Object A has a gravitational potential energy of 24 joules when it rests on a shelf 5 m above the ground. Object B has a mass that is three times the mass of Object A. What would be the gravitational potential energy of object B when it rests on a shelf 10 m above the ground?

To solve this problem, we need to understand the formula for gravitational potential energy, which is:

Potential Energy (PE) = mass (m) * gravity (g) * height (h)

Given that the gravitational potential energy of Object A is 24 joules when it is 5 m above the ground, we can find its mass by rearranging the formula:

mass (m) = PE / (g * h)

Assuming the acceleration due to gravity (g) is approximately 9.8 m/s² (standard on Earth), we can substitute the known values into the equation:

mass of A = 24 joules / (9.8 m/s² * 5 m) = 0.49 kg

Since the mass of Object B is three times the mass of Object A, the mass of B is:

mass of B = 3 * mass of A = 3 * 0.49 kg = 1.47 kg

Now, we can find the gravitational potential energy of Object B when it is 10 m above the ground by substituting the values back into the original formula:

PE of B = mass of B * g * height of B = 1.47 kg * 9.8 m/s² * 10 m = 144.06 joules

So, the gravitational potential energy of Object B when it rests on a shelf 10 m above the ground would be approximately 144.06 joules.