**Question:**What hanging mass (in kg) must be placed on the cord to keep the pulley from rotating (see the following figure)? The mass on the frictionless plane is 5.7 kg. The inner radius of the pulley is 20 cm, and the outer radius is 39 cm. (Assume the 5.7 kg mass and the hanging mass are only connected to the inner and outer radii, respectively.)**Diagram Explanation:**The diagram illustrates a pulley setup with a 5.7 kg mass resting on an inclined plane at a 33° angle. The incline is frictionless. A cord runs over the pulley, with one end attached to the 5.7 kg mass and the other end to an unknown mass \( M \) hanging vertically. The pulley has two radii: the inner radius (20 cm) and the outer radius (39 cm), which are connected to the 5.7 kg mass and the unknown mass \( M \), respectively.

Given that: Mass on the inclined plane, m=5.7 kgHanging mass=MInner radius of the pulley, r=20 cm=0.2 mOuter radius of the pulley, R=39 cm=0.39 mFBD of m: FBD of M: FBD of pulley: Since the ropes are connected to different sections of the pulley, we can assume thatthe ropes are difference and not internally connected. So to keep the pulley from rotating, the system has to be in equilibrium.From FBD of m:T1=mgsinθFrom FBD of M:T2=MgFrom FBD of pulley:ΣTorque=0T1r=T2Rmgrsinθ=MgRM=mrsinθRM=5.7×0.20×sin33°0.39M=1.59 kg≈1.6 kg (Ans)

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Physics

What hanging mass (in kg) must be placed on the cord to keep the pulley from rotating

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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