friction FM doubt

F=μR
I'm just slightly confused as to why there's a relationship between friction and the normal reaction force, as the forces are perpendicular to each other? Surely they act independently? x

Push a book along your desk.

Press down on the book and push it along your desk.

it makes sense if I think about it like that, but again aren't the fore independant? the friction shouldn't affect the reaction force?

The normal reaction force is equal and opposite to the force exerted by the object on the surface (or a component of that force depending on the angle of the surface).

So it may make more intuitive sense to you to think about it this way for a simple horizontal surface:

The maximum friction force F is proportional to the force exerted by the object on the surface. So a heavier object or an object that is pressed against the surface is harder to move as described above.

oh ok, but isn't the reaction force independent of friction? the reaction force is equal and opposite to the weight acting downwards, so how does it relate to friciton?
Sorry

No it's not independent of friction. I'm wondering what kind of explanation you're looking for. Are you happy with the fact that heavier objects or objects that are pushed down are harder to move due to increased friction?

Also note that friction arises because the surfaces are rough, So you have saw-tooth like surfaces locking/moving against each other, where the sides of each dip/tooth are at an angle (not all vertical or horizontal)
https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/6-2-friction/
So to slide the top surface horizontally, its teeth needs to "jump" into the next horizontal dip. The harder you push down, the harder it is for each tooth to rise out of the current dip and move into the next one. The angle the sides are at effectively couples the horizontal and vertical forces as at a small scale you analyze the motion along the (diagonal) side, which is affected by both horizontal and vertical forces.

As a very simplified example, consider a block on a slope (say 45 degrees). You apply both horizontal and vertical forces (downwards). The block will slide up the slope when the horizontal force > vertical force. So doubling the vertical force will mean that the horizontal force will have to be doubled to get motion up the plane (a component in the horizontal direction). This is a very simple example for one tooth / dip. Obviously the coefficient of friction represents an average of such teeth/dips and the angles etc.

A famous example
https://www.youtube.com/watch?v=AX_lCOjLCTo&ab_channel=Discovery
where the friction depends on the total contact area

No it's not independent of friction. I'm wondering what kind of explanation you're looking for. Are you happy with the fact that heavier objects or objects that are pushed down are harder to move due to increased friction?

that's really interesting thank youu xx
who owns a phonebook though lol I don't think I've ever seen one? oh wait I have, but nothing like the one in that video

idk I just want perhaps a physics-y explanation of why the components aren't/are separate x
yep that makes sense

The animation in the second section in
https://dewwool.com/factors-affecting-friction/
is what I was trying to describe. There are lots of small motions along the diagonal parts of the rough surface, these short diagonals couple the horizontal and vertical forces.

If the motion was "pure" horizontal, your original point would be correct. However, the rough surface has lots of diagonal faces which is the friction.

What @mqb2766 posted should help but please let us know if there's anything you still don't understand. You just have to imagine a surface zoomed in and see how pushing down can affect things: