# Static friction and work

1. Dec 9, 2007

### miss photon

can static friction do work?

2. Dec 9, 2007

### Staff: Mentor

What situation do you have in mind?

3. Dec 9, 2007

### pixel01

'static' means no displacement and of course there's no work done.

4. Dec 9, 2007

### arildno

It depends a bit on how you choose to define the situation.

For example, suppose you have two blocks resting on each other, the lowest lying on a frictionless plane, and you apply a force to the upper block.
Due to static friction between the two blocks, the lowest will start moving.

Many will here say that you have simple force transferral between the two blocks, not essentially different from what will happen within a single rigid body, and thus don't bother to call this work done.

However, you can, if you like, call simple force transferral as a type of work, since it fits the definition of work.

The most important thing, however, is that static friction can't do non-dissipative work.

5. Dec 9, 2007

### Staff: Mentor

In this context "static" means no slipping between the surfaces, not necessarily no displacement.

6. Dec 9, 2007

### pixel01

Sorry, but I can not figure out the scenario that there's no slipping but still displacement?. Could you explain a little bit more?

7. Dec 9, 2007

### Staff: Mentor

Did you see arildno's post? He gave an example of such. Here's another example that amounts to the same thing: Imagine a truck with a crate resting on its bed. As you step on the gas, the truck accelerates forward and friction between truckbed and crate pulls the crate along for the ride. The crate does not slip along the surface of the truckbed (no relative motion), thus it's static friction at work. But there's certainly displacement as truck and crate travel down the road.

8. Dec 9, 2007

### pixel01

I think we should consider the displacement of the crate against the truck, not the road surface. After all, it's the displacement between the two surfaces. We are all on earth and we are under some displacement , but not any work done from that.

9. Dec 9, 2007

### arildno

There is no single, "truest" reference frame, pixel01.

Kinetic energy of a specified system and work done upon it are not Galilean invariants, and never will be..

10. Dec 9, 2007

### pixel01

Should we go this far? All I would like to say is static friction can not do work because there is no displacement between them.

11. Dec 9, 2007

### arildno

Wherever is it stated that work concerns relative displacement??

The work of static friction is necessarily non-dissipative, and that covers it pretty much.

12. Dec 9, 2007

### pixel01

That's because I am confused by Doc for his saying : no slipping but not necessary no displacement. I stated at first " no displacement" with the meaning of displacement between the two surfaces. If I stand on a running bus, there's static friction between my feet and the floor, and there's no displacement between them. We should not take into account the displacement compared to the road side.

13. Dec 9, 2007

### Staff: Mentor

Well, viewing the truck & crate example from the (relatively) inertial frame of the ground, the crate's kinetic energy is increasing so something must be doing work on it. The only force acting in the direction of its displacement is static friction.

The important thing is what arildno stated about any work done by static friction being non-dissipative.

14. Dec 9, 2007

### pixel01

In that case, the static friction just plays the role of a connection, it can not do any work. If you use a string to pull a mass, can you say that the string has done some work?

15. Dec 9, 2007

### Staff: Mentor

I understand what you are trying to say: that the string is not an energy source, it's only transmitting the energy that your body has provided. It's a bit of a semantic issue.

Nonetheless, it's often useful to stick to the basic definition of work: $W = \vec{F}\cdot \vec{s}$. Strictly speaking you pull the string and the string pulls the mass.

16. Dec 9, 2007

### arildno

Which is why many prefer to call these types of work for "simple transferral of forces".

But, while this is a legitimate procedure, you could instead think like this:

1. Whenever doing physics, we need to specify which "system" we are talking about. However, what particular system we choose to work with is up to the physicist's pleasure&leisure.

I MIGHT call a wooden box a single system, but I am perfectly entitled to call it 2 systems or 25.

2. On basis on what I've chosen as my system, I will be able to identify what are the EXTERNAL forces acting upon it, and which forces are internal

3. Then, I must pick a reference frame to study my system with respect to, again, I have full freedom which reference frame I choose to work with.

Last edited: Dec 9, 2007
17. Dec 9, 2007

### pixel01

I can not agree with the saying: the string can do work. In fact which part of the string creates the work?, there are countless molecules sticked together and all under the tension force.
Come back to the crate and truck, if I place the crate onto a wooden board (may be 2 or 3) then all of it on the truckbed. There are many surfaces held by static friction. How come you can calculate the work done?
The static friction force is just similar to the sticky force, it can not create work. Well we can say that it transfer force, I agree.
This agrument makes me remember a funny situation: a man hits another with a rod and says the rod hits you, not me !

18. Dec 9, 2007

### arildno

Whichever part of the attached end of the string you choose to regard as your system.

19. Dec 9, 2007

### Staff: Mentor

Suit yourself. But the only thing that actually exerts a force on the mass is the string. But it might be more useful to treat the "mass + string" as a single system.
What do you mean "how come"?
What's the "sticky force"?
And, in a sense, he's correct!

20. Dec 9, 2007

### pixel01

Come back to the original question: can static friction do work?
I think the answer is NO.

If you pull a mass with a string, you and the string is a system, yes, and that system can do some work, sure, but not only the string. I have never heard in any situations that a string alone can do work.

Last edited: Dec 9, 2007