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 = 0.530 kg, and the length of each half of the rod is L = 0.480 m. This arrangement is held by the empty end and is whirled around in a horizontal circle at a constant rate, so that each ball is in uniform circular motion. Ball A travels at a constant speed of vA = 5.80 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

a)
Between A and B , let the tension be T1
This tension is providing centrepetal force for A
T1 = mA*vA^2/rA
=0.530* (5.8)^2 / (2*0.480)
=4.28 N

b)
w = VA/rA
= 5.8/(2*0.48)
=6.04 rad/s
vB = rB*w
= 0.48*6.04
= 2.9 m/s

For B and empty end let the tension be T2
then T2-T1 provided the necessary centrepetal force
T2-T1 = mB*vB^2/rB
T2 - 4.28 = 0.53 * (2.9)^2 / (0.48)
T2 = 13.56 N
Answer: 13.56 N

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