A 18.5 kg mass, fastened to the end of a steel wire of unstretched length 1.5 m, is whirled in a vertical circle with an angular velocity of 3 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.085 cm2. Calculate the elongation of the wire when the mass is at the lowest point of its path

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter8: Central-force Motion
Section: Chapter Questions
Problem 8.45P
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A 18.5 kg mass, fastened to the end of a steel wire of unstretched length 1.5 m, is whirled in a vertical circle with an angular velocity of 3 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.085 cm2. Calculate the elongation of the wire when the mass is at the lowest point of its path

Expert Solution
Step 1

Given:

Original length of the steel wire, L = 1.5 m

Young’s modulus of the steel = 2x1011 N/m2

Mass hung by the wire, m = 18.5 kg

Cross-sectional area of the wire, A = 0.085 cm2

Angular velocity = 3 rev/s

Step 2

Calculating the tension force in the wire when the mass is at the lowest point of the circle:

At lowest point, the block will have two forces working on it. Tension in upward direction and weight in downward direction. The net force of these forces will provide the necessary centripetal force to the mass to move in a vertical circle.

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