A particle P, of mass 40kg, placed on a rough horizontal plane, is connected to another particle Q, of mass 50kg, hanging freely, by means of a light inextensible string which passes over a smooth pul

Here is the solution to question 2(i) part b:

2(i) A particle P, of mass 40kg, placed on a rough horizontal plane, is connected to another particle Q, of mass 50kg, hanging freely, by means of a light inextensible string which passes over a smooth pulley at the top edge of the plane. Given that the plane is inclined at $30^\circ$ to the horizontal and that the coefficient of friction between the plane and particle is $\frac{\sqrt{3}}{4}$. Find:

b) the magnitude and direction of the force exerted on the string by the pulley

Step 1: Identify the forces acting on the pulley due to the string.
The string exerts two tension forces on the pulley