Question

Three packing crates of masses, M1 = 6 kg, M2 = 2 kg and M3 = 8 kg are connected by a light string of negligible mass that passes over the pulley as shown. Masses M1 and M3 lies on a 30o incline plane which slides down the plane. The coefficient of kinetic friction on the incline plane is 0.28. A. Draw a free body diagram of all the forces acting in the masses M1 and M2. [2 marks] B. Determine the tension in the string that connects M1 and M2.

Answer 1

A.

B. According to Newton's second law

$T_1-m_2g=m_2a$

$-T_1+T_2-\mu m_1g\cos30°+m_1g\sin30°=m_1a$

$-T_2-\mu m_3g\cos30°+m_3g\sin30°=m_3a$ .

So, we have

$T_1-2g=2a$

$-T_1+T_2-0.28\cdot 6\cdot9.81\cdot \cos30°+6\cdot9.81\cdot\sin30°=6a$

$-T_2-0.28\cdot8\cdot9.81\cdot\cos30°+8\cdot 9.81\cdot\sin30°=8a$

Solving the system of equations we obtain that $T_1=21.588\ (N)$ . Answer