# Confusion with Potential Energy and Work

• B

## Main Question or Discussion Point

In my physics textbook chapter of work 3 statements are made which I am having trouble sorting through.

1. When W>0 the system's energy increases, when W<0 the system's energy decreases.
2. ΔE = ΔK+ΔU+ΔTherm = W
3. ΔU = -W

Here is where my confusion begins. If I move a 1kg brick from 0m to 1m I have added potential energy, more energy is stored in the system. Statement 2 asserts that because ΔU increases, ΔE will also increase and work will be positive. Statement 1 says that W>0 so the system's energy increases. But statement 3 says that ΔU= -W, but we can see clearly that ΔU was positive and that work is also positive.

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There are two forces acting on the brick.
1. The gravitational force
2. The force exerted by your hand
When you lift the brick from 0m to 1m, the work done by you is +ve and the work by gravity is -ve.
Potential energy is a quantity to be associated only with conservative forces. The gravitational force is conservative; the force exerted by you is not.
So in the third equation, W (by gravity) is -ve and the ##\Delta U## is positive.

There are two forces acting on the brick.
1. The gravitational force
2. The force exerted by your hand
When you lift the brick from 0m to 1m, the work done by you is +ve and the work by gravity is -ve.
Potential energy is a quantity to be associated only with conservative forces. The gravitational force is conservative; the force exerted by you is not.
So in the third equation, W (by gravity) is -ve and the ##\Delta U## is positive.
What about net work done on the system? +ve or -ve? Why?

Thank you

When you first accelerate the mass upward the force up from your hand is slightly higher than the gravity force down. This means there is a smal amount of + net work done on the mass and this becomes the masses kinetic energy. As you slow your hand down towards the top the force up is less than gravity force down so +work done by you is less than -work done by gravity so net work during deceleration is negative and is equal to the loss in ke so you could think of the + work done during the acceleration bit representing the increase in ke (chemical to kinetic) and the -net work done bit at the end representing loss in ke (ke to gravitational potential)

• beamie564
@bdolle you can see from the work-energy theorem that the net work done on the brick is zero ( provided the brick is at rest in the initial and final positions).