Question

A rifle resting against a cushion fires a bullet as shown. Figure (a) below shows the event before firing the bullet. After firing the bullet, the rifle compresses the cushion by $25\text{mm}$ and comes to rest.

• A. The change in momentum of the bullet is $14.7\text{kgm/s}$.
• B. The recoil speed of the rifle immediately after firing $3.5\text{m/s}$.
• C. The average force exerted by the cushion in stopping the rifle is $1.03\text{kN}$.
• D. Work done by the rifle on the bullet is $25.73\text{J}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A The change in momentum of the bullet is $14.7\text{kgm/s}$.
B The recoil speed of the rifle immediately after firing $3.5\text{m/s}$.
C The average force exerted by the cushion in stopping the rifle is $1.03\text{kN}$.
D Work done by the rifle on the bullet is $25.73\text{J}$

Change in momentum,
$\Delta \overrightarrow{p_b}=m\Delta \overrightarrow{v_b}=0.0525(280-0)=14.7\text{kgm/s}$
$4.20\times v_r=14.7$
$\Rightarrow v_r=3.5\text{m/s}$

Work done by $F_{av}$ = Change in kinetic energy of the rifle.
$F_{av}\times 0.025=\frac{1}{2}\times 4.20\times {3.5}^2=25.73\text{J}$
$F_{av}\approx 1.03\times {10}^3\text{N}$