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Difficulty: EasyWork, Energy, and Power

A diver stands completely stationary at the edge of a 10-meter platform above a swimming pool. Which statement best describes the diver's mechanical energy while resting at this highest point?

  1. A
    Kinetic energy is at its maximum value, and gravitational potential energy is zero.
  2. Gravitational potential energy is at its maximum value, and kinetic energy is zero.Answer
  3. C
    Both kinetic energy and gravitational potential energy are at their maximum values simultaneously.
  4. D
    Total mechanical energy is zero because the diver is not currently in motion.

Answer

Gravitational potential energy is at its maximum value, and kinetic energy is zero.
Gravitational potential energy (PE=mghPE = mgh) is directly proportional to height. At the top of the 10-meter platform, elevation is at its peak, making potential energy maximum. Because the diver is stationary (v=0v = 0), kinetic energy (KE=12mv2KE = \frac{1}{2}mv^2) is zero.

Step-by-Step Solution

1
Analyze the diver's state of motion to determine kinetic energy.
The diver is stationary (v=0 m/sv = 0\text{ m/s}), so kinetic energy (KE=12mv2KE = \frac{1}{2}mv^2) is 0 J0\text{ J}.
Kinetic energy is the energy of motion and requires a non-zero velocity.
2
Analyze the diver's position to determine gravitational potential energy.
The diver is at the maximum height (h=10 mh = 10\text{ m}), so gravitational potential energy (PE=mghPE = mgh) is at its maximum.
Gravitational potential energy is directly proportional to elevation above the reference level.
3
Combine the energy states to describe total mechanical energy.
All mechanical energy exists as gravitational potential energy, with zero kinetic energy.
Total mechanical energy is the sum of kinetic and potential energies.

Key Concept

Gravitational potential energy depends on height, whereas kinetic energy depends on motion.
Estimated Time:45s
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Topics

Work, Energy, and Power

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