Question

In each of the following a force, F is acting on an object of mass, m. The direction of displacement is from west to east shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive or zero.

Answer 1

Understanding Work Done: 

Work done by a force is given by:
\[ W = F \cdot d \cdot \cos \theta \]
where \( \theta \) is the angle between the force and the displacement.

Cases:

1. Force in the same direction as displacement (\(\theta = 0^\circ\)): 
   \(\cos 0^\circ = 1\), so Work done is positive.
2. Force opposite to displacement (\(\theta = 180^\circ\)): 
   \(\cos 180^\circ = -1\), so Work done is negative.
3. Force perpendicular to displacement (\(\theta = 90^\circ\)): 
   \(\cos 90^\circ = 0\), so Work done is zero.

Conclusion:

- Work is positive if force and displacement are in the same direction.
- Work is negative if force and displacement are in opposite directions.
- Work is zero if force is perpendicular to displacement.