Two boxes on a horizontal plane with coefficient of friction µ are connected by a massless string. The left-hand box has mass m and the right-hand box has mass 2m. A force F is applied to the right-hand mass at an angle θ with respect to the horizontal so that they move to the right at constant acceleration. What is the magnitude of the tensi

T = (3μmg - Fcosθ) / 2

Explanation:

Since the boxes move to the right, the net force on box of mass 2m is

Fcosθ - 2μmg + T = ma (1) where Fcosθ = horizontal component of applied force, 2μmg = frictional force and T = tension in string and a = acceleration of box

The net force on the box with mass m is

μmg - T = ma (2) where μmg = frictional force, T = tension and a = acceleration of boxes.

Equating (1) and (2) we have

Fcosθ - 2μmg + T = μmg - T

collecting like terms

Fcosθ - 2μmg - μmg = - T - T

Fcosθ - 3μmg = - 2T

(3μmg - Fcosθ) / 2 = T

T = (3μmg - Fcosθ) / 2