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 calculate the gravitational potential energy of Object B when it rests on a shelf 10 m above the ground, we can use the formula:
Gravitational Potential Energy (PE) = mass (m) x acceleration due to gravity (g) x height (h)
First, let's find the gravitational potential energy of Object A:
Given that Object A has a gravitational potential energy of 24 joules when it rests on a shelf 5 m above the ground, we can use the formula:
24 J = mass (m_A) x 9.8 m/s^2 x 5 m
Now, let's find the mass of Object A:
Rearranging the formula to solve for mass (m_A), we have:
mass (m_A) = 24 J / (9.8 m/s^2 x 5 m)
mass (m_A) = 0.49 kg
Since Object B has three times the mass of Object A, the mass of Object B (m_B) is:
mass (m_B) = 3 x mass (m_A)
mass (m_B) = 3 x 0.49 kg
mass (m_B) = 1.47 kg
Now, let's calculate the gravitational potential energy of Object B when it rests on a shelf 10 m above the ground:
Gravitational Potential Energy (PE_B) = mass (m_B) x acceleration due to gravity (g) x height (h)
PE_B = 1.47 kg x 9.8 m/s^2 x 10 m
PE_B = 144.06 J
Therefore, the gravitational potential energy of Object B when it rests on a shelf 10 m above the ground would be approximately 144.06 joules.