# Quick Q About W equally the negative change in potential energy

• Fusilli_Jerry89
In summary, potential energy change is equal to the negative work done by gravity when moving an object upwards, despite the positive work required to do so. This discrepancy is explained by considering the change in kinetic energy and the role of gravity in opposing the direction of motion. The positive work we do is essentially using up the potential energy stored in our bodies, resulting in a decrease in overall potential energy.
Fusilli_Jerry89
We all know work equals the negative change in potential energy where there is no change in kinetic energy, but can someone explain to me how this works in the following example?

Say there is an object 100 metres away from the earth. We move this object to 2000 metres away from earth. Given that potential energy is 0 at infinity, potential energy change would be -GMm/2000 + Gmm/100 = 19GMm/2000. This is a positive number, yet the work would also be positive to move this object. How does this make sense?

Thx

The way I understand it is as follows:

We assume the object is at rest at 100 m before the move and at rest at 2000 m after the move. Its change in kinetic energy is therefore 0 J, and by the work-kinetic energy theorem, we know that net work must also be 0 J. How is this possible if we clearly needed to do positive work against the pull of gravity to move up our object?

While we do positive work, gravity is doing negative work. It is a weird concept, but it makes sense if you imagine that we need to put in effort to first speed up the object, but when it stops at 2000 m, gravity is stopping it, so whatever we do, gravity opposes against the direction of motion. This is only because change in kinetic energy is 0 J and the object needs to slow down after it first sped up.

Since potential energy can be taken to mean the amount of work gravity can do on an object at a certain height, the negative work gravity did when we moved our object upwards is "stored" as potential energy--positive work that gravity can do if we release our object.

Certainly, we have expended positive work to move our object to its higher height. This energy came from chemical processes within our body. In essence, we are using up the potential energy stored in the food we eat to do this positive work, and our overall potential energy decreases.

In this example, the work done to move the object from 100m to 2000m away from the earth is positive because the object is moving in the direction of the gravitational force. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, there is no change in kinetic energy because the object is not moving faster or slower. However, there is a change in potential energy because the object has moved to a different distance from the earth. The equation you provided for potential energy change takes into account the distance and masses of the object and the earth, and it is a positive number because the object has moved to a greater distance. Overall, the work done is positive because the object has gained potential energy, even though there is no change in kinetic energy.

## 1. What is "Quick Q About W equally the negative change in potential energy"?

"Quick Q About W equally the negative change in potential energy" is a scientific concept that relates to the relationship between work (W) and potential energy. According to the law of conservation of energy, when work is done on an object, its potential energy changes. In this concept, we are specifically looking at the negative change in potential energy.

## 2. How is work related to potential energy?

Work and potential energy are directly related. When work is done on an object, its potential energy changes. This can be seen in the formula W = -ΔPE, where W represents work, and ΔPE represents the change in potential energy. This relationship is important in understanding the behavior of objects in different energy states.

## 3. Can you provide an example of "Quick Q About W equally the negative change in potential energy"?

An example of this concept can be seen in a ball rolling down a hill. As the ball rolls down, work is being done on it by the force of gravity. This work causes a decrease in the ball's potential energy, as it is now closer to the ground. In this case, W would represent the work done by gravity, and ΔPE would represent the negative change in potential energy.

## 4. How does this concept relate to the law of conservation of energy?

This concept is directly related to the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed. In the case of "Quick Q About W equally the negative change in potential energy", the work done on an object is transferred into a change in its potential energy. This demonstrates the conservation of energy in a system.

## 5. Why is "Quick Q About W equally the negative change in potential energy" important in science?

Understanding the relationship between work and potential energy is crucial in many scientific fields, including mechanics, thermodynamics, and electricity. This concept allows scientists to analyze and predict the behavior of objects in different energy states and to design systems that efficiently transfer and transform energy. It also helps to explain the fundamental principle of the conservation of energy, which is essential in understanding the workings of our universe.

Replies
15
Views
792
Replies
6
Views
277
Replies
3
Views
302
Replies
1
Views
1K
Replies
2
Views
1K
Replies
14
Views
1K
Replies
5
Views
953
Replies
9
Views
332
Replies
4
Views
2K
Replies
7
Views
309