Section 3.1: Work by Constant Forces
Work is the transfer of energy by a force acting over a displacement. For a constant force, the definition of work is straightforward.
Definition of Work:
\( W = \vec{F} \cdot \vec{d} = F d \cos\theta \)
- \( F \): Magnitude of the constant force
- \( d \): Magnitude of the displacement
- \( \theta \): Angle between force and displacement
Work is positive if the force has a component in the direction of displacement, and negative if opposite.
Example 1
A 20 N force is applied horizontally to push a box 5 m across a frictionless surface. Find the work done.
\( W = Fd\cos\theta = 20 \times 5 \times \cos 0° = 100 \, \text{J} \)
Example 2
A 50 N force is applied at 60° to the horizontal, moving a box 4 m horizontally. Find the work done.
\( W = Fd\cos\theta = 50 \times 4 \times \cos 60° = 100 \, \text{J} \)
Practice Problems
- A 15 N force pushes a cart 6 m horizontally. Find the work done.
- A 40 N force is applied at 30° to the horizontal, moving an object 10 m. Find the work done.
- A 25 N force moves a block 3 m at 120° to the displacement. Find the work done.
- A 100 N force pulls a box 2 m at 0°. Compute the work done.
- A force of 60 N acts at 45° while moving an object 8 m. Find the work done.