# Work and Change in Kinetic Energy vs Chage in Potential Energy

This forum made possible through the generous support of SDN members, donors, and sponsors. Thank you.

#### manohman

##### Full Member
5+ Year Member

So we define work as being equal to the change in kinetic energy.

But its also the change in potential energy right?

Can both ever be true in the same situation?

Like Change in KE alone, could be when a box is stopped by friction in which case the work done by friction is the change in Kinetic Energy (right? But does this take into account heat?)

Or for Changes in PE alone, as when you lift a box from one height to another, the work done is the change in PE.

But what if a box were dropped from a plane. Negative work would be done by the air drag and positive work would be done by gravity right? In this case, would it just be the total change in energy? which takes into account both the change in KE and PE?

##### Full Member
7+ Year Member
@manohman

Total energy is always conserved. A system can lose some of that energy to heat (e.g., from friction or air resistance) but that energy simply goes into the surroundings.

I'm a bit confused on what you are asking. Yes, KE and PE can change at the same time. If you drop a box out of a plane, you lose PE but gain KE.

If you discount friction (e.g., air resistance), then the loss in PE = gain in KE.

If you account for friction, then

Loss in PE = Gain in KE + Friction

#### manohman

##### Full Member
5+ Year Member
@manohman

Total energy is always conserved. A system can lose some of that energy to heat (e.g., from friction or air resistance) but that energy simply goes into the surroundings.

I'm a bit confused on what you are asking. Yes, KE and PE can change at the same time. If you drop a box out of a plane, you lose PE but gain KE.ut

If you discount friction (e.g., air resistance), then the loss in PE = gain in KE.

If you account for friction, then

Loss in PE = Gain in KE + Friction
Sorry I wasn't clear ( i know its pretty jumbled).

I'm speaking in regards to work. Because textbooks often say that work = change in kinetic energy. Or also work = change in potential energy.
So im trying to clarify what that means/whati t means if both statements are true (work = change in kinetic and change in potential energy).

in the box example, would the net work then be the work done by air resistence then (friction)? Thanks!

##### Full Member
7+ Year Member
@manohman

I think it goes like this:

Work = delta(KE) = -delta(PE)

I'm not too sure what you mean by "net work".

Gravity does work on the box. Air resistance does work (in the opposite direction) on the box. I guess "net work" would be the sum? But I'm not sure why you would consider this.

#### Cawolf

##### PGY-2
7+ Year Member
Yes work is a change in energy.

If you drop a box from a height, it travels towards the Earth.

The free-body diagram would have a downwards force of gravity and an opposing drag force.

W = F . d (force dot displacement)

W = F . d = Fdcos(theta)

Both gravity and drag do work, just that gravity is parallel and drag is anti-parallel - so they partially cancel.

Edit: Just like @justadream said, I am not really sure what you are asking.

##### Full Member
7+ Year Member
@Cawolf
Is there any sense in "summing the work?

As in:
Gravity does work on the box. Air resistance does work (in the opposite direction) on the box. I guess "net work" would be the sum?

#### Cawolf

##### PGY-2
7+ Year Member
Not really. I think it is analogous to adding the forces as in Newton's second law.

Free body diagrams do a great job of showing forces - because they are vectors we can see how they will cancel/add/etc. Work is a scalar quantity, so "summing" it is quite awkward.

Last edited:

#### manohman

##### Full Member
5+ Year Member
ah okay. Thanks for answering. That clarifies a lot! Sorry for the lack of clarity. I guess I just didnt understand it well enough to even ask as clear question (like making a sand castle out of pudding).

• 1 user