Question

two ice skaters push off from each other. if one skater is much heavier than the other, how will their movements compare, and why?
both skaters move at the same speed in opposite directions.
only the lighter skater moves.
the heavier skater moves faster because of greater mass.
the lighter skater moves faster because the forces are equal but the masses are different.

Explanation:

According to Newton's third law, when the two skaters push off each other, the forces they exert on each other are equal in magnitude and opposite in direction. Using Newton's second law \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration), for the same force \(F\), if \(m_1>m_2\) (where \(m_1\) is the mass of the heavier skater and \(m_2\) is the mass of the lighter skater), then \(a_1=\frac{F}{m_1}\) and \(a_2 = \frac{F}{m_2}\), so \(a_2>a_1\). Velocity \(v = at\) (assuming the time of the force - application \(t\) is the same for both skaters). So the lighter skater will have a greater velocity (move faster) because for the same force (action - reaction pair), a smaller mass results in a larger acceleration.

Answer:

The lighter skater moves faster because the forces are equal but the masses are different.