Work, energy & power
Energy is the currency of the universe — every push, lift and falling stone is a story about energy moving from one form to another. In this AS-level lesson we state the principle of conservation of energy, define work precisely as W = Fs cosθ (the component of force along the displacement), and meet the work done by an expanding gas, W = pΔV. We then DERIVE the two great store formulae from first principles — kinetic energy Ek = ½mv² straight out of the work–energy idea, and the gravitational potential energy change ΔEp = mgΔh straight out of W = Fs — and use conservation of energy to solve a falling-body problem. Finally we meet efficiency = useful output ÷ total input, and power P = W/t = Fv, working every calculation line by line.
By the end you should be able to (NSSCAS Physics (AS) 1.6):
- Give examples of energy in different forms and apply the principle of conservation of energy to simple examples (e.g. kinetic ↔ potential in a pendulum)
- Explain work as the product of a force and the displacement in the direction of the force, and use W = Fs cosθ
- Calculate the work done in a range of situations, including the work done by a gas expanding against a constant pressure, W = pΔV
- Derive, from the equations of motion, the formula for kinetic energy Ek = ½mv², and recall and apply it
- Derive, from W = Fs, the formula ΔEp = mgΔh for gravitational potential energy changes near the Earth's surface, and recall and use it
- Distinguish between gravitational potential energy and elastic potential energy
- Recall and apply that efficiency = useful energy output ÷ total energy input, and discuss the implications of energy losses in practical devices
- Define power as work done per unit time, derive power as the product of force and velocity, and recall and use P = W/t and P = Fv