Solution Found!
Instead of using the system shown in Figure 3.2.6a to
Chapter , Problem 3.12(choose chapter or problem)
Instead of using the system shown in Figure 3.2.6a to raise the mass \(m_{2}\), an engineer proposes to use two simple machines, the pulley and the inclined plane, to reduce the weight required to lift \(m_{2}\). The proposed design is shown in Figure P3.12. The pulley inertias are negligible. The available horizontal space limits the angle of the inclined plane to no less than \(30^{\circ}\).
a. Suppose that the friction between the plane and the mass \(m_{2}\) is negligible. Determine the smallest value \(m_{1}\) can have to lift \(m_{2}\). Your answer should be a function of \(m_{2}\) and \(\theta\).
b. In practice, the coefficient of dynamic friction \(\mu_{d}\) between the plane and the mass \(m_{2}\) is not known precisely. Assume that the system can be started to overcome static friction. For the value of \(m_{1}=m_{2} / 2\), how large can \(\mu_{d}\) be before m1 cannot lift \(m_{2}\)?
Questions & Answers
QUESTION:
Instead of using the system shown in Figure 3.2.6a to raise the mass \(m_{2}\), an engineer proposes to use two simple machines, the pulley and the inclined plane, to reduce the weight required to lift \(m_{2}\). The proposed design is shown in Figure P3.12. The pulley inertias are negligible. The available horizontal space limits the angle of the inclined plane to no less than \(30^{\circ}\).
a. Suppose that the friction between the plane and the mass \(m_{2}\) is negligible. Determine the smallest value \(m_{1}\) can have to lift \(m_{2}\). Your answer should be a function of \(m_{2}\) and \(\theta\).
b. In practice, the coefficient of dynamic friction \(\mu_{d}\) between the plane and the mass \(m_{2}\) is not known precisely. Assume that the system can be started to overcome static friction. For the value of \(m_{1}=m_{2} / 2\), how large can \(\mu_{d}\) be before m1 cannot lift \(m_{2}\)?
Step 1 of 4
Let T be the tension in the cable attached to mass \(m_{2}\). Refer to figure below.
