# Relation of Energy with Work

1. Jun 17, 2013

### san203

Hello all.
This is not a "What is Energy" Thread but rather a question about its relation with work.
I understand that energy has been defined as the ability to do work. So why is change in energy is equal to work? Cant energy be equal to work.

Also when the force field is doing work on a object, will the work done on the object by field be equal to the work that the object can do later?
Thanks

2. Jun 17, 2013

### Staff: Mentor

Positive work creates positive potential energy as in pushing a block up an incline.

A block sliding down an incline has positive kinetic energy (negative work).

I think this is why we separate the two terms.

3. Jun 17, 2013

### WannabeNewton

The total internal energy is a state function whereas mechanical work is a process function. Put more loosely, I can easily say that a particle has "this amount of energy for the given state" but it makes no sense to say that a particle has "this amount of work for the given state".

4. Jun 17, 2013

### Staff: Mentor

So remember that energy is the capacity to do work, and that capacity is limited. As you do work you lose the capacity to do more work. So as you do work your energy decreases, and therefore the work is equal to the change in the energy.

Yes, assuming that the force field is conservative. The work done on the object by the field will increase the KE of the object, which can then be used to do work later.

5. Jun 17, 2013

### san203

I see. But i was talking about the work done by the field. why is Work done by field = change in energy of object? same reason i guess? Silly question i know, but it happens when you think about something for too too long:tongue2:

6. Jun 17, 2013

### Staff: Mentor

A conservative field has an associated potential. So an object being acted on by such a field has potential energy. As the field does work on the object the potential energy of the object is decreased, meaning that the object has a reduced capacity to do work.

For example, a rock under the influence of gravity has potential energy (mgh). At the top of a hill its potential energy is high and it has the capacity to do a lot of work by falling down. At the bottom of the hill the potential energy is low and it has little capacity to do work by falling down. The change in the rock's potential energy is equal to the work done by gravity on the rock.