Mastering physics problem 2.16

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?