Is Kinetic Friction a Conservative Force?

[Leo Liu]

If a block slides down an inclined surface under the presence of the kinetic friction, does that mean the total energy lost by the block is equal to the work done by the kinetic friction? Thanks in advance.

 

[kuruman]

Kinetic friction is absolutely not a conservative force. It fails all the tests for being one. Furthermore, it does not do work but converts mechanical energy into heat. When a block slides down an incline, part of the mechanical energy is converted into heat by friction. If the block stops on its way down, all of its mechanical energy has been converted into heat and cannot be recovered.

 

[Dale]

If a block slides down a inclined surface under the presence of the kinetic friction, does that mean the total energy lost by the block is equal to the work done by the kinetic friction? Thanks in advance.

This is a different question than in the thread title. What you are asking here is: “Is energy conserved”. And the answer is: “Yes”. The work done by kinetic friction is equal to the mechanical energy (KE + gravitational PE) lost and the thermal energy gained.

To test if friction is conservative you would need to push the box back up to the top of the ramp and see if you get that energy back. You don’t, so friction is not a conservative force.

 

[kuruman]

The work done by kinetic friction is equal to the mechanical energy (KE + gravitational PE) lost and the thermal energy gained.

Did you mean to say, "The work done by kinetic friction is equal to the mechanical energy (KE + gravitational PE) lost or the thermal energy gained."?

 

[Dale]

Did you mean to say, "The work done by kinetic friction is equal to the mechanical energy (KE + gravitational PE) lost or the thermal energy gained."?

No, "and" is correct. Mechanical energy decreases and thermal energy increases. If both did not happen then energy would not be conserved.

 

[Leo Liu]

Kinetic friction is absolutely not a conservative force. It fails all the tests for being one. Furthermore, it does not do work but converts mechanical energy into heat. When a block slides down an incline, part of the mechanical energy is converted into heat by friction. If the block stops on its way down, all of its mechanical energy has been converted into heat and cannot be recovered.

Are you saying that its potential energy has been converted into the vibrational energy of molecules of the block and the plane? Thank you.

 

[kuruman]

No, "and" is correct. Mechanical energy decreases and thermal energy increases. If both did not happen then energy would not be conserved.

I agree that mechanical energy decreases and thermal energy increases.. However I interpret the statement "The work done by kinetic friction is equal to the mechanical energy (KE + gravitational PE) lost and the thermal energy gained" to imply an equality where "The work done by friction" is on the LHS and (KE + gravitational PE) lost and the thermal energy gained is on the RHS. The "and" implies addition which shouldn't be the case.

Consider a block sliding down the incline with initial speed $v_0$ and a height drop $h$. If there is no friction, no mechanical energy is lost as potential energy $mgh$ is converted to kinetic energy. Now consider the same height drop with friction. The potential energy change is the same as in the frictionless case, but the block will have less speed than in the frictionless case. You can see that, when you do the energy accounting, the heat generated has to come from the kinetic part of mechanical energy. Clearly, the mechanical energy lost (the difference between what it was in the frictionless case and the case with friction) is the thermal energy gained. There is no work done by friction. The term $|\vec f_k \cdot \Delta\vec s|$ is the internal energy increase of the block and the ramp. In general the energy conservation equation is $$\Delta K+\Delta U+\Delta E_{therm}=0$$In terms of mechanical energy (ME),$$\Delta(ME)+\Delta E_{therm}=0$$which says that the loss of mechanical energy is equal to the gain in thermal energy.

 

[kuruman]

Are you saying that its potential energy has been converted into the vibrational energy of molecules of the block and the plane? Thank you.

Not only that, but also sound waves, making and breaking molecular bonds on the surfaces in contact, etc. The energy dissipation because of friction is a complex issue. Note that it's not only potential energy but also kinetic energy that is converted into these other forms of irrecoverable energy. A block kicked across a horizontal floor will stop when all its kinetic energy is converted into thermal energy. Potential energy does not come into play here.

 

[Dale]

I interpret the statement "The work done by kinetic friction is equal to the mechanical energy (KE + gravitational PE) lost and the thermal energy gained" implies an equality where "The work done by friction" is on the LHS and (KE + gravitational PE) lost and the thermal energy gained is on the RHS.

It is an ambiguity in English. I would say "plus" if I intended addition. I intended two separate equalities. $W=KE_{lost}$ and $W=E_{Thermal,Gained}$.

The "and" implies addition which shouldn't be the case.

But "or" doesn't fix that since both are simultaneously true, not just one or the other.

 

[kuruman]

It is an ambiguity in English. I would say "plus" if I intended addition. I intended two separate equalities. $W=KE_{lost}$ and $W=E_{Thermal,Gained}$.

But "or" doesn't fix that since both are simultaneously true, not just one or the other.

I see. Then we totally agree. Thanks for the clarification.