QuestionJune 22, 2025

A stone sphere of radius 7.00 m rests in a flat field. Relative to the ground, what is the gravitational potential energy of a 90.0-kg person sitting on the very top of the sphere? 1.23times 10^4J 7.76times 10^4J 3.88times 10^4J

A stone sphere of radius 7.00 m rests in a flat field. Relative to the ground, what is the gravitational potential energy of a 90.0-kg person sitting on the very top of the sphere? 1.23times 10^4J 7.76times 10^4J 3.88times 10^4J
A stone sphere of radius 7.00 m rests in a flat field. Relative to the ground, what is the gravitational potential energy of a 90.0-kg person sitting on the very top of the sphere? 1.23times 10^4J 7.76times 10^4J 3.88times 10^4J

Solution
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Answer

6.17\times 10^{3}J Explanation 1. Identify the height The height of the person above the ground is equal to the radius of the sphere, which is 7.00 m. 2. Use gravitational potential energy formula **Gravitational Potential Energy (U) = mgh**, where \(m = 90.0 \, \text{kg}\), \(g = 9.81 \, \text{m/s}^2\), and \(h = 7.00 \, \text{m}\). 3. Calculate the gravitational potential energy \( U = 90.0 \times 9.81 \times 7.00 = 6174.3 \, \text{J} \).

Explanation

1. Identify the height<br /> The height of the person above the ground is equal to the radius of the sphere, which is 7.00 m.<br />2. Use gravitational potential energy formula<br /> **Gravitational Potential Energy (U) = mgh**, where \(m = 90.0 \, \text{kg}\), \(g = 9.81 \, \text{m/s}^2\), and \(h = 7.00 \, \text{m}\).<br />3. Calculate the gravitational potential energy<br /> \( U = 90.0 \times 9.81 \times 7.00 = 6174.3 \, \text{J} \).
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