4.6.1 Raising a Weight

The easiest form of mechanical work to deal with is that involved in raising a weight. To make our thinking concrete, let us assume that we have a gas inside a cylinder fitted with a weightless, frictionless piston. ^4.6 We can then place a weight of mass m on the top of the piston. And we can imagine that due to various processes taking place inside the cylinder the piston (and the mass) are pushed up or down until a final resting place, the final state, is reached.

How much work is done in such a process?

To measure the amount of work done all we need do is find the net height through which the weight has been raised or lowered. Nothing else matters. The weight can be raised a distance h₁, lowered a distance h₂, and raised a third distance h₃, the work done then depends on h the net distance travelled:

$$h = h_1 + h_2 + h_3$$ (4.6.7)

and is given by:

$$w = - mgh$$ (4.6.8)

which we've seen before (Equation 4.4.1).

By the way, this raises one interesting question: if we do this experiment in outer space where g is zero (because of the lack of a gravitational field) has any work been done? The answer is no. In that case no work is done.