The relationship between friction and mass

[George2020]

Homework Statement

How does mass effect coefficient of friction and both static and kinetic friction along a horizontal surface? How does the material affect of a horizontal surface affect coefficient of friction and horizontal and static friction.

Relevant Equations

F= mu x Fn
mu= Ff/Fn

Mass is directly proportional to static and kinetic friction and inversely proportion to the coefficient of friction.
Material affects the coefficient of friction as well as both static and kinetic friction. eg rough surface will have a higher coeffieiceint of friction

 

[haruspex]

The question should refer to weight, not mass.

Mass is directly proportional to static and kinetic friction

Consider a block resting on a horizontal surface, no other forces applied. What is the frictional force?

inversely proportion to the coefficient of friction.

How do you arrive at that? (Maybe I can guess.)

rough surface will have a higher coeffieiceint of friction

Not necessarily.

 

[George2020]

Friction force is a product of coefficient of friction and normal force . However, on a horizontal surface the normal force is mass x gravity. Hence, the relationship between mass and friction is directly proportional.

How does material affect the coefficeint of friction affect and static and kinetic friction? How will a rough material not have a higher coefficient of friction? Please explain

 

[haruspex]

on a horizontal surface the normal force is mass x gravity

Even so, it should refer to weight. Gravity is different in different places.

Friction force is a product of coefficient of friction and normal force

It's not that simple for static friction. Try to answer my question in post #2.

How will a rough material not have a higher coefficient of friction?

See e.g. https://www.qualitymag.com/articles...ould-you-make-the-surface-rougher-or-smoother

 

[George2020]

On a horizontal surface the only forces acting are normal force and force of gravity. But if the gravity is constant for different places should increase the mass not increase the friction force and coefficient as well. ?

 

[Lnewqban]

Friction force is a product of coefficient of friction and normal force .
...

That concept may lead to confusion in the future.
The coefficient is established in experimental way for pair of surfaces of specific material and roughness combination.
It seems to be the same concept, but it is not, in my opinion.

That coefficient is basically telling you up to what percentage of the magnitude of a normal force can become a resistive force that opposes the relative movement of both surfaces.
Two values are found for each combination: the bigger one (static coefficient) is for before the relative movement happens, while the smaller one (dynamic coefficient) is for once there is relative movement between the surfaces.

None of those coefficients are dependent on the mass, weight or pressure on the contact patches, only on the nature of the surfaces.

 

[George2020]

Thanks for the feedback for clarifying the subject. But if I do not go into much detail and stick to basics, the material should increase both the friction and coefficient of friction. Or else how do you explain why the coefficient is fixed for different material ?
If you increase the weight do you not increase the frictional force as well more for static friction than kinetic friction. Please advise if my understanding is correct .
Thanks

 

[etotheipi]

Friction force is a product of coefficient of friction and normal force . However, on a horizontal surface the normal force is mass x gravity. Hence, the relationship between mass and friction is directly proportional.

Really you have $F_s \leq \mu N$. That just means that $F_s$ is whatever it needs to be to give static equilibrium, up to a maximum threshold.

 

[jbriggs444]

On a horizontal surface the only forces acting are normal force and force of gravity. But if the gravity is constant for different places should increase the mass not increase the friction force and coefficient as well. ?

The coefficient is (nominally at least) a constant depending only on the nature of the surfaces. It does not depend on the normal force.

 

[Lnewqban]

Thanks for the feedback for clarifying the subject. But if I do not go into much detail and stick to basics, the material should increase both the friction and coefficient of friction. Or else how do you explain why the coefficient is fixed for different material ?
If you increase the weight do you not increase the frictional force as well more for static friction than kinetic friction. Please advise if my understanding is correct .
Thanks

Sorry, I can't fully understand your last question.
A combination of two materials (at specific temperature) and surface roughness always gives you the same coefficient, for practical terms.

If you change one or both materials, then the value of the coefficient can increase or decrease.
Example: You are pushing a heavy wood piece of furniture over ceramic tile floor, then you insert a sheet of Teflon in between all points of contact in order to push with less effort.

If you want to obtain more friction from a specific combination of two materials and surface roughness, then you apply more normal force upon the surfaces in contact.
Example: When you want to decelerate your car faster, you push harder on the brake pedal, which increases the force that the calipers exert over the brake pads, among which the brake disks slide.

I have mentioned temperature above, because the coefficient for some combinations of two materials changes some with temperature (example: cheap brake pads become less effective when too hot).

 

[haruspex]

If you increase the weight do you not increase the frictional force as well more for static friction than kinetic friction.

If you increase the normal force between two sliding surfaces then you increase the kinetic friction.
In the situation you are considering, the normal force is the weight, but if you think of it as the frictional force being proportional to the weight you might fall into the trap of using that when it does not apply.

For static friction, increasing the normal force increases the maximum force of static friction. It does not necessarily increase the actual force of friction.
Consider a block mass m resting on a horizontal surface. A horizontal force F is applied, but this is not enough to slide the block. The frictional force is therefore F. If we put another mass on top to increase the weight, the frictional force is still F.