Suppose an Olympic diver who weighs 52.0 kg executes a straight dive from a 10-m platform. At the apex of the dive, the diver is 10.8 m above the surface of the water. (a) What is the potential energy of the diver at the apex of the dive, relative to the surface of the water?

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Identify the formula for gravitational potential energy: \(PE = mgh\), where \(m\) is mass, \(g\) is the acceleration due to gravity, and \(h\) is the height above the reference point.

Determine the mass \(m\) of the diver, which is given as 52.0 kg.

Use the standard acceleration due to gravity \(g = 9.8 \text{ m/s}^2\).

Identify the height \(h\) of the diver above the surface of the water, which is 10.8 m.

Substitute the values of \(m\), \(g\), and \(h\) into the potential energy formula to find the potential energy at the apex of the dive.

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주요 개념

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Potential Energy

Potential energy is the energy stored in an object due to its position in a gravitational field. It is calculated using the formula PE = mgh, where PE is potential energy, m is mass, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height above a reference point, typically the ground or water surface.

Mass

Mass is a measure of the amount of matter in an object, typically expressed in kilograms (kg). In this context, the mass of the diver is crucial for calculating potential energy, as it directly influences the energy stored due to the diver's height above the water.

Height in Gravitational Potential Energy

Height is a critical factor in determining gravitational potential energy. The greater the height of an object above a reference point, the more potential energy it possesses. In this scenario, the height of the diver above the water surface is essential for calculating the potential energy at the apex of the dive.