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Chapter 5: Problem 10

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 a 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 is zero. b) the work done by air resistance is zero. c) the work done by gravity equals the negative of the work done by air resistance. d) the work done by gravity equals the work done by air resistance. e) her kinetic energy increases.

Short Answer

Expert verified
Answer: The work done by gravity equals the negative of the work done by air resistance when the skydiver reaches terminal speed.

Step by step solution

01

Understand the Work-Kinetic Energy Theorem

The work-kinetic energy theorem states that the work done on an object is equal to the change in its kinetic energy. In mathematical terms: W = ΔK, where W is the work done, and ΔK is the change in kinetic energy.
02

Analyze the Terminal Speed Situation

When the skydiver reaches terminal speed, she is no longer accelerating, and her velocity remains constant. This means that the net force acting on her is zero, as F_net = ma and a = 0 at this point. Two forces acting on her are gravity (F_gravity = m * g) and air resistance (F_resistance). Since her net force is zero, F_gravity = F_resistance.
03

Evaluate Statement a)

Statement a) says that the work done by gravity is zero. However, the force due to gravity is acting on the skydiver and pulling her downwards, so the work done by gravity is not zero. Thus, statement a) is incorrect.
04

Evaluate Statement b)

Statement b) says that the work done by air resistance is zero. However, just like the force due to gravity, the force due to air resistance is acting on the skydiver, opposing her motion. Thus, the work done by air resistance is not zero. Therefore, statement b) is incorrect.
05

Evaluate Statement c)

Statement c) says that the work done by gravity equals the negative of the work done by air resistance. This statement indicates that the forces are acting in opposite directions and have equal magnitudes. Additionally, since the net work done on the skydiver equals the change in her kinetic energy (W = ΔK), and her kinetic energy remains constant (as her speed is constant), the net work done is zero. Therefore, statement c) is correct.
06

Conclude the Solution

The correct relationship between the work done by gravity and air resistance when the skydiver reaches terminal speed is given by statement c), which states that the work done by gravity equals the negative of the work done by air resistance.

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