# It's slope!

After working for sometime on friction I got the following result:

Suppose there is a box on top of a tilted surface and coefficient of static friction between them is $µ$. Now suppose the angle at which the surface is inclined to ground is $\theta$ and you are increasing it slowly, after reaching a certain value $\theta=p$ the force of friction reaches it's maximum point (i.e. if you now increase $\theta$ a little more, the box will fall). Then the following relation holds true: $µ=\tan(p)$

Proof:

Let the mass of the box be $m$

The diagram below will be very helpful:

The force of friction acting $=µN=µmg\cos(p)$

As net force is $0$, therefore $\cancel{mg}\sin(p)=µ\cancel{mg}\cos(p)$ $\sin(p)=µ\cos(p)$ $\boxed{µ=\tan(p)}$

Note:

• I haven't proved the diagram because I found it very easier to proof, if you want you can proof it yourself and write it in the comment it can be challenge for you!

Note by Zakir Husain
7 months, 3 weeks ago

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