You are a world-famous physicist-lawyer defending a client who hasbeen charged w

Question

You are a world-famous physicist-lawyer defending a client who hasbeen charged with murder. It is alleged that your client, Mr.Smith, shot the victim, Mr. Wesson. The detective who investigatedthe scene of the crime found a second bullet, from a shot thatmissed Mr. Wesson, that had embedded itself into a chair. You arise to cross-examine the detective.

You: In what type of chair did youfind 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: A good 3.0 centimeters. The slide marks on the dusty floorare 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: Have you tested the gun you found in Mr. Smith'spossession?

Det: I have.

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

Det: The muzzle velocity is 450 m/s.

With only a slight hesitation, you turn confidently to the jury andproclaim, "My client's gun did not fire these shots!" How are you going to convince the jury and the judge? The coefficient ofkinetic friction for "wood-wood" is 0.2.

Explanation / Answer

The bullet has momentum mv = ( .010 kg ) ( 450 m/s ) = 4.5 kg m/s.

After striking the chair, the chair has momentum 4.5 kg m / s = ( 20 kg ) v, so the velocity of the chair is 0.225 m/s and the kinetic energy is 1/2(20 kg) ( .225 m/s )² = .50625 J.

Now using the work-energy theorem: .50625 J = (20 kg )(9.8 m/s² )(.2)(d ), so the chair moves a distance of 1.29 cm.

The bullet could not have moved the chair 3 cm.

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