A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end and the combination is subjected to a tension.
A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end and the combination is subjected to a tension. Find the ratio of
(a) the stresses developed in the two wires and
(b) the strains developed. Y of steel = 2x1011 N/m2. Y of copper =1.3x1011 N/m2.
1 Answers
(a) Since both types of wires are joined end to end, the same load will be on the cross-sections of them. If the load = F and the area of cross-section =A, then stress developed in steel wire σ =F/A and the stress developed in copper wire σ¹ =F/A.
The ratio σ/σ¹ =(F/A)/(F/A) = 1
(b) Strain in copper wire = Stress in copper wire/Y =F/AY
Similarly the strain in steel wire =F/AY'
Where Y = Modulus of copper
Y' = Modulus of steel
strain in copper wire/strain in steel wire =(F/AY)/(F/AY')
=Y'/Y
=2.0 x10¹¹/1.3 x10¹¹
=2.0/1.3
= 20/13