Animation of motion

In the video I show an animation of two particles connected by a light inextensible string passing over a smooth fixed pulley on a plane and discuss the motion in preparation for the examples that follow.


Particle on a rough inclined plane with string passing over a smooth pulley

In this example I show you how to handle a problem where two particles are connected by a string passing over a pulley on a rough inclined plane.

A particle A of mass 2 kg is attached by a light inextensible string, passing over a smooth pulley to a particle B of mass 4 kg as shown in the diagram. A rests on a rough plane inclined at 30° to the horizontal.
If the particles are released from rest and the coefficient of friction between A and the plane is 0.4, find: (i) the acceleration of A, (ii) the tension in the string.