Two masses, M1, and M2 are sitting on an inclined plane that is 30 degrees to th

Question

Two masses, M1, and M2 are sitting on an inclined plane that is 30 degrees to the horizontal (theta). They connected by a string, the mass closest to the pulley (M2) is connected to a hanging mass M3. Set up the equation of motion for each of the masses. Then solve them simultaneously to determine the value of acceleration and the tension between M1 and M2 and the Tension between M2 and M3. M1=10kg,M2=20kg, M3=30 kg, Theta=30

Explanation / Answer

Equations for net forces on each object: M1 F = T1 - m1gsin(30)= m1a 10a = T1 - 49 M2 F = T2 - (T1 + m2gsin(30)) = m2a 20a = T2 - T1 - 98 M3 F = m3g - T2 = m3a 30a = 294 - T2 Now we have 3 equations and 3 unknowns: 10a - T1 =-49 --> T1 = 10a + 49 20a - T2 + T1 = - 98 30a + T2 = 294 --> T2 = 294 - 30a Now replace the values of T1 and T2 in the 2nd equation 20a - (294 - 30a) + (10a + 49) = -98 60a - 245 = -98 60a = 147 a = 2.45 m/s^2 Now plug this value for a back into the original equations T1 = 10*(2.45) + 49 = 73.5 N T2 = 294 - 30*(2.45) = 220.5 N a = 2.45 m/s^2 T1 = 10*(2.45) + 49 = 73.5 N T2 = 294 - 30*(2.45) = 220.5 N

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