A14.5 kg mass, fastened to the end of a steel wire of unstretchedlength 1.0 m, is whirled in a vertical circle with an angularvelocity of 2 rev/s at the bottom of the circle. The cross-sectionalarea of the wire is 0.065 cm2.Calculate the elongation of the wire when the mass is at the lowestpoint of its path.
A14.5 kg mass, fastened to the end of a steel wire of unstretchedlength 1.0 m, is whirled in a vertical circle with an angularvelocity of 2 rev/s at the bottom of the circle. The cross-sectionalarea of the wire is 0.065 cm2.Calculate the elongation of the wire when the mass is at the lowestpoint of its path.
Mass, m = 14.5kg
Length of the steelwire, l = 1.0 m
Angular velocity, ω= 2 rev/s
Cross-sectional area ofthe wire, a = 0.065 cm2
Let δlbe the elongation of the wire when the mass is at the lowest point ofits path.
When the mass is placedat the position of the vertical circle, the total force on the massis:
F = mg +mlω2
= 14.5 × 9.8 +14.5 × 1 × (2)2
= 200.1 N
Young’s modulusfor steel = 2 × 1011 Pa
Hence, the elongationof the wire is 1.539 × 10–4 m.
Mass, m = 14.5kg
Length of the steelwire, l = 1.0 m
Angular velocity, ω= 2 rev/s
Cross-sectional area ofthe wire, a = 0.065 cm2
Let δlbe the elongation of the wire when the mass is at the lowest point ofits path.
When the mass is placedat the position of the vertical circle, the total force on the massis:
F = mg +mlω2
= 14.5 × 9.8 +14.5 × 1 × (2)2
= 200.1 N
Young’s modulusfor steel = 2 × 1011 Pa
Hence, the elongationof the wire is 1.539 × 10–4 m.
