LEARNING OBJECTIVE 3.2.A - Describe the work done on an object or system by a given force or collection of forces.
Consider a man holding a ball in a fixed position in his outstretched hand (Refer to Figure case A). Our intuition suggests that the man does work. Yet the equation $W= F.\Delta x $ indicates that no work is done on the ball since the ball does not move and the displacement $\Delta x$ is zero.
The resolution of this conflict hinges on the observation that, although the man does no work on the ball, he does work within his own muscles and, consequently, grows tired of holding the ball. A contracted muscle is never in a state of complete rest; within it, atoms, cells, and muscle fibres engage in complicated chemical and mechanical processes that involve motion and work. This means that work is done, and wasted, internally within the muscle, while no work is done externally on the bone to which the muscle is attached or on the bowling ball supported by the bone.
Now consider the same man holding the ball as in the last example, but this time inside an elevator moving upward with a constant velocity ( Refer to Figure case B). In this case, the displacement of the ball in a frame of reference attached to the ground is not zero, and the force (push) exerted by the hand on the ball does work. The displacement S and the force are in the same direction, and consequently, the man continuously does positive work on the ball. Nevertheless, to the man, the ball feels no different when riding in the elevator than when standing on the ground. This example illustrates that the amount of work done on a body depends on the reference frame. In the reference frame of the ground, the ball is moving upward and work is done on it; in the reference frame of the elevator, the ball is at rest, and no work is done on it. The lesson we learned from this is that before proceeding with a calculation of work, we must be careful to specify the reference frame.
