Ball A is attached to one end of a rigid massless rod, while an identical ball B

Question

Ball A is attached to one end of a rigid massless rod, while an identical ball B is attached to the center of the rod, as shown in the figure. Each ball has a mass of m = 0.430 kg, and the length of each half of the rod is L = 0.360 m. This arrangement is held by the empty end and is whirled around In a horizontal drde at a constant rate, so that each ball is In I uniform circular motion. Ball A travels at a constant speed of v_A = 4.50 m/s. Find (a) the tension of the part between A and B of the rod and (b) the tension of the part between B and the empty end.

Explanation / Answer

Let the tension on Mass A , = Ta
Let the tension on Mass B , = Tb
(a)
In uniform circular motion,
Ta = m*va^2/r
Ta = (0.430 * 4.5^2)/(2*0.360)
Ta = 12.09 N

(b)
Tb - Ta = m*v^2/r
Tb = Ta + m*v^2/r
Tb = 12.09 + 12.09/2
Tb = 18.14 N

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