Work, Energy and Power

In everyday speech, holding a heavy bag feels like hard work. In physics, work is done only when a force actually moves its point of application. Work = force × displacement in the direction of the force, written W = Fs. If you push a wall and it does not move, the work done is zero, no matter how tired you get. The SI unit is the joule: one joule is the work done when a force of one newton moves a body through one metre in the direction of the force. Work can be negative too, for example friction does negative work because it acts opposite to the motion.

Energy is the capacity to do work, so it shares the same unit, the joule. A body can have energy in many forms, but in this chapter we focus on mechanical energy, which comes in two kinds. Kinetic energy is the energy a body has because it is moving, given by half its mass times its velocity squared. Potential energy is the energy a body has because of its position or height, given by mass times g times height. A drawn bow, a stretched spring and a raised hammer all store potential energy ready to do work.

When a net force does work on a body, that work shows up as a change in the body's kinetic energy. This is the work-energy theorem: the work done by the net force equals the change in kinetic energy. Speed up a car and the engine does positive work, raising its kinetic energy; brake, and friction does negative work, lowering it. This links the idea of work directly to motion, and lets you find a final speed without using the equations of motion.

Power is how fast work is done, or how fast energy is transferred: power = work divided by time. Its SI unit is the watt, where one watt is one joule per second. Two cranes that lift the same load to the same height do equal work, but the faster one is more powerful. Finally, the law of conservation of energy says energy can never be created or destroyed, only changed from one form to another. A falling ball steadily converts potential energy into kinetic energy, but at every instant the total mechanical energy stays the same.