Question

A 28.5-g object moving to the right at 18.5 cm/s overtakes and collides elastically with a 12.5-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision. (Take the positive direction to be to the right. Indicate the direction with the sign of your answer.)

Answer 1

Velocity of each object is 17.43 cm/s towards the right

Step-by-step explanation:

Momentum = Mass *velocity

Before Collision

Momentum of 28.5-g object moving to the right at 18.5 cm/s = 28.5 * 18.5

= 527.25 gcm/s

Momentum of 12.5-g object moving to the right at 15.0 cm/s = 12.5 * 15.0

= 187.5 gcm/s

Sum of their momentum before collision = 527.25 + 187.5 = 714.75 gcm/s

After collision

Momentum of the bodies = (28.5+12.5)v = 41v

v = common velocity of both objects

According to law of conservation of momentum, the sum of momentum of the bodies before collision is equal to their sum after collision.

41v = 714.75

v = 714.75/41

v = 17.43 cm/s (since their common velocity is positive, the direction will be to the right)

Since both objects move with the same velocity after collision, each object will have the same velocity which is 17.43 cm/s after the collision