Concept explainers
A ball is swung in a horizontal circle as shown below. The ball swings from various lengths of rope at the speeds indicated. Rank the tension m the ropes from greatest to least.
The rank of the tension in the ropes from greatest to least.
Answer to Problem 21A
TA>TC>TB
Explanation of Solution
Introduction:
When a mass m tied along a string moves with the speed v in a circle of radius r , then the tension in the string will be balanced by the centripetal force and is given by,
T=mv2r
Using above formula, the tension in the string in case A will be,
TA=mv2r=m(3)20.4=22.5m
Similarly, the tension in the string in case B will be,
TB=mv2r=m(3.2)20.6=17.06m
And, the tension in the string in case C will be,
TC=mv2r=m(4.0)20.8=20m
Conclusion:
Hence, the tension in the string is directly proportional to the square of velocity and inversely proportional to the radius.
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