Question

a machine gun fires n bullets per second with speed u and mass of each bullet is m. if bullets hit a wall and rebounds with same speed, then force acting on the wall is

Answer 1

a machine gun fires n bullets per second with speed u and mass of each bullet is m.
so, firing of bullet per second = n
mass of each bullet = m
so, each second , mass of bullets = mn
Let time is ∆t and initial velocity of bullet = u
then, mass of bullets = mn∆t.
initial momentum = (mn∆t)u
final momentum = -(mn∆t)u
[ because bullet rebound with same speed so, final velocity is just opposite to initial velocity]
so, change in momentum= -(mn∆t)u -(mn∆t)u
= -2(mn∆t)u = -(2mnu∆t)/∆t
= -2mnu

hence, magnitude of force acting on wall = 2mnu

Answer 2

Firing of bullet per second = n

Mass of each bullet = m

Each second, mass of bullets = mn

Let time is ∆t and initial velocity of bullet = u

then, mass of bullets = mn∆t.

Initial momentum = (mn∆t)u

Final momentum = -(mn∆t)u

Change in momentum= -(mn∆t)u -(mn∆t)u

= -2(mn∆t)u = -(2mnu∆t)/∆t

= -2mnu