Question

Identify the force present, and explain whether work is being performed in the following cases: (a) You lift a pencil off the top of a desk. (b) A spring is compressed to half its normal length.

Short answer

In case (a), the force present is gravity and the force exerted by your hand. Work is being performed since the applied force and the displacement are in the same direction (upward). In case (b), the force present is the spring force and the compression force. Work is being performed since the applied force and the displacement are in the same direction.

Step-by-step solution

Case (a): Lifting a pencil off the top of a desk

In this situation, the acting forces are the gravitational force (weight) acting on the pencil due to Earth's gravity, and the force exerted by your hand to lift the pencil. When you lift the pencil, you apply a force against gravity, causing displacement in an upward direction. Since the force applied (your hand) and the displacement of the pencil are in the same direction (upward), work is being performed.

Case (b): A spring is compressed to half its normal length

In this case, when you compress a spring, it exerts a force opposite to the direction of compression, which is the spring force. The force you apply to compress the spring is in the same direction as the displacement of the spring's individual molecules (i.e., they move closer together). As the force applied (compression force) and the displacement of the spring are in the same direction, work is being performed on the spring. To summarize: 1. In case (a), lifting a pencil off the top of a desk, the forces are gravity and the force exerted by your hand. Work is being performed as the force and displacement are in the same direction. 2. In case (b), compressing a spring to half its normal length, the forces are the spring force and the compression force. Work is being performed as the force and displacement are in the same direction.