Question

Two ice skaters, paula and ricardo, push off from each other. ricardo weighs more than paula. part a which skater, if either, has the greater momentum after the push-off? which skater, if either, has the greater momentum after the push-off? paula has the greater momentum. ricardo has the greater momentum. both skaters have momentums of equal magnitude. submitmy answersgive up part b which skater, if either, has the greater speed after the push-off? which skater, if either, has the greater speed after the push-off? paula has the greater speed. ricardo has the greater speed. both skaters have equal speeds.

Answer 1

Apply the law of conservation of momentum for this situation. The law states that the momentum of a system is constant (in absence of external forces acting on it).

The 'system' in this case are the two skaters. There is no external force on the skaters. Suppose the skaters are initially standing still. The momentum in the system is 0. This value will need to remain constant, even after the mutual push (which is a set of forces from inside the system). So we know that

(total momentum before) = (total momentum after)

Indexing the masses and velocities by the first letter of the skaters' names:

$0 = m_P\vec v_P+m_R\vec v_R\\m_P\vec v_P = m_R(-\vec v_R)$

From the last row, you can see that the skaters will have momentum of same magnitude but opposite direction, after the push off. That answers the first question: neither will have a greater momentum (both will have one of same magnitude).

Since Ricardo is heavier, from the above equality it follows that

$m_R>m_P\implies|\vec v_R|$

In words, Paula has the greater speed, after the push-off.