Physics question?

Question

A gun fires a bullet. The bullet's mass is 5g and it travels at 20m/s. Thee recoil velocity of the gun is 2m/s. What is the mass of the gun?

I'm sure you need to set up an equation where momentum before =momentum after.
Please solve showing all your work,
Thanks

Answer 1

You are correct, this is a problem involving the law of conservation of momentum....initial momentum = final momentum = zero in this case since the objects we initially at rest (we can assume).

Momentum (P) = mass (m) * velocity (v)
P = mv

If the initial momentum = 0, then final momentum = 0
If the final velocity of the bullet is 20 m/s and its mass is 5 g,
P_bullet_final = .005 kg * 20 m/s = .1 kg m/s
Which must be equal in magnitude (but opposite in direction) to the final momentum of the gun.

We know the final velocity of the gun to be 2 m/s, but we don't know the mass. This is OK since we know its final momentum should be negative .1 kg m/s,
P_gun_final = .1 kg m/s = m_gun * 2 m/s
m_gun = .1 kg m/s / 2 m/s
m = .05 kg = 50 grams.

This is an awfully light gun, but considering the bullet isn't really traveling all that fast and that the recoil velocity of the gun is 1/10 of the bullet velocity (same ratio as their masses), the answer makes sense.

Answer 2

Equal and opposite forces will act on the gun and bullet

F = m x a

So, Force on Gun = Force on Bullet
(Gun Mass x 2 m/s) = 5g x 20 m/s
Therefore, Gun Mass = [work it out yrsf]

This is a really slow bullet - must be a toy gun

Answer 3

From conservation of momentum:
m1v1+m2v2=0 (1=bullet, 2=gun)
5*20+m2*-2=0
m2=100/2=50g
Are you sure the bullet's velocity is 20m/s? I could almost overtake it on my bike!

Answer 4

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