Work, Energy, and Simple Machines

Work, kinetic and potential energy, power and the kilowatt hour, and how levers, pulleys and ramps make work easier.

Key ideas

Work is done only when a force moves its point of application in the direction of the force.
Kinetic energy is energy of motion; potential energy is energy of position or shape.
Energy changes form but the total stays the same (conservation of energy).
Power is the rate of doing work; the unit of electrical energy used at home is the kilowatt hour (one unit).
A simple machine lets a smaller effort move a larger load, but the effort must move further.
Levers: first class (fulcrum in the middle, scissors), second (load in the middle, nutcracker), third (effort in the middle, tongs).

Remember

Work, energy	W = Fs; KE = ½mv²; PE = mgh
Power	P = W ÷ t; 1 kWh = 3.6 × 10⁶ J
Lever	effort × effort arm = load × load arm
Machines	MA = load ÷ effort; efficiency = work out ÷ work in × 100%
Ideal ramp	effort = load × height ÷ length

Watch out

Saying work is done when carrying a load along level ground (the force is at 90° to the motion).
Forgetting to square the speed in ½mv².
Expecting a real machine to be 100% efficient (friction wastes some work).

Worked example

A worker pushes a box of weight 1,440 N up a ramp 3 m long onto a platform 1 m high, using an effort of 600 N along the ramp. Find the useful work done, the work put in, the efficiency of the ramp and its mechanical advantage.

Working: useful work = 1440 × 1; work put in = 600 × 3; efficiency = 1440 ÷ 1800 × 100; MA = load ÷ effort = 1440 ÷ 600

Answer: useful work 1,440 J; work put in 1,800 J; efficiency 80%; MA = 2.4