Hi, I have a question and I hope anyone could answer it:

Two touching bars 1 and 2 are placed on an inclined plane forming an angle α with the horizontal shown in Figure. The masses of the bars are equal to m_{1} and m_{2} and the coefficients of friction between the inclined plane and the bars are equal to k_{1} and k_{2} respectively, with k_{1} > k_{2} .

Find

(a) The force of interaction of the bars in the process of motion;

(b) The minimum value of the angle α at which the bars start sliding down.

Answer:

Let us indicate the positive direction of the x-axis along the incline (Fig.). Figures show the force diagram for the blocks.

Let, R be the force of interaction between the bars and they are sliding down with the same constant acceleration w.

Newton’s second law of motion in projection form along the x-axis for the blocks gives:

(b) when the block just slides down the plane w=0, so from Eqn. (3)