- #1
Kites
- 39
- 0
This problem is causing me quite a bit of grief and I could really use a guiding hand to tell me where I am going wrong. Here is the set up, then after that is what I've used to tackle it so far.
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 6.00 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.
Frictional Constant (wood-wood) = .02
What I've done:
Givens:
M_Chair = 20.0 kg
M_Bullet = .01 kg
M_System = 20.01 kg
friction_chair = (.02)(9.8 m/s^2)(20.01kg) = 39.2196 N
V_bullet = 450 m/s
Force of the bullet on the chair:
Acceleration of bullet as it approaches 0th Velocity
V_f^2 - V_i^2 =2*a*s
[(-450^2)/(2*.06)] = a
= -1,687,500 m/s^2
(bullet force)
F = m*a = .01 *-1,687,500 m/s^2
= 16875 N
(time that chair and bullet are moving)
V_f = V_i + a*t
(-450 m/s)/(-1,687,500 m/s^2) = t
= .0002667 s
FORCES ON THE CHAIR
F_bullet - Force_friction = ma
= (16875 - 39.216 )/(20.01kg) = a
= 841.3685157m/s
a*t^2 = X (X = Distance that chair has moved)
(841.369)(.0002667^2) = .0000598456 m
.00598 CM
ANSWER INCORRECT
I've tried this several times and I've reached this answer about 3 different ways. What is going wrong? Friction on the bullet inside the chair?
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 6.00 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.
Frictional Constant (wood-wood) = .02
What I've done:
Givens:
M_Chair = 20.0 kg
M_Bullet = .01 kg
M_System = 20.01 kg
friction_chair = (.02)(9.8 m/s^2)(20.01kg) = 39.2196 N
V_bullet = 450 m/s
Force of the bullet on the chair:
Acceleration of bullet as it approaches 0th Velocity
V_f^2 - V_i^2 =2*a*s
[(-450^2)/(2*.06)] = a
= -1,687,500 m/s^2
(bullet force)
F = m*a = .01 *-1,687,500 m/s^2
= 16875 N
(time that chair and bullet are moving)
V_f = V_i + a*t
(-450 m/s)/(-1,687,500 m/s^2) = t
= .0002667 s
FORCES ON THE CHAIR
F_bullet - Force_friction = ma
= (16875 - 39.216 )/(20.01kg) = a
= 841.3685157m/s
a*t^2 = X (X = Distance that chair has moved)
(841.369)(.0002667^2) = .0000598456 m
.00598 CM
ANSWER INCORRECT
I've tried this several times and I've reached this answer about 3 different ways. What is going wrong? Friction on the bullet inside the chair?