Understanding the Concepts
* Work done by gravity: Gravity does negative work when an object is lifted against it. This means the work done by gravity is the negative of the change in potential energy.
* Potential energy: The potential energy of an object at a height 'h' is given by PE = mgh, where 'm' is the mass, 'g' is the acceleration due to gravity, and 'h' is the height.
* Constant velocity: This implies that the net force on the balls is zero. Therefore, the force applied to lift the balls must be equal and opposite to the gravitational force.
Solution
1. Change in Potential Energy: Since both balls are lifted to the same height 'h', the change in potential energy for each ball is:
* ΔPE = mgh - 0 = mgh (for ball A)
* ΔPE = 2mgh - 0 = 2mgh (for ball B)
2. Work done by gravity: The work done by gravity is the negative of the change in potential energy:
* W_gravity (A) = -ΔPE = -mgh
* W_gravity (B) = -ΔPE = -2mgh
Important Note: The fact that ball B rises twice as fast is irrelevant to the work done by gravity. The work done by gravity depends only on the mass of the object, the acceleration due to gravity, and the change in height.
Therefore, the work done by the gravitational force on ball A is -mgh, and the work done on ball B is -2mgh.
