Question

Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a massless, in extensible string and a frictionless pulley as shown in figure. The wedge is inclined at 45º to the horizontal on both sides. The coefficient of friction between block A and the wedge is 2/3 and that between block B and the wedge is 1/3. If the system A and B is released from rest, find 

(i) the acceleration of A,

(ii) tension in the string, and

(iii) the magnitude and direction of the force of friction acting on A

Answer 1

Diagram shows the various forces acting on the masses and their resolution in the direction of motion. Let us consider the two masses to be a system. The forces trying to move the system, such that A moves upwards and B moves downwards 

The forces trying to stop this motion (maximum frictional force) 

⇒ acceleration of the system is zero.

(ii) Taking equilibrium of B into consideration 

Since the stopping force is more therefore the mass system will not move.