Net Work & Kinetic/Potential Energy: Clarifying the Relationship

[MIA6]

We all know that Wnet= delta KE, change in kinetic energy. But how about if something has not only kinetic energy but also potential energy, no work done by nonconservative force, then how do we find the net work? Still use change in kinetic energy while ignoring PE? If something has no kinetic energy at all, but only potential energy, then I think we can not use the formula that I gave previously but find out the change in potential energy? So to what extent, Wnet=delta KE can be used? Hope you can clarify,thanks.

 

[dynamicsolo]

We all know that Wnet= delta KE, change in kinetic energy. But how about if something has not only kinetic energy but also potential energy, no work done by nonconservative force, then how do we find the net work? Still use change in kinetic energy while ignoring PE? If something has no kinetic energy at all, but only potential energy, then I think we can not use the formula that I gave previously but find out the change in potential energy? So to what extent, Wnet=delta KE can be used? Hope you can clarify,thanks.

You would want to use the more general conservation of energy equation

KE_i + PE_i + W = KE_f + PE_f .

This takes care of situations where either an external force is doing positive work (from, say, some applied force) or negative work (from, for example, friction or air drag).

The work-kinetic energy theorem has more limited applications, as does the corresponding work-potential energy theorem (W = -\DeltaPE), since each assumes the other form of energy isn't changing.

 

[MIA6]

You would want to use the more general conservation of energy equation

KE_i + PE_i + W = KE_f + PE_f .

This takes care of situations where either an external force is doing positive work (from, say, some applied force) or negative work (from, for example, friction or air drag).

The work-kinetic energy theorem has more limited applications, as does the corresponding work-potential energy theorem (W = -\DeltaPE), since each assumes the other form of energy isn't changing.

First, here can the W you refer to be either the work done by conservative force or non-conservative force? Because on my book, it says that work done by conservative force is Wcon=-Delta PE, you said this, too, but must Wc=-delta PE, can I find work done by conservative force using the formula that you gave which go back to my first question, in addition, my book has the same formula as the one you gave, but the work my book refers to is Wnon-conservative, so I am sort of confused.

 

[dynamicsolo]

First, here can the W you refer to be either the work done by conservative force or non-conservative force? Because on my book, it says that work done by conservative force is Wcon=-Delta PE, you said this, too, but must Wc=-delta PE, can I find work done by conservative force using the formula that you gave which go back to my first question, in addition, my book has the same formula as the one you gave, but the work my book refers to is Wnon-conservative, so I am sort of confused.

If work is conservative, that means (among other things) that the sum KE + PE (called the total mechanical energy) is conserved, that is, remains constant. That tells us that W = 0 in the equation I gave, so it vanishes from the equation.

Non-conservative work means the sum KE + PE does change during the process; positive work will increase this sum, while negative work will decrease it. Various processes may cause that change only in KE, or only in PE, or in both of them. That's why this equation is more generally applicable than either of the work-energy theorems.

 

[MIA6]

Thank you so much. Finally I got it. Now I know how to use the equation relating to work and energy. But by the way, is the external force the non-conservative force which makes the total work change? maybe internal force is the conservative force that conserves the total work done? however, different books define conservative or non-conservative force differently,there are two versions of definitions, one is like independent or dependent of the path taken, the other one is as I said before, like one conserves the total work, the other does the opposite.

 

[dynamicsolo]

Thank you so much. Finally I got it. Now I know how to use the equation relating to work and energy. But by the way, is the external force the non-conservative force which makes the total work change? maybe internal force is the conservative force that conserves the total work done? however, different books define conservative or non-conservative force differently,there are two versions of definitions, one is like independent or dependent of the path taken, the other one is as I said before, like one conserves the total work, the other does the opposite.

Gravitation and electromagnetism are examples of conservative forces. As you found, a conservative force has a number of properties: the path-independence of such forces is equivalent to the property of making no change in mechanical energy.

Friction and air drag are non-conservative forces because the amount of work they do on an object is dependent on details like the velocity of the object and the total distance the object moves (rather than just the net displacement).

A force internal to a system does no net work because it will involve a pair of forces acting according to Newton's Third Law on two components of the same system. Since the forces will be equal in magnitude but opposite in direction, the net work adds to zero.

 

[MIA6]

Okay. thank you. For what kind of problem, there is only potential energy associated within, no kinetic energy so that we use Wcon=-deltaPE? Because my book says the work done by gravity as the object moves from point 1 to point 2 is equal to the negative of the difference in potential energy, which is -delta PE. But since gravity is a conservative force, is the net work supposed to be 0 which conserves the total energy as you said? And also in that case, an object drops to the ground, there is also kinetic energy associated within? And do you mean that if there is net work, the force that does the work must be non-conservative?