# A question about potential energy and work

• n3pix
In summary: In the context of this thread, "must" is incorrect because work can result in a change in kinetic energy, even if net work is zero.
n3pix
Hello,

I'm confusing about the basic terms about Conservation of Energy, Potential Energy and Work.

Consider that we have a mass ##M## above the ground (zero point) distance of ##y_{0}=h##. When we release the mass it will accelerate through it's way to ground. So the work is made by a field force (gravitation) that is ##F_{G}=-Mg##. The last position of the mass is ##y=0##. So the displacement of mass is equal to ##(y-y_{0})=(0-h)=-h##. Therefore, the work done by gravity is ##W(by gravity)=F_{G}\times(y-y_{0})=(-Mg)(-h)=Mgh##. As the definition of work (as I learnt), the work done by something is equal to the force times displacement of the body and It's equal to change in kinetic energy of that body. So, if we consider that the mass has initial velocity ##V_{0}=0## and last velocity at the moment it touch the ground ##V##. Therefore, work done by gravity is equal to ##W(by gravity)=Mgh=\Delta{KE}=\frac{1}{2}M{{V}^{2}}-\frac{1}{2}M{{V_{0}}^{2}}=\frac{1}{2}M{V^{2}}-\frac{1}{2}M\times{0}=\frac{1}{2}M{V^{2}}##.

I will now give you reverse example, mass M raised by us. To raise mass M from the ground or heigh of ##y_{0}=0## to height of ##y=h## without acceleration we must apply an upward, equal and opposite force ##F_{ag}=-F_{G}=Mg##. So the work done by us is ##W(by us)=F_{ag}(y-y_{0})=(Mg)(h-0)=Mgh##. As the definition of work, there must be change in kinetic energy of the object. The initial velocity and last velocity of the object are same and the mass has no acceleration. Therefore, ##W(by us)=Mgh=\Delta{KE}=\frac{1}{2}M{{V}^{2}}-\frac{1}{2}M{{V}^{2}}=0##.

What does this mean?

n3pix said:
As the definition of work, there must be change in kinetic energy of the object.
Realize that when you lift the object, gravity is still doing work (negative work). So the net work is zero, thus no change in KE.

n3pix and PeroK
Doc Al said:
Realize that when you lift the object, gravity is still doing work (negative work). So the net work is zero, thus no change in KE.

Wow, I didn't think this way. Thank you so much :)

berkeman
n3pix said:
As the definition of work, there must be change in kinetic energy of the object.
In the context of this thread, that statement is 'ok' but there is no inherent relationship between Work and change of KE. The work will change the total of Potential and Kinetic Energy. The longer the time taken, the less KE change will result.
Practical note: To obtain exactly zero KE change, the profile of the force over a journey of finite time would not be uniform. (e.g. you need to slow up near the top and reduce the applied force in an elevator)

n3pix
sophiecentaur said:
In the context of this thread, that statement is 'ok' but there is no inherent relationship between Work and change of KE. The work will change the total of Potential and Kinetic Energy. The longer the time taken, the less KE change will result.
Practical note: To obtain exactly zero KE change, the profile of the force over a journey of finite time would not be uniform. (e.g. you need to slow up near the top and reduce the applied force in an elevator)

n3pix said:
As the definition of work, there must be change in kinetic energy of the object.
This ("must") is incorrect.

Edit: There is a difference between work and net work, this is what @Doc Al is reminding us to keep straight.

sophiecentaur and n3pix

## 1. What is potential energy?

Potential energy is the energy that an object possesses due to its position or configuration. It can also be thought of as the energy that an object has stored within itself.

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

Potential energy is related to work through the principle of conservation of energy. When an object's potential energy changes, work is done on the object, either increasing or decreasing its potential energy.

## 3. What factors affect an object's potential energy?

The factors that affect an object's potential energy include its mass, height, and the strength of the gravitational field it is in. The formula for potential energy is PE = mgh, where m is the mass, g is the gravitational acceleration, and h is the height.

## 4. Can potential energy be converted into other forms of energy?

Yes, potential energy can be converted into other forms of energy, such as kinetic energy. When an object falls, its potential energy decreases and its kinetic energy increases.

## 5. How is potential energy used in everyday life?

Potential energy is used in various ways in everyday life. For example, potential energy from food is converted into kinetic energy to power our bodies. Potential energy stored in batteries is converted into electrical energy to power electronic devices. Potential energy from water stored in dams is converted into electrical energy to power homes and businesses.

• Mechanics
Replies
30
Views
1K
• Mechanics
Replies
2
Views
995
• Mechanics
Replies
30
Views
802
• Mechanics
Replies
13
Views
717
• Mechanics
Replies
4
Views
992
• Mechanics
Replies
12
Views
2K
• Mechanics
Replies
3
Views
483
• Mechanics
Replies
10
Views
1K
• Mechanics
Replies
10
Views
937
• Mechanics
Replies
2
Views
955