Question

. A 0.015 kg marble sliding to the right at 22.5 cm/s on a frictionless surface makes an elastic head-on collision with a 0.015 kg marble moving to the left at 18.0 cm/s. After the collision, the first marble moves to the left at 18.0 cm/s. a. Find the velocity of the second marble after the collision. b. Verify your answer by calculating the total kinetic energy before and after the collision.

Answer 1

Concept : we apply momentum conservation principle in one dimension for solution as shown below :***************************************************************************************************
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Concept: we apply momentum conservation principle in one dimension for solution as shown below: From momentum conservation momentum before collision = momentum after collision (0.015 kg) (22.5 cm/s) - (0.015 kg) (18 cm/s) = -(0.015 kg) (18 cm/s) + (0.015 kg) V or, V = 22.5 cm/s - to the right KE_before = 1/2 (0.015 kg) (0.225 m/s)^2 + 1/2 (0.015 kg) (-0.18 cm/s)^2 = 6.227 J KE_after = 1/2 (0.015 kg) (-0.18 m/s)^2 + 1/2 (0.015 kg) (0.225 m/s)^2 = 6.227 J so, KE_before = KE_after So, it's an elastic collision.