Question

A bullet of mass 50 g moving with an initial velocity of 100 m $s^{-1}$ strikes a wooden block and comes to rest after penetrating a distance 2 cm in it. Calculate
(i) initial momentum of the bullet,
(ii) final momentum of the bullet,
(iii) retardation caused by the wooden block, and
(iv) resistive force exerted by the wooden block

Answer 1

Mass, m = 50 gm = 0.05 kg.
Initial velocity, u = 100 m/s.
Final velocity, v = 0.
Distance, s = 2cm = 0.02 m.

(i) Initial momentum = mu = (0.05) (100) = 5 kg m/s

(ii) Final momentum = mv = (0.05) (0) = 0 kg m/s

(iii) Acceleration, a = (v² – u²)/2s
Or, a = (0² – 100²)/ 2(0.02)
Or, a = – 2.5 x 10⁵ ms^-2
Therefore, retardation is 2.5 x 10⁵ ms^-2

(iv) Force, F = ma
Or, F = (0.05 kg) (2.5 x 10⁵ ms^-2)
Or, F = 12500 N