Physics / Unit 5: Work, Energy and Power
5.1 Work
Notes
Work is done when a force moves an object through a displacement: $W = Fd\cos\theta$, where $\theta$ is the angle between the force and the displacement.
- Unit: the joule (J). $1 \text{ J} = 1 \text{ N·m}$.
- Force along the motion ($\theta = 0^\circ$): $W = Fd$. Force perpendicular ($\theta = 90^\circ$): $W = 0$.
- Force opposite the motion (like friction): work is negative.
- No displacement means no work, however tiring it feels.
- Example: pushing a cart with 50 N for 10 m does $50 \times 10 = 500 \text{ J}$ of work.
Practice
A student pushes a desk 3 m across the floor with a 60 N horizontal force. How much work does she do?
$W = Fd = 60 \times 3 = 180 \text{ J}$.
A waiter carries a tray at constant height across a room. How much work does his upward holding force do on the tray?
The upward force is perpendicular to the horizontal displacement, so $\cos 90^\circ = 0$.
A sled is pulled 20 m with a 40 N force at $60^\circ$ above the horizontal. How much work is done by the pull?
$W = 40 \times 20 \times \cos 60^\circ = 800 \times 0.5 = 400 \text{ J}$.
Ready for more? Take the Unit 5 test.