Question

A bullet of mass 20gm strikes a wooden plank with a velocity of 60ms^-1 and emerges out in 0.01 seconds with a velocity of 30ms^-1. Calculate 

(i) the work done by the bullet and 

(ii) the thickness of the plank.

Answer 1

Given m = 20 × 10^-3kg

u = 60ms^-1 & v = 30 ms^-1

work done = decrease in kinetic energy

= \(\frac {1}{2}\)m (u² – v²)

= \(\frac {1}{2}\)× 0.02 (60² – 30²)

= 27J

From, v = u + at

30 = 60 + a (0.01)

a =\(\frac {-30}{0.01}\) = – 3000 ms^-2

Retarding force, F = ma

= 0.02 × 3000 = 60N

work done, W = F × S

27 = 60 × S

∴ Thickness of the plank, S = \(\frac {27}{60}\)

= 0.45 m.