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World Famous Physicist Lawyer

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1. Homework Statement

You are a world-famous physicist-lawyer defending a client who has been charged with murder. It is alleged that your client, Mr. Smith, shot the victim, Mr. Wesson. The detective who investigated the scene of the crime found a second bullet, from a shot that missed Mr. Wesson, that had embedded itself into a chair. You arise to cross-examine the detective. You: In what type of chair did you find the bullet? Det: A wooden chair. You: How massive was this chair? Det: It had a mass of 20.0 kg. You: How did the chair respond to being struck with a bullet? Det: It slid across the floor. You: How far? Det: Three centimeters. The slide marks on the dusty floor are quite distinct. You: What kind of floor was it? Det: A wood floor, very nice oak planks. You: What was the mass of the bullet you retrieved from the chair? Det: Its mass was 10 g. You: And how far had it penetrated into the chair? Det: A distance of 4.00 cm. You: Have you tested the gun you found in Mr. Smith's possession? Det: I have. You: What is the muzzle velocity of bullets fired from that gun? Det: The muzzle velocity is 450 m/s. You: And the barrel length? Det: The gun has a barrel length of 62 cm.


2. Homework Equations



3. The Attempt at a Solution


I found the force on chair by the bullet if the bullet is going 450 m/s

0=(450)^2 +2a(.04m)
a= -2531250 m/s^2

F= (.01kg)(-2531250m/s^2)
So force by bullet on chair is 25312.5 N
This force acts this time:
for 0=(450m/s) + (-2531250m/s^2)(t)
t= 1.78 * 10^-4 s

Force of friction on chair : (20.01kg)(9.80)(.20) = 39.2 N

sum forces on x = Fb-kinetic friction = 25312.5N-39.2N= 25273.3 N
acceleration of chair= (20.01kg)(a)= 25273.3N a=1263 m/s^2

Impulse-momentum theorem: Impulse plus initial momentum equals final momentum
(25273.3N)(1.78*10^-4s) + 0 = (20.01kg)v
v=.225m/s this is the velocity of the chair when the bullet stops moving

distance it has gone during the impulse:
(.225m/s)^2= (0m/s)^2 + 2(1263 m/s^2)x
x=2.00*10^-5 m

after this: Force of friction = 39.2 N

(20.01kg)(a)=(-39.2N) a=-1.95 m/s^2

distance traveled during this time

(0m/s)^2=(.225 m/s)^2 + 2(-1.95m/s^2)x
x=.013 m =1.29 cm.

Is this correct, or am I making this way too complicated? If it is not correct, could you please explain how you would have done it?
 

Answers and Replies

36
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why does the problem give you the barrel length of the gun?
 
374
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I think that is useless info. Any thoughts on this one yet?
 
Andrew Mason
Science Advisor
Homework Helper
7,539
317
Why does the chair not move across the entire room?

You need another piece of information: hint: it has to do with the fact that the floor is wood, as well as the chair feet?

AM
 
374
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i took friction into account i think
 
1
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I think you are making this too complicated
 

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