Work changes energy
The work-energy theorem.
Work and energy
A ball has some energy. A fielder does work on it by throwing it, and later a goalkeeper does negative work on it by stopping it.
How do you think the work done on the ball is related to its energy?
What this lesson covers
The idea
Work done on an object equals the change in its energy; this holds for a system of objects and for forces that are not constant, and energy, like work, is measured in joules.
Work and energy
A ball has some energy. A fielder does work on it by throwing it, and later a goalkeeper does negative work on it by stopping it.
How do you think the work done on the ball is related to its energy?
- Work done equals the change in energy
- Work done has nothing to do with energy
- Work done is the same as the energy the object has
Do work on the ball
The ball starts with 20 J of energy (an example). Set the work done on it.
Change in energy
Positive work of 30 J raised the energy by 30 J, from 20 J to 50 J. Negative work of 10 J lowered it by 10 J, to 10 J. So the work done on the ball matched the change in its energy.
The work-energy theorem: work done on an object = change in its energy. It also holds for a system of objects and when the forces are not constant. Energy, like work, is measured in joules (J).
Notes
Work done on an object = change in its energy, in joules. This holds for a system and for forces that are not constant.
Check yourself
An object has 15 J of energy. Positive work of 20 J is done on it. What is its energy afterwards, in J?
Answer: 35 J
Change in energy = work done = 20 J, so the energy is 15 J + 20 J = 35 J.
The energy of an object rises from 10 J to 45 J. How much work was done on it, in J?
Answer: 35 J
Work done = 45 J − 10 J = 35 J.
Negative work is done on an object. Its energy…
Does the work-energy theorem hold when the forces are not constant?
- increases. Positive work increases the energy. Negative work decreases it.
- decreases — correct. Yes!
- stays the same. Work done on an object equals the change in its energy, so negative work changes it. It decreases.
- No, it holds for a constant force on a single object. The book says it also holds for a system of objects and when the forces are not constant.
- No, it holds only for an object at rest. The theorem is not limited to objects at rest. It holds for moving objects too.
- Yes, it also holds for forces that are not constant — correct. Yes!