question archive A metal ball (mass m) with a hole through it is threaded on a frictionless vertical rod

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A metal ball (mass m) with a hole through it is threaded on a frictionless vertical rod. A massless string (length i) attached to the ball runs over a massless. frictionless pulley and supports a block of mass M. as shown in Figure 4.27. The positions of the two masses can be speci?ed by the one angle 6. (3) Write down the potential energy U (9). {The PE is given easily in terms of the heights shown as it and H. Eliminate these two variables in favor of 19 and the constants b and I. Assume that the pulley and ball have negligible size.) (b) By differentiating U (19] ?nd whether the system has an equilibrium position. and for what values of m and M equilibrium can occur. Discuss the stability of any equilibrium positions.

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