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. Determine the tension in the string that connects m1 and m2

Answer 1

$W_{1x}+ W_{3x} - fr = (m_1 + m_3) a\\ N_1 - W_{1y} + N_3- W_{3y} = 0\\ N_1+ N_3 = W_{1y} + W_{3y},$

$\sin 30° =\frac{ W_x}{W}\\ W_x = W \sin 30°\\ \cos 30° = \frac{W_{y} }{ W}\\ W_{y} = W \cos 30°,$

$N_1+ N_3 = W_1 \cos 30° + W_3 \cos 30°\\ W_{1x} + W_{3x} - μ (m_1 + m_3) g \cos30° = (m_1 + m_3) a\\ a =\frac{ m_1g \sin 30° + m_3g \sin 30° - μ (m_1 + m_3) g \cos 30° }{m_1 + m_3}\\ a = g \sin 30 °- μ g \cos30°,$

$a = 9.8 \sin 30 °- 0.28\cdot 9.8 \cos 30°\\ a = 4.9 - 2.38\\ a = 2.5 ~\frac{m}{s^2}.$