College Physics
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Author: Raymond A. Serway, Chris Vuille
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C7 14.) A woman with a mass of 55 kg climbs a set of stairs that are h = 3 m high. How much gravitational potential energy does she gain?
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![### Problem Statement:
A woman with a mass of 55 kg climbs a set of stairs that are \( h = 3 \, \text{m} \) high. How much gravitational potential energy does she gain?
### Diagram Explanation:
The image shows a series of silhouettes of a woman climbing a staircase. The stairs lead to a height labeled \( h \). An arrow points vertically from the base of the stairs to the top, indicating the vertical height (\( h \)) of 3 meters.
### Gravitational Potential Energy Calculation:
Gravitational potential energy (GPE) is calculated using the formula:
\[ \text{GPE} = m \cdot g \cdot h \]
where:
- \( m = 55 \, \text{kg} \) (mass of the woman)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 3 \, \text{m} \) (height of the stairs)
Substituting the values, we calculate:
\[ \text{GPE} = 55 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m} \]
\[ \text{GPE} = 1617 \, \text{J} \]
Therefore, the woman gains 1617 joules of gravitational potential energy.](https://content.bartleby.com/qna-images/question/960fc787-666a-4e12-903f-c51352ba9685/3317f3a3-39a4-45cc-bd4e-4dbe8448e367/t6vmdmq_processed.jpeg)
Transcribed Image Text:### Problem Statement:
A woman with a mass of 55 kg climbs a set of stairs that are \( h = 3 \, \text{m} \) high. How much gravitational potential energy does she gain?
### Diagram Explanation:
The image shows a series of silhouettes of a woman climbing a staircase. The stairs lead to a height labeled \( h \). An arrow points vertically from the base of the stairs to the top, indicating the vertical height (\( h \)) of 3 meters.
### Gravitational Potential Energy Calculation:
Gravitational potential energy (GPE) is calculated using the formula:
\[ \text{GPE} = m \cdot g \cdot h \]
where:
- \( m = 55 \, \text{kg} \) (mass of the woman)
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 3 \, \text{m} \) (height of the stairs)
Substituting the values, we calculate:
\[ \text{GPE} = 55 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 3 \, \text{m} \]
\[ \text{GPE} = 1617 \, \text{J} \]
Therefore, the woman gains 1617 joules of gravitational potential energy.
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