A vertical metal cylinder of radius 2 cm and length 2m is fixed at the lower end and a load of 100 kg is put on it. Find
A vertical metal cylinder of radius 2 cm and length 2m is fixed at the lower end and a load of 100 kg is put on it. Find
(a) the stress
(b) the strain and
(c) the compression of the cylinder. Young's modulus of the metal = 2 x 1011 N/m2.
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2 Answers
(a) Length of the cylinder L = 2 m
Area of cross-section A =πr² =π(2/100)² m² =4π/10000 m²
Force on the cylinder F = 100*10 N =1000 N
Hence the stress =F/A =1000/(4π/10000) N/m²
=(1/4π)*10⁷ N/m²
=0.0796 x10⁷ N/m²
=7.96 x10⁵ N/m²
(b) Strain = Stress/Y =(F/A)/Y
={7.96 x10⁵}/2.0 x10¹¹
=3.98 x10⁻⁶ ≈4 x10⁻⁶
(c) Let the compression of the cylinder = l m
The strain =l/L = l/2
→4 x10⁻⁶ =l/2
→l =8 x10⁻⁶ m
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