You are a world-famous physicist-lawyer defending a client who has been charged

Question

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: 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. with only a slight hesitation, you turn confidently to the jury and proclaim, "my client's gun did not fire these shots!" how are you going to convince the jury and the judge?

Explanation / Answer

Mass of Bullet = 10 * 10^-3 Kg
Mass of Chair = 30.3 Kg

Penentration in Chair = 8.0 * 10^-2 m
muzzle velocity = 450 m/s
barrel length = 62 * 10^-2 m

Initial Momentum of Bullet = mb * muzzle velocity
Initial Momentum of Bullet = 10*10^-3 * 450 Kg m/s
Initial Momentum of Bullet = 4.5 Kg m/s

Momentum of Chair = m*v

Using Momentum Conservation -
Initial Momentum = Final Momentum
4.5 Kg m/s = mc * vc
4.5 = 30 * vc
vc = 0.15 m/s

Friction Force = u*N = 0.2*(30+0.01)*9.8
Acceleration = u*(mc + mb)*g/(mc +mb)
a = u*g = 0.2*9.8 m/s^2
a = 1.96 m/s^2
Final Velocity = 0

V^2 = u^2 + 2*a*s
0 = 0.15^2 - 2*1.96*s
s = 0.0057 m
s = 0.57 cm

Thus we can clearly see. bullet cannot move chair by 3.0 cm.
Distance this chair could slid under given conditions = 0.57 cm

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