You are analyzing an Atwood machine with masses m1 and m2 connected over a pulley by a massless, unstretchable string. The left-hand mass, m1, rests on an inclined plane forming an angle, θ = 30∘, with the horizontal direction and has a coefficient of kinetic friction, μ. Suppose m1 = 1 kg, m2 = 2 kg, and μ = 0.2 Determine the equations of motion for the masses m1 and m2. Solve the equations of motion for the acceleration, and the tension. Find their numerical values.
![Two blocks A and B with masses mA = 10 kg and mB = 4 kg are connected by an inextensible cable and released from rest shown in Figure 1 (where block A is placed in position C ). The coefficients of kinetic friction between two blocks and the 30∘ inclined plane are μA = 0.1 and mB = 0.3. The cable is in tension in the entire motion and the sizes of blocks are negligible. (Take gravitational acceleration as 10 m/s2) (a) Draw separate free body diagrams of blocks A and B. Indicate clearly all the forces, directions of motion and coordinate systems. [4 marks] b) Based on the free body diagrams in part (a), establish the equations of motion for blocks A and B and determine the tension in the cable between two blocks. [12 marks] (c) Determine the time required for block A to move 2.5 m from positions C to D along the incline and the velocity of block A when it reaches position D. [4 marks] Figure 1](https://www.doubtrix.com/uploads/editor/3466504776qCVzpwjiZa.png)