# A question about potential energy and work

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?

Mentor
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
n3pix
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
Gold Member
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
n3pix
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)

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