Question

1. a marble is on a table 2.4 m above the ground. what is the mass of the marble if it has a gravitational potential energy of 568 j.

Explanation:

Step1: Recall the gravitational potential energy formula

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

Step2: Solve for mass \(m\)

Rearrange the formula \(U = mgh\) to solve for \(m\). We get \(m=\frac{U}{gh}\).
Substitute \(U = 568\space J\), \(g = 9.8\space m/s^{2}\), and \(h = 2.4\space m\) into the formula:

$$m=\frac{568}{9.8\times2.4}$$

First, calculate \(9.8\times2.4 = 23.52\).
Then, \(m=\frac{568}{23.52}\approx24.15\space kg\)

Answer:

The mass of the marble is approximately \(24.15\space kg\)