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Question
An object of mass 1 kg travelling in a straight line with a velocity of 10 ms−1 collides with, and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.
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Solution
Mass of object, m1 = 1 kg
The velocity of an object before the collision, u1 = 10 m s-1
Mass of wooden block, m2 = 5 kg
The velocity of the wooden block before the collision, u2= 0
(i) ∴ Total momentum before the impact = m1 u1 + m2 u2
= 1 × 10 + 5 × 0
= 10 kg ms-1
According to the law of conservation of momentum (as no net external force acts on the system),
Total momentum after the impact = Total momentum before the impact = 10 kg ms-1
(ii) Mass of combined object, M = mass of object + mass of block
= 1 + 5
= 6 kg
Let V = Velocity of the combined object after collision
∴ Momentum of combined object = MV
= (6V) kg ms-1
Now, the momentum of the combined object Total momentum after the impact
i.e., 6V = 10
or V = `10/6`
= 1.67 ms-1
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