# Static friction and work

#### miss photon

can static friction do work?

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#### pixel01

can static friction do work?
'static' means no displacement and of course there's no work done.

#### arildno

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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.

#### Doc Al

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'static' means no displacement and of course there's no work done.
In this context "static" means no slipping between the surfaces, not necessarily no displacement.

#### pixel01

In this context "static" means no slipping between the surfaces, not necessarily no displacement.
Sorry, but I can not figure out the scenario that there's no slipping but still displacement?. Could you explain a little bit more?

#### Doc Al

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

#### pixel01

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.
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.

#### arildno

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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..

#### 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.

#### arildno

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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.
Wherever is it stated that work concerns relative displacement??

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

#### pixel01

Wherever is it stated that work concerns relative displacement??

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

#### Doc Al

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All I would like to say is static friction can not do work because there is no displacement between them.
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.

#### pixel01

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.
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?

#### Doc Al

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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?
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.

#### arildno

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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?
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.

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#### pixel01

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.
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 !

#### arildno

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In fact which part of the string creates the work?, there are countless molecules sticked together and all under the tension force."
Whichever part of the attached end of the string you choose to regard as your system.

#### Doc Al

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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.
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.
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?
What do you mean "how come"?
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.
What's the "sticky force"?
This agrument makes me remember a funny situation: a man hits another with a rod and says the rod hits you, not me !
And, in a sense, he's correct!

#### 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.

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#### arildno

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What determines whether a force is "external" or "internal"?
Some intrinsic feature of reality, or the physicist's arbitrary choice of study object?

#### arildno

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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 can do work.
And you can be one system, exerting force upon a second system called the string, exerting force upon a third system called a block, or whatever.

#### pixel01

Suit yourself. But the only thing that actually exerts a force on

And, in a sense, he's correct!
Can a man argue like that before court?

#### arildno

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"Sure enough, but you hold moral responsibility for predictable consequences of your own actions".

#### russ_watters

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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.
You are simply reading too far into the situation and applying unnecessary constraints. Ie:
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.
You are defining your system wrong. We want to know the work done on the lower box with respect to the ground. So there is motion and there is work being done. Where does it come from if not the static friction? The only thing applying a force to the second block to make it move is the static friction between the two boxes.

Put it another way: if the friction between the two boxes were zero, would there be any force on the lower block or motion of that block?

To use the string example, if the static friction between your fingers and the string was zero, would work be performed on the object you are trying to pull?

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