Static friction force: Consider a block on a sheet of paper....

[Caio Graco]

Homework Statement

Can static friction force work?

Relevant Equations

Fat = u.N

Consider a block on a sheet of paper. If the sheet is pulled without sliding the block, who has done work on the block (since it has undergone a kinetic energy variation)? I can not see another force doing work other than the static frictional force on the block.

 

[PhanthomJay]

That is correct, as long as the block is accelerating with respect to the ground. The work done by friction by the paper on the block is positive work with respect to the ground. Work like energy is relative. From the reference frame of the paper, friction does no work on the block , because there is no motion with respect to the paper.

 

[Caio Graco]

That is correct, as long as the block is accelerating with respect to the ground. The work done by friction by the paper on the block is positive work with respect to the ground. Work like energy is relative. From the reference frame of the paper, friction does no work on the block , because there is no motion with respect to the paper.

OK thank you. It is easy to see that if the paper is pulled into the starting position, bringing the block to the starting position also (at rest), the total work on the block will be zero. Does this mean that the static friction force is conservative?

 

[jbriggs444]

OK thank you. It is easy to see that if the paper is pulled into the starting position, bringing the block to the starting position also (at rest), the total work on the block will be zero. Does this mean that the static friction force is conservative?

For a force to be conservative, the work done has to be zero over every possible closed loop. It is not sufficient that the work done is zero over some particular closed path.

 

[Caio Graco]

For a force to be conservative, the work done has to be zero over every possible closed loop. It is not sufficient that the work done is zero over some particular closed path.

It is true. If you pull the paper so that the block returns to the initial position (under any trajectory) for the same initial rest condition, the work will be zero for any trajectory, which would at first indicate that the static frictional force is conservative. However, if the initial position of the block has some velocity, this already shows a case in which the work is non-zero, which indicates that the static friction force is non-conservative. I believe this is what you call my attention.

So can I say that the static friction force is dissipative? It is?

 

[jbriggs444]

However, if the initial position of the block has some velocity, this already shows a case in which the work is non-zero, which indicates that the static friction force is non-conservative. I believe this is what you call my attention.

Yes. If the block started at rest, moved with the paper throughout and ended with some non-zero velocity, that would demonstrate that static friction is not a conservative force. [Similarly, if it had started in motion and ended at rest. Or started in motion and ended with a different speed].

So can I say that the static friction force is dissipative? It is?

I am not comfortable using the term "dissipative" for static friction. The third law force pair involved with static friction never dissipates any mechanical energy into heat. So although it is not "conservative", I would not call static friction "dissipative".

However, a quick trip to Google indicates that many sources consider "dissipative" and "non-conservative" to be synonymous.

 

[Mister T]

I can not see another force doing work other than the static frictional force on the block.

Your hand (presuming it's you doing the pulling) is exerting a force on the sheet.

By the way, whatever energy you expend doing this will cause the temperatures of the surfaces that do slide against each other to warm up.

 

[Caio Graco]

Your hand (presuming it's you doing the pulling) is exerting a force on the sheet.

By the way, whatever energy you expend doing this will cause the temperatures of the surfaces that do slide against each other to warm up.

Considering the paper-block system it is easy to see that my hand pulling paper is the one who performs work on the system. But if we consider as a system only the block, who does work on the system (on the block)? According to what we discussed in the above posts is the static friction force. Do you agree with that too? And if you agree, in your opinion can we say that the static friction force is dissipative (nonconservative)?

 

[PhanthomJay]

I may have not interpreted your comment earlier about no net work being done by friction when it is accelerated toward the start position and then brought to rest by releasing the force. Correct.
Cobservativeforces are forces associated wit a potential energy function. Unlike non conservativeforces, there is no heat loss when work is done. Springand gravity forces are conservative. Just about every other force in intro physics isnoncoservative.

 

[vela]

So can I say that the static friction force is dissipative?

No, the force isn't causing mechanical energy to be lost and converted to thermal energy. A dissipative force is non-conservative, but not all non-conservative forces are dissipative.

As @Phantomjay has noted, the only conservative forces you'll see in intro physics are gravity, the ideal spring force, and, I'd add, the electrostatic force.

 

[Caio Graco]

...but not all non-conservative forces are dissipative.

If you search on Google, you will see that nonconservative and dissipative forces are given as synonyms. Just as noted @ jbriggs444 in post # 6:

"However, the quick trip to Google indicates that many sources consider" dissipative "and" non-conservative "to be synonymous."

So can I say that a non-conservative force can be dissipative (decrease the mechanical energy of a system) or can it be even motor (increase the mechanical energy of a system)? For example: In the case of one block on another, when the bottom is pulled quickly so that the top one slides being accelerated by the kinetic frictional force. Considering the system as the two blocks, the kinetic friction force would be dissipative, but considering the system as only the top block, this would be a case in which the kinetic friction force (which is non-conservative) would not be dissipative and yes motor (provides power to the block)?

Conclusion: The force of kinetic friction, even if it is non-conservative, can be dissipative or motor. This is it?

 

[jbriggs444]

Conclusion: The force of kinetic friction, even if it is non-conservative, can be dissipative or motor. This is it?

One of our members, @sophiecentaur has a signature line that I've always liked: "Classification is the enemy of understanding". The important thing is knowing how something behaves, not what label can be slapped on it.

Yes, if one drops a piece of wood onto a belt sander and watches it fly away, and if one draws system boundaries so that the piece of wood is inside the system and the moving belt is outside, the force of kinetic friction will have added mechanical energy to the system.

The label "dissipative" on the force does not tell you this. The fact that an external force was applied to a block that was (on average during the application of the force) moving tells you this.

 

[sophiecentaur]

One of our members, @sophiecentaur has a signature line that I've always liked: "Classification is the enemy of understanding". The important thing is knowing how something behaves, not what label can be slapped on it.

Yes, if one drops a piece of wood onto a belt sander and watches it fly away, and if one draws system boundaries so that the piece of wood is inside the system and the moving belt is outside, the force of kinetic friction will have added mechanical energy to the system.

The label "dissipative" on the force does not tell you this. The fact that an external force was applied to a block that was (on average during the application of the force) moving tells you this.

Strange how this confusion exists when, in other circumstances, people are quite happy to talk in terms of Efficiency in machines when the Work OUT comes from the Work IN due to slipping friction in a mechanism. (Clutches, dragsters etc.) It's all those over simplified 'definitions' that you find in textbooks that are to blame.
'Friction' does not always imply loss of energy but the Laws of Friction we are taught tend to be presented in that context.