# Work Energy Theorem and kinetic energy

The work energy theorem says that ''The work done by the net force acting on a body results change only in its kinetic energy. ''

But if the resultant force is in vertically up direction it will surely change its potential energy too, so whats the solution here.

Tide
Homework Helper
Indeed, if there is a net vertical force the kinetic energy changes -- and so does the potential energy. What, exactly, is the problem?

Well thats the problem

the theorem says that only the kinetic energy changes whereas in this case the potential energy also changes

jtbell
Mentor
damitr said:
The work energy theorem says that ''The work done by the net force acting on a body results change only in its kinetic energy. ''

Is that what your textbook says, exactly? It's not the way I would state the work-energy theorem. I would state it simply as "The work done by the net force acting on a body equals the change in its [the body's] kinetic energy." (No "only".) Or, better, "The net work done by all the forces acting on a body equals the change in its kinetic energy."

The work-energy theorem in this form makes no reference to potential energy at all, and has no implication about what happens to the potential energy.

Even with the modified definition

"The net work done by all the forces acting on a body equals the change in its kinetic energy."

it still does not answer the quastion even here is no mention about the change in potential energy, only kinetic energy is mentioned and thats what the real trouble is.

Doc Al
Mentor
The so-called Work-Energy theorem is fine as stated. Note that the net force includes gravity, so no need to mention potential energy.

If there is a net upward force on an object (and it undergoes an upward displacement), its KE will increase in accord with the work-energy theorem.

As you have said "the net force includes gravity, so no need to mention potential energy."

I have not understood this statement of yours.

What do you exactly mean by ?

Do we not have to take into consideration the potential energy that has been changed ?

And from what I have learnt the work done by the external forces only changes the total energy of the system. In this case it seems that the total energy is changing, kinetic as per the work-energy theorem, and potential due to increase in height.

If I am wrong in reasoning anywhere, if so please point out.

jtbell
Mentor
If you include potential energy along with the kinetic energy, then you must exclude from the net force, the force that is associated with the potential energy. In your situation, if you take "net force" to mean the sum of all forces except gravity, then the work done by that net force equals the change in the sum of kinetic and (gravitational) potential energy.

To put it more precisely, there are two kinds of forces: conservative forces, which have potential energy associated with them, and non-conservative forces, which don't have potential energy associated with them. Define the mechanical energy as the sum of kinetic energy K and the potential energy U:

$$E_{mech} = K + U$$

Also define $W_{nc}$ as the net work done by the non-conservative forces only. Then you can write the work-energy theorem as

$$W_{nc} = \Delta E_{mech} = \Delta (K + U)$$

In this version of the work-energy theorem, the effects of gravity are included on the right side of the equation, via U. $W_{nc}$ does not include work done by the graviational force.

In the original version of the work-energy theorem,

$$W_{net} = \Delta K$$

the effects of gravity are included on the left side of the equation. That is, the work done by the gravitational force is included in $W_{net}$.

Doc Al
Mentor
damitr said:
As you have said "the net force includes gravity, so no need to mention potential energy."

I have not understood this statement of yours.

What do you exactly mean by ?
The purpose of gravitational potential energy is to account for the effect of gravity, so if you consider the object's weight as an external force then you don't also include potential energy--you'd be counting it twice!

Do we not have to take into consideration the potential energy that has been changed ?

And from what I have learnt the work done by the external forces only changes the total energy of the system. In this case it seems that the total energy is changing, kinetic as per the work-energy theorem, and potential due to increase in height.

If I am wrong in reasoning anywhere, if so please point out.
The work-energy theorem is accurate as stated: the work done by the net force leads to a change in kinetic energy. If you want to consider the work done by by forces other than gravity, then you can say that that work done equals the change in KE + PE.

An example may help. Say you lift an object of mass m a height h at constant speed. What's the net force? The force you apply (up) must equal the weight (down), so the net force is zero. Thus, according to the W-E theorem, the change in KE is zero. On the other hand, if you only consider the applied force F=mg (up), then the work done by that force is mgh, which equals the change in "KE + PE" which is mgh. Make sense?

[Looks like jtbell beat me to it!] • 1 person
rcgldr
Homework Helper
In the case of work done moving an object along a surface, some of the work done results in a rise in temperature due to friction, not kinetic energy.

Doc Al
Mentor
Jeff Reid said:
In the case of work done moving an object along a surface, some of the work done results in a rise in temperature due to friction, not kinetic energy.
True, but the work done by the net force will equal the change in KE.