Question

A 10-g bullet leaves a rifle barrel with a velocity of 600 m/s to the east. If the barrel is 1 m long, the bullet accelerates inside with constant acceleration and the gun has a mass of 4 kg, what is: a) the recoil velocity of the rifle? b) the force exerted on the bullet? c) the time during which the bullet was accelerated? d) the impulse supplied to the bullet?

Answer 1

a)

m = mass of bullet = 10 g = 0.010 kg

M = mass of the gun = 4 kg

V_i = initial velocity of bullet and gun before fire = 0 m/s

v = velocity of bullet after fire = 600 m/s

V = velocity of gun after fire = ?

Using conservation of momentum

(m + M) V_i = m v + MV

(m + M) (0) = (0.010) (600) + 4 V

V = - 1.5 m/s

b)

a = acceleration

v = final speed of bullet = 600 m/s

v_o = initial speed of bullet = 0 m/s

d = distance traveled = 1 m

Using the equation

v² = v_o² + 2 a d

600² = 0² + 2 a (1)

a = 1.8 x 10⁵ m/s²

Force on the bullet is given as

F = ma

F = (0.010) (1.8 x 10⁵)

F = 1800 N

c)

Using Impulse-change in momentum equation

F t = m (v - v_o)

1800 t = (0.010) (600 - 0 )

t = 3.33 x 10^-3 sec

d)

Impulse is given as

Impulse = m (v - v_o)

Impulse = (0.010) (600 - 0 )

Impulse = 6 Ns