Working against gravity

Finding the potential energy of a raised object begins as a work problem, and the answer turns out to be the same number.

Figure to be added

Figure 18.5 — a 3 kg block being lifted by a hand, with an upward force of 30 N marked above it and its 30 N weight marked below, beside a vertical scale showing the 2 m it is raised through and the block drawn in dashed outline at the top.

The problem

Find the work that must be done to raise a mass of 3 kg through a height of 2 m.

weight of the 3 kg mass = 3 kg × 10 m s^-2 = 30 N

force needed to lift it = 30 N

height raised = 2 m

work done = 30 N × 2 m

= 60 J

From work done to energy stored

The work that had to be done is 60 J. Since that energy was spent putting the object where it now is, the object holds 60 J at a height of 2 m. Its potential energy at that height is 60 J.

Calculate the work, and you have the energy

There is no separate procedure for potential energy. Work out what it cost to raise the object, and that is what the object is holding.

Why this one is called gravitational

The work here was done against gravity — the force being overcome was the object's weight. Potential energy stored this way is therefore called gravitational potential energy, to keep it apart from the elastic kind stored by changing an object's shape.