Question

1. A person swings a 0.543-kg tether ball tied to a 4.51-m rope in an approximately horizontal circle. If the maximum tension the rope can withstand before breaking is 11.9 N, what is the maximum angular speed of the ball?

2. What is the maximum angular speed of the ball if the rope is only 3.86 m?

Answer 1

Solution)

Given,

Mass, m=0.543 kg

Length, r=4.51 m

Tension, T=11.9 N

Part a)

We know, Tension, T= mv^2/r

11.9=(0.543*v^2)/4.51

So, maximum angular speed, v= 9.94 rad/s (Ans)

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Part b)

New length of rope, r'= 3.86 m

So, T= mv^2/r'

Substitute values,

11.9 N=0.543 kg*v^2/(3.86)

Speed, v= 9.197 m/s (Ans)

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