What is the mass of an object that is hanging 12.6 m above the surface of the earth and has a potential energy of 2778.3 J?

Steps to Solve

1. Identify the formula for potential energy

The formula for gravitational potential energy (PE) is given by: $$ PE = mgh $$ where:

• $PE$ is potential energy (in joules)
• $m$ is mass (in kilograms)
• $g$ is the acceleration due to gravity (approximately $9.81 , \text{m/s}^2$)
• $h$ is height (in meters)

2. Substitute known values into the equation

Given:

• $PE = 2778.3 , \text{J}$
• $h = 12.6 , \text{m}$
• $g = 9.81 , \text{m/s}^2$

We can rearrange the formula to solve for mass ($m$): $$ m = \frac{PE}{gh} $$

3. Perform the calculations

Substituting the known values into our rearranged equation: $$ m = \frac{2778.3}{(9.81)(12.6)} $$

4. Calculate the denominator

First, calculate $g \cdot h$: $$ g \cdot h = (9.81)(12.6) = 123.486 , \text{m}^2/\text{s}^2 $$

5. Calculate mass

Now substitute this value back into the equation for mass: $$ m = \frac{2778.3}{123.486} \approx 22.5 , \text{kg} $$