A compact mass M is attached to the end of a uniform rod, of equal mass M and le

Question

A compact mass M is attached to the end of a uniform rod, of equal mass M and length L that is pivoted at the top (Fig. P15.51). (a) Determine the tensions in the rod at the pivot and at the point P when the system is stationary. (Use M, L, y, and g in your equations as appropriate.) at the pivot T = at the point p T= (b) Calculate the period of oscillation for small displacements from equilibrium, and determine this period for L = 1.70 m. (Suggestions: Model the object at the end of the rod as a particle and use the following equation: T = 2 pi squareroot I/mgd.)

Explanation / Answer

a) when the system is stationary then tension at the pivot will be equal to the total weight of rod and compact mass.

So tension at the pivot will be (Mg + Mg) = 2Mg

Tension at point P will be equal the to weight which is below point P.

So that weight will be equal to = (Mg + Myg/L)

b) moment of inertia of rod and mass about pivot point = (ML² + ML²/3) = (4/3)ML²

And distance of center of mass from the pivot point = (M*L+M*L/2)/(2M) = ¾L

So d = ¾L

So T = 2((4/3)ML²/(Mg(¾L)) = 2((16/9)L/g) = 2((16*1.7)/(9*9.81)) = 1.113 s

So T = 1.113 s

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