(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two blocks with the same mass m = 1 kg are stationary on two slopes with slope angles of 30 and 45 degrees. Both blocks are connected with the larger one in the middle via two pulleys.

Made a sketch to make it clearer:

[tex]\alpha[/tex]= 30°

[tex]\beta[/tex]=45°

m = 1 kg

M = mass of the large block in the middle

Question: What is the static friction coefficient of the two blocks, if both of them start sliding at the same time, when M is big enough? Coefficient is the same for both blocks.

2. Relevant equations

Equation for static friction coefficient:

[tex]\mu[/tex]_{s}= F_{s}/F_{N}(F_{S}is static friction force, F_{N}is normal force)

F_{N}= mg[tex]\times[/tex]cos[tex]\phi[/tex] (Phi being either 30 or 45 degrees)

3. The attempt at a solution

Both coefficients are the same, so the ratio of both static friction forces and normal forces must be the same.

Now if the system is in equilibrium, both static friction forces must be euqal to the force with which the body in the center with mass M is pulling them upwards the slope (that would me Mxg or Mxg/2 for each block) MINUS the dynamic component of force of mass of each block (which is assisting the static friction force with pulling downwards).

But here it gets messy, as I'm just not sure enough about all the forces involved and how to properly evaluate them and I have a feeling I'm really over complicating things.

I apologize for any nonsense that I've might written and I'd be happy to provide some additional info if it's needed. Thanks in advance.

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# Static friction coefficient on different slopes

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