Finding mass of block B with two blocks on inclined planes and friction

[skaterbasist]

I have a conceptual problem regarding the following scenario:

Try to imagine a triangle with two blocks on each side, attached together with a rope, and a pulley at the tip of the triangle.

Block A & B are attached to each other through a rope. Blocks A & B are in static equilibrium, each on an inclined plane of angle theta and phi. The pulley at the top of this triangle has a frictionless pulley. Block A has a static friction coefficient of 0.1, and block B has a static coefficient of 0.2. Block A has a mass of 10kg, and we are asked to find the mass of Block B with the given information.

Now, my problem is, in which direction do we assume the static frictional force to be? Since the two blocks are in static equilibrium, do we assume that that the static force is up the plane in each separate free-body diagram? Do we assume that the tendency of friction and movement is in one particular direction and then draw a free-body diagram, with the static frictional force going up on one side and down on the other side [of the surfaces in the triangle]? And why does the mass of block B depend on which assumption we use [I tried solving the problem and got 4.87kg when we assumed the direction of friction to go in one direction and 7.66kg when we assumed the direction of friction to go in the other direction).

I'm having difficulties understanding which assumptions to use to find the correct mass of block B.

Please keep in mind that the problem is assuming that both block A and B are in static equilibrium with no motion or movements.

Thank you!

 

[Studiot]

Is this homework?

You have seven variables, (W_a; W_B; T; F_a; F_b; R_a and R_b)

You are given one and can generate six linear equations: Either vert an horiz equilibrium or parallel and normal equilibrium at A and B; and two friction equations.

You should therefore be able to solve the system uniquely with the friction forces being + or - according to whether you guessed their direction correctly or not.

You have not stated the values of theta and phi so I cannot check your working, but I expect there is an erithmetic error is you have two answers.