Question

An object of mass 1 kg travelling in a straight line with a velocity of 10 m s–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.

Answer 1

Mass of the object, m1 = 1 kg
The velocity of the object before the collision, v1 = 10 m/s
Mass of the stationary wooden block, m2 = 5 kg
The velocity of the wooden block before the collision, v2 = 0 m/s
∴ Total momentum before collision = m1 v1 + m2 v2 = 1 (10) + 5 (0) = 10 kg m s-1
It is given that after the collision, the object and the wooden block stick together.
The total mass of the combined system = m1 + m2
The 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) v1
=(10) + 5 (0)
= (1 + 5)v
= v = $\frac{10}{6}$
= $\frac{5}{3}$ m/s
The total momentum after collision = 10 and the velocity of a combined object is $\frac{5}{3}$ m/s.