There is a gun which mass is M = 4 kg. The length of the gun's barrel is l = 50 cm. I need to find the average recoil force while shooting the bullet which mass is m = 5g. The speed of bullet when it leaves the gun's barrel is v = 930 m/s.
The Attempt at a Solution
Acceleration of the bullet is:
a = v^2/(2*l);
To get out of the barrel it takes time which is:
t = v/a = 2*l/v;
The average momentum of the bullet when it is in barrel is equal:
p(ave bullet) = mv/2;
But the gun gets the same average momentum (momentum conservation law):
p(ave gun) = mv/2;
So this means that the average gun's recoil force is:
F = p(ave gun)/t = mv/2 : 2l/v = mv^2/(4*l);
I am really a little bit confused. I haven't used gun's mass M in the solution. Isn't here any mistakes in the solution?
Thanks in advance.