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 = 0.440 kg, and the length of each half of the rod is L = 0.450 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 = 4.70 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

For Block A :

from the force diagram,

tension force provides the necessary centripetal force

TA = m VA2 / (2L)

TA = (0.440) (4.70)2 / (2 x 0.450)

TA = 10.8 N

the angular velocity remains same for both A and B

VA/(2L) = VB /L

VB = 4.70 / 2

VB = 2.35 m/s

B)

For Block B:

from the force diagram,

force equation can be given as :

TB - TA = m VB2 / (L)

TB - 10.8 = (0.440) (2.35)2 / (0.450)

TB = 16.2 N

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