# Can only non-conservative force cause change in total kinetic energy?

By work-energy theorem: total work done on a mass equals the total change in kinetic energy. So, is there any case where only non-conservative forces are acting on a mass and this causes total change in kinetic energy? If yes please give an example.

Edit: I mean,

Wnc = K2-K1.

Any force that can do work has the potential to cause a change in kinetic energy in accordance with the work energy theorem which states that the net work done on an object equals its change in kinetic energy.

Everyday non-conservative contact forces, like those involved when you push an object in a horizontal direction, can result in a change in kinetic energy as long as the net work done is not zero.

An example is if you push an object from rest on a frictionless horizontal surface. The work you do accelerates the object giving it kinetic energy.

An example where the change in kinetic energy is zero is when you push an object with constant velocity on a surface with friction. The positive work you do when pushing the object a distance $$d$$ equals the negative work done by kinetic friction over the same distance $$d$$, for a change in kinetic energy of zero. The negative friction work takes the energy you gave to the object and dissipates it as heat at the contacting surfaces.

Hope this helps.

Any force that causes movement through a distance changes the kinetic energy. For a conservative force, it is convenient to represent the change in kinetic energy as the negative of the change in a potential energy.

The definition of a non-conservative force is simply one which cannot be expressed as a gradient of a scalar potential, in other words the potential lost/gained from a system is path dependent. Work can still be done by a non-conservative force but the total energy of the mass will not be constant as it dissipates into the system. An obvious example is friction, this is not a conservative force yet it lowers the kinetic energy.

• But see for a body to initially move it must require an external force. Then, total kinetic energy equals work done by external force plus friction. I was asking for an example where only non-conservative force equals the change in kinetic energy.
– user253572
Commented Nov 5, 2020 at 15:53
• Also, the work done by non-conservative forces is path-dependent.
– user253572
Commented Nov 5, 2020 at 16:02
• @SuzyBae Why should the external force be conservative? Commented Nov 5, 2020 at 16:07
• Sorry I mis-read your question, I didn't see "only". I suppose something like the force of a stationary particle in a fluid flow might match that condition but that is basically friction(or drag) from the stationary frame of the mass so I am not sure that counts. I cannot think of any examples of systems in nature of purely non-conservative force but any that cannot be derived as the gradient of a scalar potential (i.e. path dependent) then that should match your criterion. Commented Nov 5, 2020 at 16:07
• @KristianStokkereit If I push a book across my desk with my hand, the force I apply to the book is non-conservative. Commented Nov 5, 2020 at 16:10