Final answer:
The air conditioner gained gravitational potential energy due to the work done by the crane lifting it. This energy can be computed using the formula PE = mgh, where all the work done by the crane is converted into gravitational potential energy as there is no horizontal displacement involved.
Step-by-step explanation:
The change in gravitational potential energy of the air conditioner as it is lifted by the crane is a result of the work done by the crane. When the crane exerts a force to lift the air conditioner against gravity, it does work on the air conditioner. This work is converted into gravitational potential energy, increasing the total energy of the air conditioner as it is raised to a higher elevation. Thus, the correct answer is that the air conditioner gained energy due to the crane's work. The rise in gravitational potential energy can be calculated using the formula PE = mgh, where m is the mass of the air conditioner, g is the acceleration due to gravity, and h is the height it is raised. Since the crane lifted the air conditioner from the ground to the roof without any horizontal displacement, there is no work done against friction and the entire work done by the crane is stored as the air conditioner’s gravitational potential energy.