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?
*trapeze artist
*the person with more mass
*assistant
(b) Who, if either, strikes the net with a greater speed?
*trapeze artist
*assistant
*neither
(a) Gravity does the greatest amount of work on the person with more mass.
To explain this, we need to understand that work is defined as the transfer of energy. In this case, the work done by gravity is equal to the change in gravitational potential energy.
For both the trapeze artist and the assistant, the starting point is the same - they are both at rest and at the same height above the ground. As they fall, their gravitational potential energy decreases and is converted into kinetic energy.
However, the trapeze artist is likely to have less mass than the assistant since trapeze artists need to be light to perform their acrobatic moves. Therefore, the assistant would have more mass.
Since work is directly proportional to the mass, when both the trapeze artist and the assistant fall freely, gravity does more work on the assistant due to their larger mass.
(b) Both the trapeze artist and the assistant will strike the net with the same speed.
To explain this, we need to consider that both the trapeze artist and the assistant start from the same height above the ground and experience free fall to the net.
When falling freely, neglecting air resistance and assuming the same height, all objects will fall at the same acceleration, which is the acceleration due to gravity. This means that both the trapeze artist and the assistant will accelerate at the same rate as they fall, and their speed will increase uniformly.
Therefore, at the moment they hit the net, both the trapeze artist and the assistant will have the same speed.