Mechanical work and power

Holding a heavy bag is tiring; lifting it onto a shelf is another action. How do we distinguish a person's effort from the mechanical effect on the bag itself? We will check whether it moves and how the force is directed.

Compare holding a bag still with lifting it. The hand exerts a force in both cases, but the bag changes position only when lifted. Mechanical work A describes energy transferred by a force during displacement. We will discuss energy soon; for now, work belongs to a particular force acting on a particular object. If the bag does not move, the hand does zero work on it, although energy-consuming processes continue inside the person's body.

A crate moves right. A rightward pull transfers energy to it and does positive work; leftward friction does negative work. Gravity is vertical, so it does zero work during strictly horizontal displacement. It neither assists nor opposes that particular displacement. A force being present therefore does not guarantee nonzero work: check both displacement and the force's direction.

The larger a constant pull and the farther it moves a crate in its direction, the greater the energy transferred. For a constant force in the direction of displacement, A = Fs. Double either force at fixed displacement or displacement at fixed force, and work doubles. F is in N, s in m and A in joules: 1 Дж = 1 Н·м. Here s means straight-line displacement along the force; zero displacement gives zero work.

If a constant force points directly opposite the displacement, A = −Fs: the sign indicates the opposite sense of energy transfer. At an arbitrary angle, only the force component along displacement counts, so Fs alone is insufficient. Draw the directions first. For example, gravity does negative work when a load rises and positive work when it descends. The force's name does not determine the sign; the actual motion does.

Two winches lift identical loads to the same height, with equal initial and final speeds. The required useful work is the same. But the first finishes sooner, transferring the same energy in less time. Power describes this difference: the rate of doing work. Higher power need not mean more work in a particular lift; the same work may simply be done faster.

Divide work by duration to find the average work per second: N = A/t. This is average power over t > 0. Its unit is the watt, 1 Вт = 1 Дж/с. Doing the same work in half the time doubles power; doubling work in the same time does too. Here N denotes power, not normal force: the quantity and unit tell us what the symbol means.

Work of 600 J answers 'how much energy was transferred?' Constant power of 600 W means 600 J transferred each second; average power of 600 W says this only on average over the chosen interval. To find total work at constant power, we also need time: A = Nt. A powerful device running briefly can therefore transfer less energy than a weaker one running for longer. Joules and watts answer different questions.

A winch pulls a load with a constant force of 300 N along a straight displacement of 4 m in 20 s. Find the work and average power.

Force and displacement have the same direction, so A = Fs = 300·4 = 1200 Дж.

Divide work by time: N = 1200/20 = 60 Вт.

An average of 60 J is transferred per second, giving 1200 J over 20 s.

Work: 1200 J; average power: 60 W.

Work concerns a particular force acting during displacement; a person's tiredness does not measure work on a stationary load.

A = Fs applies to a constant force along displacement; the opposite direction gives negative work, and a perpendicular direction gives zero.

Power N = A/t compares the rate of work. To know the energy transferred, we also need the duration.

Simple machines let us do work with less force. We will find out what makes this possible.