A skydiver is subject to two forces: gravity and air resistance. Falling vertically, she reaches a constant terminal speed at some time after jumping from the plane. Since she is moving at a constant velocity from that time until her chute opens, we conclude from the work kinetic energy theorem that, over that time interval,
A. The work done by gravity equals the negative of the work done by the air resistance.
B. The work done by gravity is zero.
C. The work done by gravity equals the work done by air resistance.
D. The work done by air resistance is 0.
E. Her kinetic energy increases.
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A. No net work is done when she is at the terminal velocity
Well, isn't this a "terminal" velocity question? Let me explain it to you in a way that hopefully won't cause you to have a "plummet" in understanding.
When a skydiver falls vertically, two forces are at play: gravity pulling them down and air resistance pushing against their motion. As the skydiver accelerates, the force of gravity is greater than the force of air resistance. But as they continue to fall and gather speed, air resistance increases until it matches the force of gravity.
Now, when the skydiver reaches terminal velocity, their speed remains constant because the forces of gravity and air resistance balance out. Since velocity is constant, we can conclude that the net work done on the skydiver is zero. This means that the work done by gravity is equal to the negative work done by air resistance.
So, the answer is A. The work done by gravity equals the negative of the work done by air resistance. Just like a clown on a unicycle, the forces have a perfectly balanced act going on.
According to the work-kinetic energy theorem, the work done on an object is equal to the change in its kinetic energy. In this scenario, the skydiver is moving at a constant velocity, which means her kinetic energy is not changing. Therefore, the work done on the skydiver by both gravity and air resistance must be equal to zero.
Option B: The work done by gravity is zero.
This is the correct answer since the skydiver is not changing her kinetic energy, and the work done by gravity is zero.
To determine the correct answer, let's analyze the forces and work involved in the situation.
When the skydiver jumps from the plane, the only two forces acting on her are gravity and air resistance. Initially, as she falls, her speed increases due to the downward force of gravity. However, as she gains speed, the upward force of air resistance also increases.
Eventually, the force of air resistance becomes equal and opposite to the force of gravity, balancing each other out. At this point, the net force acting on the skydiver is zero, and she reaches a constant velocity known as the terminal speed.
According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. In this case, once the skydiver reaches her terminal velocity, her kinetic energy remains constant until her parachute opens.
Now let's evaluate the options given:
A. The work done by gravity equals the negative of the work done by air resistance.
This option is not accurate because the work done by gravity and the work done by air resistance are not equal in magnitude. The work done by air resistance is the negative of the work done by gravity, but their magnitudes are not necessarily the same.
B. The work done by gravity is zero.
This option is also incorrect because gravity is doing work while the skydiver is falling. The work done by gravity is responsible for the skydiver's increase in gravitational potential energy as she descends.
C. The work done by gravity equals the work done by air resistance.
This option is not true since the magnitudes of the work done by gravity and air resistance are not equal. The work done by air resistance helps to counteract the work done by gravity, but they are not equal.
D. The work done by air resistance is 0.
This option is false because air resistance is actively doing work on the skydiver as she falls. It helps balance out the force of gravity.
E. Her kinetic energy increases.
This option is not correct because once the skydiver reaches terminal velocity, her kinetic energy remains constant until her parachute opens. There is no increase in kinetic energy.
Based on the analysis above, we can conclude that none of the given options are correct. The correct answer is not provided in the options.