Two ice skaters stand face-to-face on perfectly frictionless ice
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
Two ice skaters stand face-to-face on perfectly frictionless ice. Skater A has a mass of 60 kg and Skater B has a mass of 40 kg. Initially the pair is at rest with their hands touching so that the line joining their centers of mass is horizontal and isolated from external horizontal forces. After they push off, Skater A moves to the left while Skater B moves to the right.
Answer the following questions about the motion of the system’s center of mass (CM).
(a) Describe qualitatively the horizontal motion of the CM before, during, and immediately after the shove. In your answer, refer explicitly to the presence or absence of external horizontal forces on the two-skater system.
(b) Suppose Skater A’s speed after the shove is observed to be smaller in magnitude than Skater B’s speed. Explain how this observation is consistent with the location of the CM relative to the two skaters.
(c) A stationary observer standing on the shore marks a point on the ice directly beneath the CM at the instant just before the skaters push off. Discuss whether this point remains directly beneath the CM at all later times, and justify your answer without using explicit numerical calculations.