Question
Read the text about an object in motion. Aaron heard that his new air conditioner was ready to be plcked up in the basement of his apartment building. Aaron brought the air conditioner to his sixth-floor apartment, where he installed it in a high window, Later, he accidentally bumped the air conditioner, and it fell out of the window and onto the street below. When was the most gravitational potential energy stored between the air conditioner and Earth? Assume that the air conditioner's mass did not change. when the air conditioner was ready to be picked up in the basement when the air conditioner was in the window of Aaron's apartment when the air conditioner was about to hit the street
Ask by Hills West. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The air conditioner had the most gravitational potential energy when it was in the window of Aaron's apartment on the sixth floor.
Solution
The most gravitational potential energy (GPE) is stored when an object is at its highest position relative to the Earth. Gravitational potential energy is calculated using the formula:
\[ \text{GPE} = m \times g \times h \]
Where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity,
- \( h \) is the height above the reference point (in this case, the street).
Let's evaluate each scenario:
1. **When the air conditioner was ready to be picked up in the basement:**
- **Height (\( h \))**: Lowest point
- **GPE**: Lowest
2. **When the air conditioner was in the window of Aaron's apartment:**
- **Height (\( h \))**: Highest point (sixth floor)
- **GPE**: Highest
3. **When the air conditioner was about to hit the street:**
- **Height (\( h \))**: Lowest point (just above the street)
- **GPE**: Lowest
**Conclusion:** The air conditioner had the most gravitational potential energy **when it was in the window of Aaron's apartment** on the sixth floor.
**Answer:**
When the air conditioner was in the window of Aaron’s apartment
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Simplify this solution Bonus Knowledge
The most gravitational potential energy was stored when the air conditioner was in the window of Aaron's apartment. At that height, it was positioned at its highest point relative to the ground, maximizing the potential energy due to gravity. The higher the object is from the Earth's surface, the more gravitational potential energy it possesses! Interestingly, as soon as Aaron bumped it and it started to fall, that potential energy began converting into kinetic energy. When it hit the street, all that potential energy transformed into movement, showcasing a thrilling real-world example of physics in action!
