# Would a force of friction exist in this situation?

I have studied that friction is due to breaking of molecular bonds between surfaces while they are in motion. In the case below, I feel that since there isn't any motion, there will be no frictional force. But when I asked my physics teacher he said that there would be a frictional force, but I don't see why. The yellow lines represent fixed walls, and u is the coefficient of friction. The block is being pushed against the fixed wall with a force F.

• Friction force is being applied by a surface when there is tendency of relative motion between the surfaces in contact. Basically when a surface is rough and a body is placed over it and force is being applied then the contact forces force between the surfaces is not perpendicular to them but at some angle to vertical. So it has two components: vertical (normal force) and horizontal (called friction force). The coefficient of friction is the tan inverse of the angle between contact force and normal force. So, in short, there will be friction and this friction in the question is static.
– Manu
Sep 1, 2020 at 8:05
• @Manu you have mentioned that static friction is applied when there is tendency of relative motion between the surfaces. Can you explain how can there possibly be a tendency of relative motion in this scenario? Sep 1, 2020 at 11:58

It's possible there is a frictional force, but it is not required. Imagine a block on an inclined plane, held in place solely by static friction. One could hold another block on the incline and slide it up toward the first block, taking more of the weight of the stationary block as it presses up against it. At some point, the entire weight of the block will be supported from below, and there will be no frictional force holding it in place.

This situation is identical. Without knowing the exact specifics of how the block and wall are in contact, it could be the case that the wall is the only thing resisting the block, in which case there is no frictional force. Or, it could be the case that friction is the only thing resisting the block, in which case the wall provides no normal force. Or, it could be anywhere in between these two extremes.

A common interpretation of this scenario would be that the wall provides the entire normal force and that friction does nothing - this would perhaps be the most logical interpretation. The opposite interpretation, where the wall provides no force at all, would be a bit unusual, since there would be no reason to include the wall in the diagram in the first place. The intermediate interpretation where the wall provides some force and friction provides some force is also a bit unusual, since there is no information given to calculate the balance between them.

TL; DR: The frictional force may exist in this scenario, but it's impossible to say whether it's equal and opposite to F, zero, or anywhere in between from the information given.

• I agree that if you saw this in a homework problem you might be expected to assume that the wall is providing all the force, but also in that case the teacher would be making a bad assumption. Most real-life situations have forces that can't be determined without using a more detailed model, but homework problems often give the opposite impression. Sep 1, 2020 at 13:40

We know from experiment that friction occurs even when there is no relative motion between surfaces - this is called "static friction". So logically friction cannot be due solely to the breaking of molecular bonds between surfaces that are in motion relative to one another, because if it were then there would be no static friction. Also, if the molecular bonds between surfaces in contact were the sole cause of friction then we would see a measurable resistance when we lift one object off another one - and we do not observe that.

Static friction is due to microscopic roughness or asperity of surfaces - even surfaces that are polished to a mirror finish are not truly smooth at microscopic scales. However, this is an aspect of materials science that is not totally clear - Wikipedia says

The relationship between frictional interactions and asperity geometry is complex and poorly understood.

• Static friction starts acting only when there is a tendency of relative motion between the surfaces. How can there be relative motion in this scenario? Sep 1, 2020 at 11:59
• @ReetJaiswal I was only trying to correct the questioner’s misunderstanding of the source of friction and their mistaken idea that there is no friction without relative motion. I agree there is no friction if the block is being pushed against a fixed wall. Sep 1, 2020 at 12:10
• I think static friction is there. Suppose there are ridges in the lower surface and when the block is pushed then the part of block in contact of the the ridge will push it. Due to which a contact force is applied by the surface (as a reaction) and it is at some angle to the vertical direction giving a horizontal component (friction). And as the block is always in contact with the surface due to wall means it will not move. So it will be static friction or in extreme condition the limiting friction.
– Manu
Sep 1, 2020 at 12:24
• I don't know whether my reasoning us correct or not but I think friction would be there. Please correct me if there is flaw in my reasoning
– Manu
Sep 1, 2020 at 12:26
• I strongly believe it is not correct, at least according to newtonian mechanics(I'm not sure what current research and studies say about what happens at microscopic levels). Friction is strongly tied with motion or the tendency for motion. When we talk about friction in problems, we usually refer to roughness as a uniform property of the surfaces that has no purpose but to oppose relative motion. Therefore frictional force will arise ONLY when there is a possibility for the block to move. Of course when we talk about the real world, friction is MUCH more complicated than that. Sep 1, 2020 at 15:01

Think about it this way. If the horizontal surface was frictionless (i.e., $$μ=0$$), would the object move? No, because the wall would exert a force on the object equal and opposite to the applied force $$F$$ for a net force of zero. Therefore there is no need for a static friction force on the horizontal surface to prevent motion of the object.

However, a good "test" to determine whether or not static friction is actually relied upon in the situation depicted, is to remove the wall and see if the object moves.

Hope this help.

• You can flip this logic around to arrive at the opposite conclusion - if you remove the wall, it's still possible that the object won't move because friction will provide an equal an opposite force to the applied force F. Therefore, friction is the only force and the wall does nothing. Sep 1, 2020 at 13:39
• I would argue that if you remove the wall with the applied force $F$ present then the only reason for the object not moving is the presence of static friction. If there were no wall and no applied force $F$ on the object, then there would be no static friction even if the surface is not frictionless. A static friction force only exists in opposition to an external applied force parallel to the surface. Without a static friction force a free body diagram of the object will show it is in equilibrium. Sep 1, 2020 at 13:52
• Right, if you remove the wall, the block can still be held in place by static friction. If you remove friction, the block can still be held in place by the wall. Neither of those thought experiments illustrate whether the block is actually held in place by static friction, the wall, or both. Not sure how the scenario of F=0 enters into this, as that scenario is wholly uninteresting, with no frictional from the floor or normal force from the wall. Sep 1, 2020 at 13:59
• I don't think $F=0$ is uninteresting. Many folks don't understand that a static friction force does not exist unless it is opposing another force and that its magnitude varies with the applied force until the maximum possible static friction force is reached. So, taking the wall away, a static friction force only exists if $F$ does not equal zero, even if the surface is not frictionless. Sep 1, 2020 at 14:04
• @NuclearWang I think I see your point now. The only way to know whether or not the wall is preventing motion due to the applied force is to remove the wall. I have revised my answer accordingly. Sep 1, 2020 at 14:22

If this is a 'problem' based purely on newtonian mechanics, then NO, no frictional forces will act as there is no tendency, or even a possibility of the block to move relative to the surface, and that is exactly what is required for static friction.

What some others have mentioned, like @Manu , is that the little ridges in the surfaces will contribute to providing a contact force whose component parallel to surfaces will oppose the motion, hence, static friction. But this definition of friction is just not what is conventional when we define friction as $$F=\mu.N$$ In this definition, friction is a uniform, combined property of the two surfaces. We don't even go into the dynamics of the ridges on the microscopic scale, which is quite complex.

Therefore, if you really want to measure the frictional force in a real scenario, I would suggest placing a weighing machine(or some other normal force measuring device) between the block and the wall. This is because in the real scenario, a fraction of the force should be compensated by the ridges in the floor surface(as the little ridges act like individual systems, like individual walls), and the rest will be returned by the normal force from the rigid wall; thus equilibrium is still maintained.The only scenario that seems impossible to exist is the one where none of the applied force reaches the wall.