this is my last question, i promise!?

Question

There is a gun in which the barrel length is 62cm and has a muzzle velocity of 450m/s. A wooden chair of 30 kg sits on a wooden floor. A bullet of 10g penetrates the chair and the bullet lodges itself into the chair 9 centimeters. How far back, in centimeters, did the chair fly back? The coefficient of kinetic friction between the chair and the floor is 0.2

I'm not really sure how to approach this problem other than trying to use momentum conservation but do I need to find the force of the bullet on the chair to find the acceleration and then use momentum conservation to find the velocity, but i don't think that works. Any direction please?

Answer 1

It sounds like you're on the right track. From the momentum of the bullet, you should be able to find the force it exerts upon the chair by a simple integration of how long the bullet is applying force upon the chair (think 450m/s to 0m/s in relation to the 9 cm). Once you have that, then a simple free-body force diagram with the applied force of the bullet and the resistance with friction with momentum conservation should give you the distance. Good luck.

Answer 2

Bryan boy! Why don’t you quote the problem instead of retelling it? This “novel” about a chair and bullet looks somewhat confusing indeed! What can these 62cm of barrel length do with it? And does it really matter that bullet stuck in the chair in 9cm?
If bullet’s m=10g and bullet’s velocity v=450m/s, its potent energy E=m*v*v/2. All its energy would be given to a piece of wood M=30kg, that starts to move and then stops in Scm, because of kinetic friction. Equation using energy conservation:
m*v*v/2=F*S, where F=M*g*0.2 - the friction force.
S=.01*450*450/2/30/9.81/.2=17.2m
(impressing isn’t it?)
And never promise to stop asking!

Answer 3

s=?
Bullet0--->450m/s -----------Chair[]------->Chair[]
m=10/1000kg m=30kg
=.01kg <--------
f=uR

force of kinetic friction, f=uR, where u is the coefficient of friction of 0.2, and R is the force normal to the floor.
R=30*9.8N

f=0.2*30*9.8
=58.8N

Work=f*s
=58.8*s


KE before impact =1/2mv^2
=1/2*0.01*450^2
=1012.5 J
Based on the principle of conservation of energy:

KE before impact =Work done

1012.5=58.8s
s=1012.5/58.8
=17.2m
=1720cm

We don't need the length of the muzzle and the depth the bullet was imbedded in the chair to be able to solve the problem.