for instance,

means that the holes are in a line and means that when one hole is up, the other is down. Assume that

the bullet must travel through the set of disks within a single revolution.

Hint 1. Consider hole positions

The relative position of the holes can be used to find the bullet's speed. Remember, the shaft will have

rotated while the bullet travels between the disks.

Hint 2. How long does it take for the disks to rotate by an angle ?

The disks rotate by 2 in time . How long will it take them to rotate by ?

Give your answer in terms of , , and constants such as .

Hint 1. Checking your formula

If your formula is correct, when you plug 2 in for , your answer will be .

ANSWER:

 

2   J

R

J

J -  J - R

J

R  J

 J R

R J 

11/10/2014 HW_Week2

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ANSWER:

Correct

Exercise 2.14

A race car starts from rest and travels east along a straight and level track. For the first 5.0 of the car's motion, the

eastward component of the car's velocity is given by .

Part A

What is the acceleration of the car when = 14.8 ?

Express your answer with the appropriate units.

ANSWER:

Correct

Motion of Two Rockets

Learning Goal:

To learn to use images of an object in motion to determine velocity and acceleration.

Two toy rockets are traveling in the same direction (taken to be the x axis). A diagram is shown of a timeexposure

image

where a stroboscope has illuminated the rockets at the uniform time intervals indicated.

J =

J

R

2 = R

J

T

W40 -  NT U

W4 NT

　4 = 7.58

NT

11/10/2014 HW_Week2

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Part A

At what time(s) do the rockets have the same velocity?

Hint 1. How to determine the velocity

The diagram shows position, not velocity. You can't find instantaneous velocity from this diagram, but you

can determine the average velocity between two times and :

.

Note that no position values are given in the diagram; you will need to estimate these based on the distance

between successive positions of the rockets.

ANSWER:

Correct

Part B

At what time(s) do the rockets have the same x position?

ANSWER:

0 0

2BWH<00>-

40Ã40

0Ã0

at time only

at time only

at times and

at some instant in time between and

at no time shown in the figure

0 - 

0 - 

0 -  0 - 

0 -  0 - 

11/10/2014 HW_Week2

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Correct

Part C

At what time(s) do the two rockets have the same acceleration?

Hint 1. How to determine the acceleration

The velocity is related to the spacing between images in a stroboscopic diagram. Since acceleration is the

rate at which velocity changes, the acceleration is related to the how much this spacing changes from one

interval to the next.

ANSWER:

Correct

Part D

The motion of the rocket labeled A is an example of motion with uniform (i.e., constant) __________.

ANSWER:

at time only

at time only

at times and

at some instant in time between and

at no time shown in the figure

0 - 

0 - 

0 -  0 - 

0 -  0 - 

at time only

at time only

at times and

at some instant in time between and

at no time shown in the figure

0 - 

0 - 

0 -  0 - 

0 -  0 - 

and nonzero acceleration

velocity

displacement

time

11/10/2014 HW_Week2

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Correct

Part E

The motion of the rocket labeled B is an example of motion with uniform (i.e., constant) __________.

ANSWER:

Correct

Part F

At what time(s) is rocket A ahead of rocket B?

Hint 1. Use the diagram

You can answer this question by looking at the diagram and identifying the time(s) when rocket A is to the

right of rocket B.

ANSWER:

Correct

Velocity from Graphs of Position versus Time

An object moves along the x axis during four separate trials. Graphs of position versus time for each trial are shown in

the figure.

and nonzero acceleration

velocity

displacement

time

before only

after only

before and after

between and

at no time(s) shown in the figure

0 - 

0 - 

0 -  0 - 

0 -  0 - 

11/10/2014 HW_Week2

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Part A

During which trial or trials is the object's velocity not constant?

Check all that apply.

Hint 1. Finding velocity from a position versus time graph

On a graph of coordinate x as a function of time , the instantaneous velocity at any point is equal to the

slope of the curve at that point.

Hint 2. Equation for slope

The slope of a line is its rise divided by the run:

.

ANSWER:

Correct

The graph of the motion during Trial B has a changing slope and therefore is not constant. The other trials all

have graphs with constant slope and thus correspond to motion with constant velocity.

Part B

During which trial or trials is the magnitude of the average velocity the largest?

0

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U

Trial A

Trial B

Trial C

Trial D

11/10/2014 HW_Week2

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Check all that apply.

Hint 1. Definition of average velocity

Recall that

.

Then note that the question asks only about the magnitude of the velocity.

ANSWER:

Correct

While Trial B and Trial D do not have the same average velocity, the only difference is the direction! The

magnitudes are the same. Neither one is "larger" than the other, and it is only because of how we chose our

axes that Trial B has a positive average velocity while Trial D has a negative average velocity. In Trial C the

object does not move, so it has an average velocity of zero. During Trial A the object has a positive average

velocity but its magnitude is less than that in Trial B and Trial D.

± Average Velocity from a Position vs. Time Graph

Learning Goal:

To learn to read a graph of position versus time and to calculate average velocity.

In this problem you will determine the average velocity of a

moving object from the graph of its position as a function

of time . A traveling object might move at different speeds

and in different directions during an interval of time, but if we

ask at what constant velocity the object would have to travel to

achieve the same displacement over the given time interval,

that is what we call the object's average velocity. We will use

the notation to indicate average velocity over the

time interval from to . For instance, is the

average velocity over the time interval from to .

Part A

BWFSBHF WFMPDJUZ- -  QPTJUJPO

 UJNF

Y

U

Trial A

Trial B

Trial C

Trial D

40