what is the mass of an object that is hanging  12.6 meters above the surface of the earth and has a gravitational potential energy of 2778.3j

To find the mass of the object, we can use the gravitational potential energy formula:

\[
\text{Potential Energy} (U) = m \cdot g \cdot h
\]

Where:
- \( U \) is the gravitational potential energy (2778.3 Joules),
- \( m \) is the mass of the object (which we need to find),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \) on Earth),
- \( h \) is the height above the ground (12.6 meters).

Rearrange the formula to solve for mass \( m \):

\[
m = \frac{U}{g \cdot h}
\]

Now, substitute the given values:

\[
m = \frac{2778.3 \, \text{J}}{9.8 \, \text{m/s}^2 \times 12.6 \, \text{m}}
\]

\[
m = \frac{2778.3 \, \text{J}}{123.48 \, \text{m}^2/\text{s}^2}
\]

\[
m \approx 22.5 \, \text{kg}
\]

So, the mass of the object is approximately 22.5 kilograms.

Would you like more details or have any questions?

Here are some related questions:
1. How would the mass change if the height were reduced by half?
2. What would the potential energy be if the mass were doubled at the same height?
3. How high would a 30 kg object need to be to have the same potential energy?
4. If the object were on the Moon, where gravity is weaker, what would its mass be for the same potential energy?
5. How does the potential energy change if the mass and height are both doubled?

**Tip:** When dealing with gravitational potential energy, it's helpful to remember that mass and height are directly proportional to the energy stored. If either increases while the other stays constant, the potential energy increases accordingly.

Learn how to calculate the mass of an object hanging 12.6 meters above Earth's surface from its gravitational potential energy of 2778.3 Joules. Step-by-step solution using gravitational potential energy formula. Suitable for high school physics students.

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