Question

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

Dinby: A wooden chair.

You: How massive was this chair?

Dinby: It had a mass of 20 kg.

You: How did the chair respond to being struck with a bullet?

Dinby: It slid across the floor. You: How far?

Dinby: Three centimeters. The slide marks on the dusty floor are quite distinct.

You: What kind of floor was it?

Dinby: A wood floor.

You: What was the mass of the bullet you retrieved from the chair?

Dinby: Its mass was 10 g.

You: Have you tested the gun you found in Mr. Lawton's possession?

Dinby: I have.

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

Dinby: The muzzle velocity is 450 m/s.

With only slight hesitation, you turn confidently to the jury and proclaim, "My client's gun did not fire those shots!"

How are you going to convince the jury and judge?

Answer 1

Mass of the bullet,

Mass of the chair,

Velocity of the bullet,

Distance displaced by the chair+bullet,

Due to the conservation of linear momentum,

where is the velocity of chair+bullet

Thus the kinetic energy of the combined system (bullet +chair)

  

Coefficient of kinetic friction of wood on wood,

Thus the frictional force on the combined system

Thus the workdone by the frictional force to stop the chair with bullet,

Since the chair with the bullet is stopped by the frictional force, we must have,

  

Thus by the gun of Mr. Lawton, chair with the bullet will travel only 1.29 cm. Hence he is innocent.