A 20 g bullet pierces through a plate of mass M1 = 1 kg and then comes to rest inside a second plate of mass M2 = 2.98 kg (refer figure). It is found that the two plates, initially at rest, now move with equal velocity v. Find the velocity of the bullet (in m/s) when it is between M1 and M2. Given that it entered M1 with 100 m/s.

Engineering

Physics

Newtons Second Law of Motion

Collision

Momentum and Energy Conservation for System of Particles

Question

A 20 g bullet pierces through a plate of mass M₁ = 1 kg and then comes to rest inside a second plate of mass M₂ = 2.98 kg (refer figure). It is found that the two plates, initially at rest, now move with equal velocity v. Find the velocity of the bullet (in m/s) when it is between M₁ and M₂. Given that it entered M₁ with 100 m/s.

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From the principle of conservation of linear momentum we have
                   mu = M₁v + mv’
and               mv’ = (m + M₂)v
or               20u = 1000v + 20v’
and               20v’ = (20 + 2980)v
or                   u = 50v + v’       ...(i)
and                   v’ = 150 v       ...(ii)
From (i) and (ii), we get   3u = v’ + 3v’ = 4v’   or   v’ = 3u/4 = 75