Question

Solve the following examples:

(1) An object of mass 16 kg moves with an acceleration of 3 m/s². Calculate the force acting on it. If the same force is applied to another object of mass 24 kg, what will be the acceleration?

[Ans : 48 N, 2 m/s²]

(2) A bullet of mass 10 g moving with velocity of 1.5 m/s hits a thick wooden plank of mass 90 g. The plank is initially at rest, but when it gets hit by the bullet, the bullet remains in the plank and both move with a certain speed. Calculate the speed with which plank containing the bullet moves?

[Ans : 0.15 m/s]

Answer 1

(1) Mass of the object, m = 16 kg

Acceleration of the object, a = 3 m/s²

So, force on the object, F = ....?

We know, force = massacceleration

⇒ F = 163

⇒ F = 48 N

Second part,

Mass of the object, m’ = 24 kg

Force on the object, F = 48 N

Acceleration of the object, a’ = ….?

⇒ a’ = F/m’

⇒ a’ = 48/24

⇒ a’ = 2m/s²

(2) Mass of a bullet, m = 10 g = 0.01 kg

Speed of bullet, v = 1.5m/s

Mass of wooden plank, M = 90 g = 0.09 kg

Let the speed of plank containing plank be V.

According to the law of conservation of momentum,

Total momentum before collision = Total momentum after collision

⇒ mv +M0 = (M+m)V

⇒ 0.011.5 = (0.09+0.01)V

⇒ 1.5 = 10V

⇒ V = 0.15 m/s