A 0.30-kg puck, initially at rest on a frictionless horizontal surface, is struck by a 0.20-kg puck that is initially moving along the x-axis with a velocity of 5.2 m/s. After the collision, the 0.20-kg puck has a speed of 3.1 m/s at an angle of θ = 53° to the positive x-axis. (a) Determine the velocity of the 0.30-kg puck after the collision, (b) Find the fraction of kinetic energy lost in the collision.

Answer :

The fraction of kinetic energy lost in the collision is 13.5%.

Explanation :

Given that,

Mass of stationary puck = 0.30 kg

Mass of moving puck = 0.20 kg

Speed = 5.2 m/s

Speed = 3.1 m/s

Angle = 53°

(a). We need to calculate the velocity

Using Conservation of momentum

Along x ,

Put the value into the formula

Along y,

Put the value into the formula

We need to calculate the velocity of the 0.30 kg  puck after the collision

Using formula of velocity

Put the value into the formula

(b). We need to calculate the kinetic energy lost in the collision

Kinetic energy before collision

Kinetic energy after collision

The ratio of kinetic energy

Kinetic energy lost

Put the value into the formula

Hence, The fraction of kinetic energy lost in the collision is 13.5%.