# Vectorial issue of friction

• schrodingerwitch
In summary: In the example above, if the surfaces are horizontal, the friction force is horizontal and in the opposite direction of the object's velocity.In summary, the frictional force between an object and a horizontal surface is dependent on the friction coefficient and the normal force, but its direction is always opposite to the object's motion. This relationship is based on the law of friction and is consistent with experimental physics. The units for the frictional force are implied by this law. This concept is not explicitly mentioned in most textbooks, but is crucial for understanding the nature of friction.
schrodingerwitch
Considering an stopped object in a horizontal plane, the frictional force between the object and the plane would be the product of the friction coefficient (static or kinetic if there was movement between the surfaces) by normal. Since the normal in this case would be given by N (vector) = - mg j (unit), we would have the frictional force given by F (vector) = - mgμ j (unit).
But we know that the frictional force must act against the direction of the object's movement, so its unit vector must have direction î (unitary).

Is this change in the unit vector simply a convention that comes from agreement with experimental physics or is there some kind of vector transformation that makes this vector j^ already become a vector î?

The books I researched were Halliday, Tipler, Moysés and Young and Freedman. In none of them did I see comments about it, so I think it might be trivial, but I wanted to clear that doubt. The only book that talked about it was Alonso and Finn - A University Course, but it was just a comment and I found it confusing.

schrodingerwitch said:
Is this change in the unit vector simply a convention that comes from agreement with experimental physics or is there some kind of vector transformation that makes this vector j^ already become a vector î?
It's a consequence of the law of friction, where the resisting force of friction is in the direction of relative motion of the surfaces and depends on the magnitude of the normal force between the surfaces. The unit vectors are implied by and deduced from the law.

I'll restate what @PeroK just explained, but slightly differently.
schrodingerwitch said:
Considering an stopped object in a horizontal plane, the frictional force between the object and the plane would be the product of the friction coefficient (static or kinetic if there was movement between the surfaces) by normal. Since the normal in this case would be given by N (vector) = - mg j (unit), we would have the frictional force given by F (vector) = - mgμ j (unit).
No, the frictional force is not the product of the friction coefficient (a scalar) and the normal force (a vector) acting on the surface. (If so, the friction force would be perpendicular to the surface, as you note.) Instead, the magnitude of the friction force (for kinetic friction, at least) is given by the product of the friction coefficient (a scalar) and the magnitude of the normal force (another scalar).

The direction of the friction force (as @PeroK explained) always opposes the sliding between the surfaces and is parallel to those surfaces.

vanhees71 and PeroK

## 1. What is the vectorial issue of friction?

The vectorial issue of friction refers to the fact that friction is a vector quantity, meaning it has both magnitude and direction. This means that the direction of frictional force can affect the overall motion of an object.

## 2. How does the direction of friction affect an object's motion?

The direction of friction can either oppose or assist the motion of an object. For example, if the frictional force is in the opposite direction of an object's motion, it will slow down the object. On the other hand, if the frictional force is in the same direction as the object's motion, it can actually help the object move.

## 3. What factors affect the direction of friction?

The direction of friction is affected by the surface materials, the weight of the objects in contact, and the angle at which the objects are in contact. These factors can influence the magnitude and direction of the frictional force.

## 4. How does friction affect the efficiency of machines?

Friction can decrease the efficiency of machines by converting some of the input energy into heat. This means that some of the energy put into a machine is lost due to friction, resulting in a decrease in efficiency.

## 5. How can we reduce the negative effects of friction in machines?

To reduce the negative effects of friction in machines, lubricants can be used to decrease the amount of friction between moving parts. Additionally, using materials with lower coefficients of friction can also help reduce the negative impact of friction on machine efficiency.

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