Question

A bullet of mass 6.45 g is fired from a 66.0 cm-long rifle barrel at 237 m/s. The mass of the rifle is 4.50 kg. Determine the acceleration of the bullet as well as the recoil acceleration of the rifle.

Answer 1

Given, the mass of the bullet,

m= 6.45 gm = 0.00645 kg

Also, distance S covered by the bullet

S= 66 cm = 0.66 m

Initially, both the bullet and the rifle were at rest. Hence initial velocity u of the bullet would be

u = 0

Now using the eqn of motion given by

This is exactly the same time took by rifle to accelerate.

Now, by applying law of conservation of momentum, the total momentum before and after firing the shot should be constant.

Initially both the bullet and the rifle were at rest. However, after firing bullet acquired velocity v and rife acquired V.

Hence we can write

mv + MV = 0

Where M is the mass of rifle and m is the mass of bullet.

i.e MV = -mv

Or V = -mv/M

We know the values of m, v and M.

i.e m = 0.00645 kg, M = 4.50 kg and v = 237 m/s

Hence, we can calculate recoil velocity of rifle i.e V

The negative sign indicates that the recoil velocity is in a direction opposite to which the bullet is fired.

In magnitude, V = 0.00645*237/4.50

= 0.3397 m/s

Now in order to calculate the value of acceleration of rifle, we discussed earlier that rifle would take same amount of time as the bullet to accelerate.

Now, acceleration A = change in velocity of rifle/time

= final velocity -initial velocity/t

= V - 0/t

i.e A = V/t

= 0.3397/0.0055

= 61.76 m/s^{​​​​​​2}