Answer to Question #242909 in Physics for rshiii

Question

12. Two figure skaters, one weighing 625 N and the other 725 N, push off against each other on frictionless ice. (a) If the heavier skater travels at 1.50 m/s, how fast will the lighter one travel? (b) How much kinetic energy is “created” during the skaters’ maneuver, and where does this energy come from?

Answer 1

(a) Apply momentum conservation:

$$0=m_1v_1+m_2v_2,\\\space\\ v_2=-v_1\frac{m_1}{m_2}=-1.75\text{ m/s}.$$

The '-' means that the other one moves in the opposite direction.

(b) The energy is

$$E=\frac12(m_1v_1+m_2v_2)=180\text{ J}.$$

This energy comes from their muscles, which receive the energy from the chemical reactions in the body.