# Static friction force on a block in a tunnel

Linked to this question: Comparing Static Frictions

Suppose there is a cuboidal vertical tunnel, and a cubical block in it such that all surface of the block are in contact with the four walls of the cuboidal tunnel respectively. All walls of the tunnel are rough with different $\mu_s$'s. And the weight of the block is $m$ and it is a point mass such that it has only 3 translational degree of freedoms.

The block is in mechanical-equilibrium.

Now the block is being pulled vertically downwards by gravity, whose force is $mg$ and upwards by the four walls of the tunnel which apply static friction.

How to measure static friction provided by four walls? Can we even measure?

• This is a completely unrealistic situation as you have to consider a) The clearances b) Any tilt of the block c) non-flatness of the walls. The force to unstick the block varies greatly with these factors mentioned. – John Alexiou May 17 '13 at 14:11
• Can you tilt the tunnel and allow only one wall to be in contact at the time? – John Alexiou May 17 '13 at 14:13
• @ja72 No, and which law of physics is being violated if such a situation is possible ? – user23503 May 17 '13 at 14:59
• How are you going to make perfectly flat walls and a perfectly fitting cube. What happens if the temperature drops and now you have a press-fit situation, or the temp rises and you have too much clearance? How are you going to control the interface geometry to make a robust measurement? – John Alexiou May 17 '13 at 15:21
• These are not physical laws . Just real-life situations . Is it even possible to have a friction-less surface ? NO , but you have those in physics questions . – user23503 May 17 '13 at 15:23

A short and academic answer would be to simply say that the friction is equal to the gravity force in case of equilibrium. So you just need to know or measure the gravitational force exerted on your cube, which you already know as $mg$ if you know the mass of the cube $m$ and the acceleration of gravity $g$.