Question

You are a world-famous physicist-lawyer defending a client who has been charged with murder. It is alleged that your client shot the victim. The detective who investigated the scene of the crime found a second bullet, from a shot that missed and 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 30.0 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 8.00 cm .

You: Have you tested the gun you found in my client’s possession?

Det: I have.

You: What is the muzzle velocity of bullets fired from that gun?

Det: The muzzle velocity is 350 m/s .

You: And the barrel length?

Det: The gun has a barrel length of 62 cm.

With only a slight hesitation, you turn confidently to the jury and proclaim, "My client's gun did not fire these shots!" Calculate the distance this chair could slid under given conditions to convince the jury and the judge. The coefficient of kinetic friction for "wood-wood" is 0.2.

Answer 1

Work done by friction = - umgd

= - 0.2*30.01*9.8*0.03

= - 1.7646 J

KE just after bullet got embedded = 1.7646 J

momentum of wood bullet system = sqrt(2mKE)

= sqrt(1.7646*2*30.01)

= 10.29 kgm/s

Momentum of bullet should be same just after it got fired.

v = p/m

=10.29/0.010

= 1029 m/s

But the muzzle velocity of the gun is 350 m/s...so client was found innocent.

To calculate distance d,

Momentum of bullet = 350*0.010 = 3.5

KE of bullet chair system = p^2/2m = 3.5^2/(2×30.01)

= 0.204 J

Distance d = 0.204/umg

= 0.204/(0.2*30.01*9.8)

= 0.00347 m

= 0.347 cm Answer