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A 14.5 kg mass, fastened to the end of a...

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0m, s whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 `cm^(2)`. Calculate the elongation of the wire when the mass is at the lowest point of its path.

Text Solution

Verified by Experts

Here, `m=14.5kg,l=r=1m,v=2rps,A=0.065xx10^(-4)m^(2)`
Total pulling force on mass, when it is at the lowest position
of the vertical circle is
`F=mg+mromega^(2)`
`=mg+mr4piv^(2)`
`=14.5xx9.8+14.5xx1xx4xx((22)/(7))^(2)xx2^(2)`
`=142.1+2291.6`
`=2433.7N`
`y=(F)/(A)xx(l)/(Deltal) or Deltal=(Fl)/(Ay)`
`=(2433.7xx1)/((0.065xx10^(-4))xx(2xx10^(11)))`
`=1.87xx10^(-3)m`
`=1.87mm`.
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