# Static Frictional Force and Work

#### xeguy

There's a disagreement going on in my department regarding whether the static frictional force does any work. My argument rests on the fact that static friction has zero displacement, hence zero work.

The other side gives the example of a system consisting of a block on a piece of paper, both sliding along due to the presence of an external force pulling the paper. The net force on the block is due to the frictional force between the block and paper. Their claim is that this net frictional force is caused by static friction, and since the paper is displaced with respect to the table the block-paper system is on, the static frictional force does work on the block.

I tried countering with the fact that the static frictional force is internal to the system, but they're hung up on the block moving wrt the table. Also, I tried to consider that this frictional force was not correlated with any reference frame that it was not in contact with, ie; block and paper can have similar frames, as well as table- paper, and system-table. No luck there. I know I'm not crazy, but maybe someone else has a better example to show that static friction cannot do work!

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#### xeguy

The disclaimer now being put forth is that the static frictional force can do work if the contact point is in motion. As for me fixing my coordinate system to the truck, they still don't like it since it is a non-intertial reference frame.

#### mmwave

I love this question but I promise no great insight in my answer.

I have to agree that putting your reference frame on the moving block is complicating things.

Let's consider first the block + paper as unit. You pull on the paper with a force such that the block + paper gets a net force of Fpull - ffriction = (Mblock + mpaper) * a
where ffriction is the friction force between the paper and the table.

Your energy input is the work done Fnet * d

Now why would you try to divide the work into work done against friiction between the paper and the block and then between the paper and the table? The friction between the paper and the table is not changed by how we try to divide up the work, so that term is not changed, the distance is not changed so the friction between the paper and the table still 'does all the work'.

I say that static friction does no work here. Comments?

#### HallsofIvy

Homework Helper
Work is force times the distance over which the force is applied.

If you have an object being kept from moving by static friction, then that friction does no work. It doesn't matter if the whole "assembly" is moving- there is no motion caused by the force.

#### scott_sieger

May be a little side tracked to the question but,

If one allows two magnets to stick to each other and you move the combination some distance are the magnets doing any work.

I have been hypoth. that when two objects are joined together their inertia is also joined so there for they are one and the same thing.

When a magnet enters the influence of another magnet then it's inertia is now bound by the other magnet. Conservation of forces comes in to play.

Any way I hope my hypoth. may help you as you have me

#### turin

Homework Helper
I'd have to think about the initial situation somemore, but, considering a block on a piece of paper moving at constant velocity, then there is no acceleration. Newton's second law says that there is therefore no net force. Further more, the block is not accelerating and the paper is not accelerating, so the force from static friction between the block and paper is zero in this situation. I still don't know what to think about those small moments between starting from rest and then obtaining a constant velocity.

#### russ_watters

Mentor
Originally posted by HallsofIvy
Work is force times the distance over which the force is applied.

If you have an object being kept from moving by static friction, then that friction does no work. It doesn't matter if the whole "assembly" is moving- there is no motion caused by the force.
You're the math master, but I'm gonna halfta disagree. As said before, its a frame of reference problem.

The problem given - a block on a piece of paper is a bad example for 3 reasons, first and foremost its incomplete. It isn't stated if the block/paper system is accelerating. If there is no acceleration, there is no static friction force between the block and paper! How can we forget Newton's 1st law?!?!? So to clarify, we must state two cases - one where the system is under constant acceleration and one where it is moving at constant speed.

Second, people are arguing over the definition of the system. It must be set and agreed upon otherwise people are arguing about different things. For work to be done on the block, 2 things must be present: a force and a displacement. Therefore the system is the piece of paper and the block and the table is external for the purpose of measuring displacement.

Now lets do my second case first: constant speed block. We have external force being applied to the paper, external displacement being measured along the table. Work? Nope. Or rather, no work is being done on the block: its moving at constant speed so according to Newton's first, there is no force on it. However, the PAPER has both a force and a displacement. Work is being done on the piece of paper. Trick question, and it doesn't really help us, does it? We want to know if you can do work on the block with static friction.

So my first case was constant acceleration. Now you have a static friction force between the block and the paper and a displacement. Clearly the only force acting on the block to cause its acceleration is the static friction force between it and the paper. Therefore: work is being done by that static friction force.

xeguy, you are arguing from both sides of the plate: you need to provide an example where work is being done otherwise there is nothing to argue. If the motion is measured externally, there must also be a measurable external force. If you measure the force internally (just the friction between the paper and block) you also measure the displacement internally (ie, ZERO).

Now my 3rd objection is just simply that its a needlessly complicated example - no point in bringing in the dynamic friction issue. How about a weight suspended by a string. Apply a force equal to the weight, and no motion, no work. Apply a bigger force, you get acceleration and work. Where's the static friction? Well its in your hand, gripping the string!

#### HallsofIvy

Homework Helper
Clearly the only force acting on the block to cause its acceleration is the static friction force between it and the paper. Therefore: work is being done by that static friction force.
No, the static friction is not doing work. Whatever force is moving the whole system is doing the work.

#### turin

Homework Helper
Originally posted by HallsofIvy
No, the static friction is not doing work. Whatever force is moving the whole system is doing the work.
If the force due to static friction were zero, what would the block do?

#### russ_watters

Mentor
Originally posted by HallsofIvy
No, the static friction is not doing work. Whatever force is moving the whole system is doing the work.
If the block is accelerating, there must be a force exerted directly on it which is causing the acceleration.

Ok, asking another way: if the static friction force isn't doing work/causing motion, what is it doing? Its an unbalanced force unless it is being opposed by something.

Also, tension in a wire: static force? Can it cause motion? Can it do work? By your definition, it appears the only way to do work on something is by pushing it - not pulling it.

#### scott_sieger

may be the word "potential" needs to come into the discussion.

Certainly there is potential to do work.

#### russ_watters

Mentor
Thought of another analogy: We seem to agree that if you push on a block with your finger, the force between your finger and the block is the force causing the motion and therefore the one doing the work.

Now what if you push at an angle from the top? The static friction between your finger and the block makes the block move forward.

#### xeguy

Thanks for the comments so far. Among my peers I seem to be the only one who doesn't like this being called "work done by the static frictional force."

Here's a more lucid example. Consider a box in a pickup truck which is accelerating in the +x-direction. There is a net force in the +x-direction, and friction between the road and the truck and the box and the truck acting in the -x-direction. The only force on the box is due to friction between the box and the truck. The attached cartoon shows it pictorially.

Since the box and the truck are both accelerating there must be a net force on the box in the x-direction. Since the only force acting on the box is friction due to the truck, this frictional force must do work. From energy considerations, the box has a change in KE, so work must be done on the box. The net displacement of both the box and the truck is wrt to the ground.

I can't argue the point that there is work done on the box. I also can't argue that the only force on the box is due to friction. I can't agree that by their definition, this is static friction. The force due to static friction is the force between two objects in contact which must be exceeded before a displacement (slippage) occurs.

I don't understand how this definition can be valid when looking at the displacement wrt an object not causing the static frictional force.

So how to rectify the fact that the box has work done on it and the only force acting on it is due to the truck? I contend it can't be counted as static friction, but I can't come up with a solid justification for it.

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#### xeguy

Originally posted by scott_sieger
May be a little side tracked to the question but,

If one allows two magnets to stick to each other and you move the combination some distance are the magnets doing any work.

I have been hypoth. that when two objects are joined together their inertia is also joined so there for they are one and the same thing.

When a magnet enters the influence of another magnet then it's inertia is now bound by the other magnet. Conservation of forces comes in to play.

Any way I hope my hypoth. may help you as you have me
You should be able to analyze the individual forces acting on each of the components of the system, as well as the system itself, and get the same answers. The net acceleration of the system is the same as that of its components.

In your example I would say the magnets themselves do no work. The only force on them with a net displacement is the one you are exerting on it. It would be that force that does work on the system.

**Corrected typo.

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#### xeguy

Also, the masses of the truck and box are different.

#### xeguy

Originally posted by russ_watters

Now lets do my second case first: constant speed block. We have external force being applied to the paper, external displacement being measured along the table. Work? Nope. Or rather, no work is being done on the block: its moving at constant speed so according to Newton's first, there is no force on it. However, the PAPER has both a force and a displacement. Work is being done on the piece of paper. Trick question, and it doesn't really help us, does it? We want to know if you can do work on the block with static friction.
If the block and paper are moving together at a constant velocity, they both have zero net force acting on them. There is friction on the paper due to the table which acts opposite to the external force. If there wasn't friction between table and paper, the paper and hence the system would be accelerating.

#### russ_watters

Mentor
Originally posted by xeguy
I can't agree that by their definition, this is static friction. The force due to static friction is the force between two objects in contact which must be exceeded before a displacement (slippage) occurs.
Static friction is any static friction, not just the theoretical maximum static friction. HERE is a graphical representation.
I don't understand how this definition can be valid when looking at the displacement wrt an object not causing the static frictional force.
Not sure I understand. Why does it matter where the force comes from? A free body diagram shows nothing but the force at the point where it touches the object. It simplly doesn't matter if (in my example) you are pushing the box with your finger or with a stick. Its not part of the calculations.
So how to rectify the fact that the box has work done on it and the only force acting on it is due to the truck? I contend it can't be counted as static friction, but I can't come up with a solid justification for it.
Sorry, but there is only way to reconcile the discrepancy....
If the block and paper are moving together at a constant velocity, they both have zero net force acting on them. There is friction on the paper due to the table which acts opposite to the external force. If there wasn't friction between table and paper, the paper and hence the system would be accelerating
Yes. But that still means that the force pulling the paper is doing work on it. And that of course also means the friction force between the paper and the table is doing negative work on it. The block has no lateral forces acting on it at all.

#### xeguy

Originally posted by russ_watters
Static friction is any static friction, not just the theoretical maximum static friction. HERE is a graphical representation.
Very true. Either way, the displacement as a result of static friction wrt the two surfaces in contact is zero.

Not sure I understand. Why does it matter where the force comes from? A free body diagram shows nothing but the force at the point where it touches the object. It simplly doesn't matter if (in my example) you are pushing the box with your finger or with a stick. Its not part of the calculations.
In the truck example I posted above, we are looking at the work done by the force of friction on the box due to the truck. I don't think it should be called "static friction" considering we are looking at a force which acts over zero distance between two objects in contact. Unfortunately, this is boiling down into an argument about semantics. If this is a case of "static friction doing work" then a lot of physics students are being given incorrect information because many textbooks state that static friction does no work. The caveat in this example is that the point of contact between the two surfaces is accelerating. I can buy it as a frictional force, but to call it static friction seems misleading.

Sorry, but there is only way to reconcile the discrepancy....
Which is...?

Yes. But that still means that the force pulling the paper is doing work on it. And that of course also means the friction force between the paper and the table is doing negative work on it. The block has no lateral forces acting on it at all.
Sorry, I should've said net work.

#### russ_watters

Mentor
Originally posted by xeguy
Which is...?
Accept that static friction forces can do work.
In the truck example I posted above, we are looking at the work done by the force of friction on the box due to the truck. I don't think it should be called "static friction" considering we are looking at a force which acts over zero distance between two objects in contact. Unfortunately, this is boiling down into an argument about semantics. If this is a case of "static friction doing work" then a lot of physics students are being given incorrect information because many textbooks state that static friction does no work. The caveat in this example is that the point of contact between the two surfaces is accelerating. I can buy it as a frictional force, but to call it static friction seems misleading.
What would you call it? In any case, I'd be interested to read a physics text that says specifically that static forces can't do work.

Also, there is no way to define your frame of reference to both include the static friction force and eliminate the motion while still ending up with balanced forces. It seems to me you are describing the motion in one frame of reference and the force in a different one.

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#### xeguy

Originally posted by russ_watters
Accept that static friction forces can do work. What would you call it? In any case, I'd be interested to read a physics text that says specifically that static forces can't do work.
This has to be a special case then. I would call it the work done by friction, but it's just semantics. Refer to any number of introductory texts which discuss the work done by static friction.

Also, there is no way to define your frame of reference to both include the static friction force and eliminate the motion while still ending up with balanced forces. It seems to me you are describing the motion in one frame of reference and the force in a different one.
Exactly the problem. No one wants to do the analysis from a non-inertial frame. :-)

#### krab

Originally posted by russ_watters
...So my first case was constant acceleration. Now you have a static friction force between the block and the paper and a displacement. Clearly the only force acting on the block to cause its acceleration is the static friction force between it and the paper. Therefore: work is being done by that static friction force.

... How about a weight suspended by a string. Apply a force equal to the weight, and no motion, no work. Apply a bigger force, you get acceleration and work. Where's the static friction? Well its in your hand, gripping the string!
Russ, your line of reasoning sounds downright silly to me. Static friction occurs because of molecular forces between two objects. In a sense, two objects become one. If these forces can be thought of as doing work when you accelerate something, then so can all the forces between all the atoms holding something together. For me, this concept lacks any physical utility. Much simpler to state that the bigger force supplied by your hand, times the distance over which it is applied, is equal to the increase in energy of the weight. If the string slips, then there is dynamic friction, and it is easy to calculate the energy that is converted to heat. Static friction doesn't have to come into any of these calculations. It is only a means of transmitting a force through a body. See http://rabi.phys.virginia.edu/106/2001/ps2a.html [Broken] especially problems 5 and 6.

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#### turin

Homework Helper
Originally posted by xeguy
I would call it the work done by friction, but it's just semantics.
Exactly.

#### turin

Homework Helper
Originally posted by russ_watters
... there is no way to define your frame of reference to both include the static friction force and eliminate the motion while still ending up with balanced forces.
We do it with gravity all the time in the first semester physics. If the free body diagram has an unbalanced force, the way I drew the free body diagram was to draw an arrow off to the side pointing in the direction of the resultant acceleration. However, gravity was always treated as weight, even though gravity is actually an acceleration. All you have to do is stick a force on the free body diagram in the opposite direction of the resultant acceleration and equal to mass of the body times the resultant acceleration.

Originally posted by xeguy
I would call it the work done by friction, but it's just semantics.
Exactly.

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