An object has a gravitational potential energy of 24 joules when it rests on a shelf 3 m above the ground. What would be its gravitational potential energy when it is lowered to a shelf 1 m above the ground?
To calculate the change in gravitational potential energy, we need to subtract the initial gravitational potential energy from the final gravitational potential energy.
Given that the initial gravitational potential energy is 24 joules when the object is on a shelf 3 m above the ground, we can use the formula for gravitational potential energy:
Gravitational Potential Energy = mgh
where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and h is the height.
Let's assume the mass of the object is constant for simplicity. So, we can ignore it in our calculations and focus on the change in height.
Initial gravitational potential energy when the object is on a shelf 3 m above the ground:
Potential Energy_initial = m * g * h_initial = 24 joules
Final gravitational potential energy when the object is on a shelf 1 m above the ground:
Potential Energy_final = m * g * h_final
To find the change in gravitational potential energy, we can subtract the initial potential energy from the final potential energy:
Change in Potential Energy = Potential Energy_final - Potential Energy_initial
Change in Potential Energy = (m * g * h_final) - (m * g * h_initial)
As we can see, the mass of the object and the acceleration due to gravity appear on both sides of the equation, so we can cancel them out:
Change in Potential Energy = g * (h_final - h_initial)
Substituting the given values:
Change in Potential Energy = 9.8 m/s^2 * (1 m - 3 m)
Change in Potential Energy = -19.6 joules
Therefore, the gravitational potential energy would be -19.6 joules when the object is lowered to a shelf 1 m above the ground. The negative sign indicates that the object has lost potential energy as it has moved downward.
one-third of 24 joules
PE=weight*height