Three masses m_1 = 1kg, m_2 = 2kg, and m_3 = 3kg are situated on an inclined pla

Question

Three masses m_1 = 1kg, m_2 = 2kg, and m_3 = 3kg are situated on an inclined plane (theta = 30degree) and connected by two strings. a) If the system is stationary and. the tension in the ropes are T_12(rope connecting m_1 and m_2), and T_23 (rope connecting m_2 and m_3), find the static frictional forces f_1s, f_2s and f_3s on the respective masses, m_1, m_2 and m_3. b) If the system is moving down the inclined plane and the coefficients of kinetic friction are mu_k1 = 0.1, mu_k2 = 0.2, and mu_k3 = 0.3 for the respective masses, find the tensions T_12 and T_23 in the strings (treated as massless).

Explanation / Answer

m1 = 1 kg

m2 = 2 kg

m3 = 3kg

Inclination of plane = 30 degree.

(a.) on mass m1

m1*g*Sin(30) = T12 + f1s

or   F1s = g/2 - T12 .

F2s = g + T12 . - T23 .

F3s = 3g/2 + T23 .

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