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Hugo wanted to see the view from the top floor of a skyscraper. He got in an elevator on the first floor of the building and rode all the way to the top. He got off the elevator and walked across a flat floor to the edge of a nearby balcony, where he could see for miles around. When was the least gravitational potential energy stored between Hugo and Earth? Assume that Hugo's mass did not change. when he was about to ride the elevator to the top floor when he reached the top floor in the elevator when he was standing on the edge of the balcony

Ask by Lynch Johnston. in the United States
Jan 25,2025

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The least gravitational potential energy was stored when Hugo was about to ride the elevator to the top floor.

Solution

Gravitational potential energy (GPE) between an object and Earth is given by the formula: \[ \text{GPE} = mgh \] where: - \( m \) is the mass of the object (in this case, Hugo), - \( g \) is the acceleration due to gravity, - \( h \) is the height above a reference point. In this scenario: - **When Hugo is about to ride the elevator**: He is at the lowest height (\( h \)), so his GPE is at its minimum. - **When he reaches the top floor in the elevator**: His height (\( h \)) increases, thus increasing his GPE. - **When he stands on the edge of the balcony**: His height is the same as on the top floor or slightly higher, maintaining or slightly increasing his GPE. Therefore, the **least gravitational potential energy** is stored **when Hugo is at the lowest point**, which is **just before he enters the elevator**. **Answer:** When he was about to ride the elevator to the top floor.

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The least gravitational potential energy was stored when he was about to ride the elevator to the top floor. At this moment, Hugo was at the lowest point of his journey, which means the gravitational potential energy relative to the Earth was at its minimum. As he ascended, this energy increased due to the height gained. When he reached the top floor in the elevator and walked across to the balcony edge, he had maximum gravitational potential energy since height is a crucial factor in calculating this energy. So, Hugo stored the most gravitational potential energy just before he stood on the balcony, taking in that breathtaking view!

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