When lifting a load twice as high in half the time, what happens to the potential energy?

When a load is lifted, the potential energy gained by the load is directly related to the height it is raised and the force acting on it, which is equal to the weight of the load. The potential energy (PE) can be calculated using the formula:

[ PE = mgh ]

where ( m ) is the mass of the load, ( g ) is the acceleration due to gravity, and ( h ) is the height to which the load is lifted.

In this scenario, if the load is lifted to a height that is twice as much (i.e., from height ( h ) to height ( 2h )), the potential energy change can be calculated as follows:

1. Original potential energy when lifted to height ( h ): [ PE_1 = mgh ]

2. New potential energy when lifted to height ( 2h ): [ PE_2 = mg(2h) = 2mgh ]

Since potential energy is proportional to height, when the height is doubled (from ( h ) to ( 2h )), the potential energy will also double. This matches with the intuitive understanding that lifting an object higher increases the energy stored