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š¬ Lifting bags
Lift one wheat bag to a height, then three bags, then one bag three times higher. When have you done "more work" — and can we pin that down with a number?
How is work done by a constant force defined?
- Lifting 3 bags (instead of 1) to the same height needs 3 times the force over the same distance → 3 times the work. Lifting 1 bag 3 times higher needs the same force over 3 times the distance → again 3 times the work.
- So: work done = force applied × displacement in the direction of the force. $$W = F \times s$$
- Applying a larger force over the same distance, or the same force over a larger distance, both do proportionally more work.
What is the SI unit of work, the joule?
- The SI unit of work is the joule (J) . Since force is in newton (N) and displacement in metre (m): $$1\ \text{J} = 1\ \text{N} \times 1\ \text{m}$$
- One joule of work is done when a force of 1 N displaces an object 1 m in the direction of the force. As \(1\ \text{N} = 1\ \text{kg m s}^{-2}\), we get \(1\ \text{J} = 1\ \text{kg m}^2 \text{s}^{-2}\).
- Work can also be read as the area under a force-displacement graph (e.g. \(10\ \text{N} \times 1\ \text{m} = 10\ \text{J}\)); this even works when the force is not constant.
Important Definitions
- Work — work done on an object by a constant force is the force applied multiplied by the displacement in the direction of the force.
- Joule (J) — the SI unit of work; 1 J of work is done when a force of 1 N moves an object 1 m in the direction of the force.
ā Note
- While describing work done, it is important to specify the force (or agency) doing the work and the object on which the work is done.
