A 0.015-kg marble moving to the right at 0.40 m/s has a head-on, elastic collision with a 0.045-kg marble sitting at rest on a smooth, level surface. Which of the following are the correct magnitudes and directions of the velocities of the two marbles after the collision? 0.015 kg marble 0.045 kg marble
A)0.15 m/s, left 0.25 m/s, right
B)0.10 m/s, right 0.30 m/s, right
C)zero m/s 0.25 m/s, right
D)0.20 m/s, left 0.20 m/s, right
E)0.40 m/s, left zero m/s

Question

Quizplus · Accepted Answer

Conservation of momentum tells us that the total momentum before and after the collision must be the same. 
Initial momentum = (0.015 kg)(0.4 m/s) = 0.006 kg*m/s to the right
Final momentum = (0.015 kg)v1 + (0.045 kg)v2
Since the second marble was at rest initially, we know that its final velocity must be to the right. 
Using conservation of momentum: 
0.006 kg*m/s = (0.015 kg)v1 + (0.045 kg)v2 
We also have conservation of kinetic energy since the collision is elastic: 
Initial kinetic energy = 1/2(0.015 kg)(0.4 m/s)² = 0.0012 J
Final kinetic energy = 1/2(0.015 kg)v1² + 1/2(0.045 kg)v2²
Using conservation of kinetic energy: 
0.0012 J = 1/2(0.015 kg)v1² + 1/2(0.045 kg)v2² 
Solving these two equations simultaneously, we get v1 = -0.20 m/s and v2 = 0.20 m/s to the right. Therefore, the correct answer is D.

A 0015-Kg Marble Moving to the Right at 0