an object whose mass is 43 kg is hanging on a thin wire. the object has a gravitational potential energy of 3160.5 joules how high is the object above the ground show your work

To find the height at which the object is located above the ground, we can use the formula for gravitational potential energy:

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

Where:
- \( U \) is the gravitational potential energy (3160.5 Joules),
- \( m \) is the mass of the object (43 kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \) on Earth),
- \( h \) is the height above the ground.

We can rearrange the formula to solve for height \( h \):

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

Now, substitute the values:

\[
h = \frac{3160.5 \, \text{J}}{43 \, \text{kg} \times 9.8 \, \text{m/s}^2}
\]

\[
h = \frac{3160.5 \, \text{J}}{421.4 \, \text{kg} \cdot \text{m/s}^2}
\]

\[
h \approx 7.5 \, \text{m}
\]

So, the object is approximately 7.5 meters above the ground.

Would you like more details or have any questions?

Here are some related questions:
1. What happens to the potential energy if the height is doubled?
2. How would the height change if the mass were doubled but the potential energy stayed the same?
3. What is the potential energy of the object if it were at a height of 10 meters?
4. How does gravitational potential energy vary with changes in gravitational acceleration?
5. If the object were on a different planet with twice the gravity, what would its potential energy be at the same height?

**Tip:** Gravitational potential energy depends directly on the height and mass, meaning if either increases, the potential energy will increase proportionally.

Learn how to calculate gravitational potential energy when an object with a mass of 43 kg is hanging 7.5 meters above the ground. Understand the formula U = m * g * h and its application in physics problems. Suitable for high school students studying physics.

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