Question

A 0.015 kg marble moving to the right at 0.225 m/s makes an elastic head-on collision with a 0.030 kg shooter marble moving to the left at 0.180 m/s. After the collision, the smaller marble moves to the left at 0.315 m/s. What is the velocity of the 0.030 kg marble after the collision

Answer 1

Answer:

0.09 m/s to the right

Explanation:

The principle of conservation of linear momentum states that in a system of colliding objects, the total momentum before collision is equal to the total momentum after collision, provided there is no external force.

The total momentum, in this question, is the sum of the momentum of the the two marbles. We assume velocity to the right is positive while to the left is negative. Thus, total initial momentum is

$P_i = 0.015\times0.225+ 0.030 \times(-0.180) = 0.002025$

After collision, the first marble goes left. Let the velocity of the other marble be v. Then we have

$P_f = 0.015\times(-0.315) + 0.030v = 0.030v - 0.004725$

Equating both momenta,

$P_i = P_f$

$0.002025 = 0.030v - 0.004725$

$v = 0.09 \text{ m/s}$

Hence, the larger goes right with a velocity of 0.09 m/s (since it has a positive sign).