An object of mass 2 kg travelling in a straight line with a velocity of 10 ms–1 collides with and sticks to a stationary object of mass 6 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. 1
Answers
Explanation:
Mass of the object, m1 = 1 kg
Velocity of the object before collision, v1 = 10 m/s
Mass of the stationary wooden block, m2 = 5 kg
Velocity of the wooden block before collision, v2 = 0 m/s
ˆ´ Total momentum before collision = m1 v1 + m2 v2
= 1 (10) + 5 (0) = 10 kg m sˆ’1
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
m1 v1 + m2 v2 = (m1 + m2) v
1 (10) + 5 (0) = (1 + 5) v
v = 10 / 6
= 5 / 3
The total momentum after collision is also 10 kg m/s.
Total momentum just before the impact = 10 kg m sˆ’1
Total momentum just after the impact = (m1 + m2) v = 6 — 5 / 3 = 10 kg ms-1
Hence, velocity of the combined object after collision = 5 / 3 ms-1