# Confusion with Potential Energy and Work

• bdolle
In summary: This is because the change in kinetic energy is equal to the change in potential energy. In summary, the work-energy theorem states that when the net work done on a system is zero, the change in kinetic energy is equal to the change in potential energy. This is represented in the equations given, where statement 2 shows that the change in energy (ΔE) is equal to the sum of changes in kinetic energy (ΔK), potential energy (ΔU), and thermal energy (ΔTherm). Statement 1 explains that when work (W) is positive, the system's energy increases, and when work is negative, the system's energy decreases. Finally, statement 3 clarifies that the change in potential energy (
bdolle
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.

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.

Aniruddha@94 said:
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).

## What is potential energy?

Potential energy is the energy that an object possesses due to its position or configuration. It is stored energy that has the potential to do work.

## What is work?

Work is defined as the force applied to an object multiplied by the distance over which the force is applied. In other words, work is done when a force causes an object to move.

## What is the relationship between potential energy and work?

Potential energy and work are closely related as they both involve energy being transferred or transformed. When an object has potential energy, that energy can be converted into work, which is the transfer of energy from one object to another.

## How is potential energy calculated?

Potential energy can be calculated using the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

## Can potential energy be negative?

Yes, potential energy can be negative. This typically occurs when the reference point for potential energy is set at a higher point than the object's position, resulting in a negative value for potential energy. It is important to consider the reference point when calculating potential energy.

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