A trapeze artist, starting from rest, swings downward on the bar, lets go at the bottom of the swing, and falls freely to the net. An assistant, standing on the same platform as the trapeze artist, jumps from rest straight downward. Friction and air resistance are negligible.
(a) On which person, if either, does gravity do the greatest amount of work?
*the person with more mass
*trapeze artist
*assistant
Explain
(b) Who, if either, strikes the net with a greater speed?
assistant
trapeze artist
neither
(a) Gravity does the greatest amount of work on the person with more mass.
To understand why, we need to consider the concept of work. Work is defined as the product of force and displacement along the direction of the force. In this case, the force of gravity is acting vertically downwards on both the trapeze artist and the assistant.
The work done by gravity can be calculated using the formula:
Work = force x displacement x cos(theta)
Since the force of gravity is constant and perpendicular to the displacement, the angle (theta) between force and displacement is 0 degrees, which means cos(theta) = 1. Therefore, the work done by gravity is directly proportional to the vertical displacement.
Both the trapeze artist and the assistant start from rest and fall freely to the net, meaning they have the same vertical displacement. However, in this scenario, we are told that the person with more mass experiences a greater amount of work done by gravity. This suggests that the trapeze artist has more mass than the assistant.
(b) Neither the assistant nor the trapeze artist strikes the net with a greater speed.
According to the law of conservation of energy, the total mechanical energy of a system remains constant if no external forces are acting on it. In this case, friction and air resistance are negligible, meaning there are no significant external forces.
Both the trapeze artist and the assistant start from rest, so their initial gravitational potential energy is the same. As they fall freely, this potential energy is converted entirely into kinetic energy. Since their initial potential energy is the same and there are no external forces, both the trapeze artist and the assistant will reach the net with the same speed.