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Computer] Figure 4.28 shows a massless wheel of radius R,
Chapter 4, Problem 4.37(choose chapter or problem)
Computer] Figure 4.28 shows a massless wheel of radius R, mounted on a frictionless, horizontal axle. A point mass M is glued to the edge of the wheel, and a mass m hangs from a string wrapped around the perimeter of the wheel. (a) Write down the total PE of the two masses as a function of the angle 0. (b) Use this to find the values of m and M for which there are any positions of equilibrium Describe the equilibrium positions, discuss their stability, and explain your answers in terms of torques. (c) Plot U (0) for the cases that m = 0.7M and m = 0.8M, and use your graphs to describe the behavior of the system if I release it from rest at 0 = 0. (d) Find the critical value of m/M on one side of which the system oscillates and on the other side of which it does not (if released from rest at 0 = 0).
Questions & Answers
QUESTION:
Computer] Figure 4.28 shows a massless wheel of radius R, mounted on a frictionless, horizontal axle. A point mass M is glued to the edge of the wheel, and a mass m hangs from a string wrapped around the perimeter of the wheel. (a) Write down the total PE of the two masses as a function of the angle 0. (b) Use this to find the values of m and M for which there are any positions of equilibrium Describe the equilibrium positions, discuss their stability, and explain your answers in terms of torques. (c) Plot U (0) for the cases that m = 0.7M and m = 0.8M, and use your graphs to describe the behavior of the system if I release it from rest at 0 = 0. (d) Find the critical value of m/M on one side of which the system oscillates and on the other side of which it does not (if released from rest at 0 = 0).
ANSWER:Step 1 of 8
(a) Let us take the zero of PE when \(\phi = 0\). As the wheel turns through angle \(\phi\) , the mass \(M\) rises by \(R(I- cos \phi )\) and \(m\) descends by \(R\phi\) .