Question

1. what is the mass of an object that is hanging 12.6m above the surface of the earth and has a gravitational potential energy of 2778.3j? 11. an object has a gravitational potential energy that is 833 j. its height above ground is 4.25 m. what is its mass?

Explanation:

Step1: Identify the formula

The formula for gravitational potential energy is \(U = mgh\), where \(U\) is gravitational potential energy, \(m\) is mass, \(g\) is acceleration due to gravity (\(g = 9.8\ m/s^{2}\)), and \(h\) is height.

Step2: Solve for mass \(m\)

Rearrange the formula to \(m=\frac{U}{gh}\).
For problem 10:
Substitute \(U = 2778.3\ J\), \(g = 9.8\ m/s^{2}\), and \(h = 12.6\ m\) into the formula:
\(m=\frac{2778.3}{9.8\times12.6}\)
\(m=\frac{2778.3}{123.48}\)
\(m = 22.5\ kg\)
For problem 11:
Substitute \(U = 833\ J\), \(g = 9.8\ m/s^{2}\), and \(h = 4.25\ m\) into the formula:
\(m=\frac{833}{9.8\times4.25}\)
\(m=\frac{833}{41.65}\)
\(m = 20\ kg\)

Answer:

1. \(22.5\ kg\)
2. \(20\ kg\)