A photograph of the two-dimensional elastic collision of two particles shows a particle of mass m₁approaching a stationary particle of mass m₂. As a result of their interaction, the incident particle moves away along a line that makes an angle of 30° with its original path, and the other particle moves away along a line that makes an angle of 30° to the other side of the original path of the incident particle. What is the ratio of the masses, m₁/m₂? A) 0.5 B) 1 C) 2 D) 3 E) 4

Question

Quizplus · Accepted Answer

Momentum is conserved in both the x and y directions. In the x direction, the initial momentum is m1vi, and the final momentum is m1v1cos30° + m2v2cos30°. In the y direction, the initial momentum is 0, and the final momentum is m1v1sin30° + m2v2sin30°. Since the collision is elastic, the total kinetic energy is conserved, so 1/2m1v1^2 = 1/2m1v1^2cos^230° + 1/2m2v2^2cos^230° + 1/2m1v1^2sin^230° + 1/2m2v2^2sin^230°. Solving for m1/m2, we get m1/m2 = 2.

A Photograph of the Two-Dimensional Elastic Collision of Two Particles