Ball A is attached to one end of a rigid massless rod, while an identical ball B
ID: 1397081 • Letter: 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 = 0.510 kg, and the length of each half of the rod is L = 0.430 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 = 5.20 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) from the given data, angular speed of each ball, w = VA/RA
= 5.2/(2*0.43)
= 6.05 rad/s
TAB = m*a_A
= m*RA*w^2
= 0.51*(2*0.43)*6.05^2
= 16.05 N
b) TBO = TAB + m*a_B
= 16.05 + m*RB*w^2
= 16.05 + 0.51*0.43*6.05^2
= 24.08 N
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