Understanding the Relationship Between Friction and Normal Force

[monjinho]

Homework Statement

The force of friction is equal to the normal force times the coefficient of friction

Homework Equations

f=Rμ

The Attempt at a Solution

so i was trying to understand this and failed to do so for such a long time...

If a man is pushing a box and i wanted to find the force of the box, I would have to find the frictional force and subtract it from the force the man is applying to the box. From this I know that the frictional force is existing horizontally. But when i look at the equation above, i see that the frictional force is the NORMAL FORCE times the coefficient of friction! The direction of the normal force is pointing up and how can you add or subtract so freely with a horizontal force(the force man is applying to the box) when the vectors are different?

I guess my question is: how can you have the frictional force be horizontal when you are mutiplying a constant with the normal force which is a vertical value??

 

[ehild]

F=μR is only the magnitude of kinetic friction. As for the direction, it is parallel with the surface and opposes any relative motion between body and surface.

ehild

 

[monjinho]

F=μR is only the magnitude of kinetic friction. As for the direction, it is parallel with the surface and opposes any relative motion between body and surface.

ehild

? I was expecting more of an explaining than an answering...can you help me understand this problem?

 

[ehild]

I do not get you. I explained that your statement "The force of friction is equal to the normal force times the coefficient of friction" is not true. It should be "The magnitude of the force of friction is equal to the magnitude of the normal force times the coefficient of kinetic friction". The letters in f=Rμ do not mean vectors: they are scalar quantities, magnitude of forces. Why do you think that the force of friction is parallel to the normal force?

ehild

 

[monjinho]

I do not get you. I explained that your statement "The force of friction is equal to the normal force times the coefficient of friction" is not true. It should be "The magnitude of the force of friction is equal to the magnitude of the normal force times the coefficient of kinetic friction". The letters in f=Rμ do not mean vectors: they are scalar quantities, magnitude of forces. Why do you think that the force of friction is parallel to the normal force?

ehild

i do not think that the force of friction is parallel to the normal force. My question was since the frictional force is horizontal -or opposing the force- even if it's not vector, how can we get a horizontal frictional value when we multiply normal force (vertical) against the coefficient of friction? Even if its not a vector, we do subtract the frictional force from the force the man is applying and we know that the man's force is horizontal. I'm sorry if my question is confusing...:(

 

[ehild]

You do not multiply the normal force by the coefficient of friction. You have to multiply the magnitude of the normal force, and get also a scalar - the magnitude of the force of friction. But the force of friction is a vector and the normal force is also a vector, only their magnitudes are related through the coefficient of friction.

ehild

 

[monjinho]

I'm sorry. If you can expand a little, what does 'the force of friction is a vector and the normal force is also a vector, only their magnitudes are related through the coefficient of friction.' mean? How are they related through the coefficient of friction?

 

[SteamKing]

See equation in OP.

Friction force values (magnitudes) are determined largely by experiment. Experiments showed that there is a direct relationship between the magnitude of the normal force exerted by an object versus the measured magnitude of the friction force. The coefficient of friction is the ratio of two measured force magnitudes: the frictional force (acting parallel to the direction of travel) and the normal force (acting perpendicular to the direction of travel).

 

[eczeno]

the definition of $$\mu$$ is the ratio |F| / |R|. where |F| and |R| are the magnitudes of the forces F and R. thus the formula:

F = $$\mu$$ R should be written as |F| = $$\mu$$ |R| and is really just the definition of $$\mu$$. it is not a 'law of nature' as such, just a good definition that holds true under very general conditions.

 

[monjinho]

If μ is the ratio of |F| / |R|, how would you get the frictional force in the first place? Wouldn't you need the coefficient of friction? Supposing that there wasn't the coefficient of friction, is it possible that the frictional force could just equal the normal force??

I guess the main thing i don't understand is how we can get a horizontal force value when we multiply two things that are not related at all by magnitude(direction). If it is simply a scalar force, we still need the direction and need to know where the force is pointing toward for later problems.

 

[SammyS]

If μ is the ratio of |F| / |R|, how would you get the frictional force in the first place? Wouldn't you need the coefficient of friction? Supposing that there wasn't the coefficient of friction, is it possible that the frictional force could just equal the normal force??

Only in magnitude, not direction. Also, this would simply mean that the coefficient of friction is 1 .

 

[monjinho]

Only in magnitude, not direction. Also, this would simply mean that the coefficient of friction is 1 .

But don't we need the direction of the force for later problems? It seems like everything about the frictional force is not related to direction or vector at all...

 

[SammyS]

You must supply information about the direction of the force of friction from other information regarding the situation.

Kinetic friction on a moving object generally is in a direction opposite the direction of the relative velocity of the object with respect to the surface it is in contact with.

Static friction generally opposes the relative motion between two surfaces which are in contact.

 

[ehild]

If μ is the ratio of |F| / |R|, how would you get the frictional force in the first place? Wouldn't you need the coefficient of friction? Supposing that there wasn't the coefficient of friction, is it possible that the frictional force could just equal the normal force??

Monjinho,

Physics is based on experience. You have experience of force when you push a crate on the floor, don't you? You need to exert force to move it even with constant speed, so

i. there should be a resistive force between the crate and floor that opposes motion.

Pushing the crate on a smooth surface requires less force than pushing it along a rough one, like concrete.

ii. This resistive force depends on the quality of the surfaces.

You need greater force to push the same crate when it is full of heavy objects than the empty one.

iii. The resistive force depends on the weight of the object.


One can conclude that there is a resistive force that opposes the applied force when an object is moved along a horizontal surface. You call the phenomenon "friction" and the resistive force "force of friction".

You can even measure this force, in an experiment. Connect a spring to a box and pull the spring. The length of the spring increases and the force applied to the box is proportional to the increase of length.

From your experiment, you find an approximate linear relation between the weight of the object and the resistive force, the force of friction. It is interesting, as the weight is a vertical force and the resistance is horizontal, but you experience that their magnitudes are related and proportional to each other.

You ask a friend to push the box downward, and you find that higher force is needed to pull the box now. So you conclude that it is not the weight, but the force that presses the ground, (the normal force between the box and ground) that counts. The magnitude of the resistive force against sliding , the force of friction, is proportional to the magnitude of the normal force. You call this factor of proportionality the "coefficient of friction"

You can think about the cause of this resistive force. What happens if an object slides on a surface? What causes a horizontal force from the vertical one?

The surfaces are not perfectly smooth. See attached picture. If the object moves, the spikes of its surface press against those of the ground, and the spikes of the ground exert force against the object, see the red arrows. In order to slide, the unevenness has to be smoothed out somehow - by tearing the peaks off or press them away. You can see a mark when you push something along a sandy surface, as the grains of sand were moved away or pressed together. A breaking car leaves a skid mark. So there is some interaction between the sliding surfaces that can even permanently change them.

I guess the main thing i don't understand is how we can get a horizontal force value when we multiply two things that are not related at all by magnitude(direction). If it is simply a scalar force, we still need the direction and need to know where the force is pointing toward for later problems.

Those two things -the normal force and force of friction- are related , you experience it. There is no such thing as "scalar force". Force is a vector quantity, has both magnitude and direction. The force of friction is caused by the interaction between the sliding surfaces, and points along the surfaces touching each other, and it is opposite to the velocity of the moving object with respect to the surface it moves on.

ehild

 

[monjinho]

Monjinho,

Physics is based on experience. You have experience of force when you push a crate on the floor, don't you? You need to exert force to move it even with constant speed, so

i. there should be a resistive force between the crate and floor that opposes motion.

Pushing the crate on a smooth surface requires less force than pushing it along a rough one, like concrete.

ii. This resistive force depends on the quality of the surfaces.

You need greater force to push the same crate when it is full of heavy objects than the empty one.

iii. The resistive force depends on the weight of the object.


One can conclude that there is a resistive force that opposes the applied force when an object is moved along a horizontal surface. You call the phenomenon "friction" and the resistive force "force of friction".

You can even measure this force, in an experiment. Connect a spring to a box and pull the spring. The length of the spring increases and the force applied to the box is proportional to the increase of length.

From your experiment, you find an approximate linear relation between the weight of the object and the resistive force, the force of friction. It is interesting, as the weight is a vertical force and the resistance is horizontal, but you experience that their magnitudes are related and proportional to each other.

You ask a friend to push the box downward, and you find that higher force is needed to pull the box now. So you conclude that it is not the weight, but the force that presses the ground, (the normal force between the box and ground) that counts. The magnitude of the resistive force against sliding , the force of friction, is proportional to the magnitude of the normal force. You call this factor of proportionality the "coefficient of friction"

You can think about the cause of this resistive force. What happens if an object slides on a surface? What causes a horizontal force from the vertical one?

The surfaces are not perfectly smooth. See attached picture. If the object moves, the spikes of its surface press against those of the ground, and the spikes of the ground exert force against the object, see the red arrows. In order to slide, the unevenness has to be smoothed out somehow - by tearing the peaks off or press them away. You can see a mark when you push something along a sandy surface, as the grains of sand were moved away or pressed together. A breaking car leaves a skid mark. So there is some interaction between the sliding surfaces that can even permanently change them.



Those two things -the normal force and force of friction- are related , you experience it. There is no such thing as "scalar force". Force is a vector quantity, has both magnitude and direction. The force of friction is caused by the interaction between the sliding surfaces, and points along the surfaces touching each other, and it is opposite to the velocity of the moving object with respect to the surface it moves on.

ehild

WOW..thank you so much. I think I understand now. This is awesome =)

 

[eczeno]

I would like to commend ehild on taking the time to answer this question so elegantly and in such detail. this is not an insignificant task, and it was done simply to ease the confusion of a stranger. something to ponder.

 

[ehild]

WOW..thank you so much. I think I understand now. This is awesome =)

I am pleased that you feel to understand friction. It is more complicated than that, but enough for a start.

ehild

 

[ehild]

Thank you, Eczeno.

ehild

 

[eczeno]

cheers