Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
W = (F cos θ) d
Where,
- W is the work done by the force.
- F is the force, d is the displacement caused by the force
- θ is the angle between the force vector and the displacement vector
Case I – In this case, the direction of force acting on the block is perpendicular to the displacement. Therefore, work done by force on the block will be zero.
W = F × cos θ × d
The angle between the force and displacement is 90o.
W = F × cos 90 × d
W = 0 (since cos 90 = 0)
Case II – In this case, the direction of force acting on the block is in the direction of displacement. Therefore, work done by force on the block will be positive.
W = F × cos θ × d
The angle between the force and displacement is 0o.
W = F × cos 0 × d
W = F × d (since cos 0 = 1)
Case III – In this case, the direction of force acting on the block is opposite to the direction of displacement. Therefore, work done by force on the block will be negative.
W = F × cos θ × d
The angle between the force and displacement is 180o.
W = F × cos 180o × d
W = – F × d (since cos 180o = -1)