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Chapter 5: Problem 23

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

Expert verified
In both cases, work is being performed. (a) In lifting a pencil off the desk, the force exerted by your hand opposes gravity, and the pencil is displaced vertically upwards. (b) In compressing a spring, an external force acts inwards, displacing the spring from its normal length to half its normal length.

Step by step solution

01

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

1. Identify the forces acting on the pencil: There are two forces acting on the pencil - the gravitational force acting downwards and the force exerted by your hand acting upwards (opposite to the gravitational force). 2. Find if there is any displacement: When you lift the pencil off the desk, it is being displaced vertically upwards. 3. Check if work is being performed: Yes, work is being performed in this case because there is a force acting on the pencil (the force exerted by your hand) and the pencil is being displaced in the same direction as the force (vertically upwards).
02

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

1. Identify the forces acting on the spring: When the spring gets compressed it means an external force is being applied inwards. The force from the spring is also acting in the opposite direction (outwards) due to Hooke's Law. 2. Find if there is any displacement: The spring is being displaced from its normal length to half its normal length, meaning that there is a displacement. 3. Check if work is being performed: Yes, work is being performed in this case because there is an external force acting on the spring (compressing it) and the spring is being displaced in the same direction as the force (inwards).

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