Final answer:
The increase in gravitational potential energy when the height of an object is doubled from h to 2h is mgh, where m is the mass of the object and g is the acceleration due to gravity.
Step-by-step explanation:
The student is asking about the increase in gravitational potential energy (APEg) when an object's height above Earth's surface is doubled. The formula APEg = mgh helps calculate the change in potential energy due to a change in height (h), where m is the mass of the object and g is the acceleration due to gravity. Initially, the object is at height h and has a certain potential energy. When the height is increased to 2h, we calculate the new potential energy and then find the difference.
At height h, the potential energy is mgh. At height 2h, the potential energy is mg(2h) = 2mgh. To find the increase in potential energy, we subtract the initial potential energy from the final potential energy:
\(\Delta APEg = 2mgh - mgh = mgh\)
Therefore, the increase in potential energy when an object's height is doubled from h to 2h is equal to the object's initial potential energy at height h, which is mgh.