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Question 15
An object of mass 1 kg travelling in a straight line with a velocity of 10 ms1 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 the object, m1 = 1 kg
Velocity of the object before collision, v1=10 ms1
Mass of the stationary wooden block, m2 = 5 kg
Velocity of the wooden block before collision, v2 = 0
Total momentum before collision
=m1v1+m2v2
=1(10)+5(0)=10 kgms1
It is given that after collision, the object and the wooden block stick together.
Total mass of the combined system =m1+m2
Velocity of the combined object = v
According to the law of conservation of momentum:
Total momentum before collision = Total momentum after collision
m1v1+m2v2=(m1+m2)v
1 (10) + 5 (0) = (1 + 5) v
v = 106 = 53 ms1
The total momentum after collision is also 10 kgms1
Total momentum just before the impact =10 kgms1
Total momentum just after the impact =(m1+m2)v=6×53=10 kgms1
Hence, velocity of the combined object after collision = 53 ms1

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