U = mgh
Potential energy at a height.
Higher and higher
You lift a ball a little above the ground, then much higher. Each time you do work on it.
How do you think the energy stored in the ball changes as it is lifted higher?
What this lesson covers
The idea
An object of mass m raised to height h above the ground (taken as zero potential energy) has potential energy U = mgh, the work done against the force mg; so the greater its height, the greater its potential energy.
Higher and higher
You lift a ball a little above the ground, then much higher. Each time you do work on it.
How do you think the energy stored in the ball changes as it is lifted higher?
- It becomes greater
- It becomes smaller
- It stays the same
Raise the ball
Take g = 10 m s⁻², as the book does in its examples. Set the mass and the height.
Work against mg
To raise the ball gradually you apply a force equal to mg through the height h, so the work is mg × h. That work appears as the potential energy: with the potential energy zero on the ground, U = mgh. A greater height gives a greater potential energy.
An object of mass m raised to a height h above the ground (taken as zero potential energy) has potential energy U = mgh, the work done against the force mg. The greater the height, the greater the potential energy.
Notes
U = mgh: the work done against the force mg in raising mass m to a height h. Greater height, greater potential energy.
Check yourself
A cricket ball of mass 0.2 kg is thrown 10 m above the ground. Take g = 10 m s⁻². What is its potential energy at the top, in J?
Answer: 20 J
U = 0.2 kg × 10 m s⁻² × 10 m = 20 J.
A 3 kg object is raised to 4 m above the ground. Take g = 10 m s⁻². What is its potential energy, in J?
Answer: 120 J
U = 3 kg × 10 m s⁻² × 4 m = 120 J.
The same object is raised to a greater height. Its potential energy…
The potential energy U = mgh equals…
- is smaller. More work is needed to raise it higher, so it has more potential energy.
- is the same. U = mgh grows with h, so the greater height gives a greater potential energy.
- is greater — correct. Yes!
- the work done against the force mg in raising the object through h — correct. Yes!
- the kinetic energy of the object while it rests on the ground. An object at rest has zero kinetic energy. The expression comes from the work done in raising the object gradually through the height h.
- the force mg alone. The force is mg. The potential energy is that force multiplied by the height h.