(Solution) - Instead of using the system shown in Figure 3 2 6a to -(2025 Original AI-Free Solution)

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Instead of using the system shown in Figure 3.2.6a to raise the mass m2, an engineer proposes to use two simple machines, the pulley and the inclined plane, to reduce the weight required to lift m2. The proposed design is shown in Figure. The pulley inertias are negligible. The available horizontal space limits the angle of the inclined plane to no less than 30°.
a. Suppose that the friction between the plane and the mass W2 is negligible. Determine the smallest value m1 can have to lift m2. Your answer should be a function of m2 and ?.
b. In practice, the coefficient of dynamic friction ?d between the plane and the mass m2 is not known precisely. Assume that the system can be started to overcome static friction. For the value of m1 = m2/2, how large can ?d be before m1 cannot lift m2?