A new bought Air conditioning unit weighing 95.2345 lbs and was attached to the window of a four 
story building ranging for about 29.4349 ft. Calculate the Gravitational Potential Energy?

The **gravitational potential energy (GPE)** of an object can be calculated using the formula:

\[
\text{GPE} = mgh
\]

Where:
- \( m \) is the mass of the object in kilograms (kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( h \) is the height in meters (m).

### Step 1: Convert the mass from pounds (lbs) to kilograms (kg).
The conversion factor from pounds to kilograms is:
\[
1 \, \text{lb} = 0.453592 \, \text{kg}
\]
Thus, the mass of the air conditioning unit is:
\[
m = 95.2345 \, \text{lbs} \times 0.453592 \, \text{kg/lb} = 43.2154 \, \text{kg}
\]

### Step 2: Convert the height from feet (ft) to meters (m).
The conversion factor from feet to meters is:
\[
1 \, \text{ft} = 0.3048 \, \text{m}
\]
Thus, the height of the building is:
\[
h = 29.4349 \, \text{ft} \times 0.3048 \, \text{m/ft} = 8.9702 \, \text{m}
\]

### Step 3: Calculate the gravitational potential energy.
Now, applying the formula:
\[
\text{GPE} = 43.2154 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 8.9702 \, \text{m}
\]
\[
\text{GPE} = 3789.76 \, \text{J}
\]

Thus, the **gravitational potential energy** of the air conditioning unit is approximately **3789.76 joules (J)**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does gravitational potential energy depend on mass and height?
2. What happens to the gravitational potential energy if the height is doubled?
3. How would the gravitational potential energy change if the air conditioning unit were on the moon?
4. Can you derive the formula for gravitational potential energy?
5. How does the gravitational potential energy of an object relate to its kinetic energy?

**Tip:** Gravitational potential energy increases linearly with height and mass.

A new bought Air conditioning unit weighing 95.2345 lbs and was attached to the window of a four story building ranging for about 29.4349 ft. Calculate the Gravitational Potential Energy?

Learn how to calculate the gravitational potential energy of a 95.2345 lbs air conditioning unit placed at a height of 29.4349 feet. This problem involves converting units to SI, using the GPE formula, and understanding key concepts of physics. Suitable for students in Grades 9-12.

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