Suppose that in the same Atwood setup another string is attached to the bottom o

Question

Suppose that in the same Atwood setup another string is attached to the bottom of m1 and a constant force f is applied, retarding the upward motion of m1. If m1 = 4.70 kg and m2 = 9.40 kg, what value of f will reduce the acceleration of the system by 50%?
N

Explanation / Answer

T = 4.7*(9.81+a) and T + 9.4*a = 9.4*9.81 =>4.7*9.81 + 4.7a + 9.4a = 9.4*9.81 =>4.7*3*a = 4.7*1*9.81 =>a = 9.81/3 reduce the acceleration by 50 % => a = 9.81/6 T = 4.7*(9.81+a) + f =>T = 4.7*(9.81+(9.81/6)) + f and T + 9.4*a = 9.4*9.81 =>4.7*(9.81+(9.81/6)) + f + (9.4*(9.81/6)) = 9.4*9.81 =>f = 23.0535 N

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