please provide good explanation thank you A pulley system is attached securely t

Question

please provide good explanation thank you

A pulley system is attached securely to the corner of a ceiling and connects to masses M_1 and M_3 as shown. Under M_3 sits another mass, M_2. Mass M_1 rests on a 65 degree incline, while masses M_2 and M_3 are on a 23 degree incline. The coefficient of kinetic friction between the masses and the inclines is mu_k = 0.10, while the coefficient of static friction between M_2 and M_3 is mu_s = 0.90. If M_2 = 1.20 kg and M_3 = 1.50 kg, what is the maximum mass for M_1 such that M_3 does not slip off of M_2 as M_3 is pulled (accelerated) up the incline?

Explanation / Answer

Here, Maximum mass of M1 = (M2g * sin23 - uk * M2g * cos23 + M3g * sin23 - us * M3g * cos23)/(g * sin65)

         = (1.2 * 9.8 * sin23 - 0.10 * 1.2 * 9.8 * cos23 + 1.5 * 9.8 * sin23 - 0.1 * 1.5 * 9.8 * cos23)/(0.9 * 9.8 * sin65)

        = 0.988 kg

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