Two steel wires are connected together, end to end, and attached to a wall as sh

Question

Two steel wires are connected together, end to end, and attached to a wall as shown below. The two wires have the same length and elastic modulus, but the ratio of the radius of the first wire to the radius of the second wire is 9 : 2. As the wires are initially the same length, the midpoint of the combination coincides with the connection point. An applied force then stretches the combination by 2.750 mm while the two wires stay connected together. After the wires are stretched, what is ?, the distance from the midpoint to the connection point?

Explanation / Answer

et the youngs modulus of steel be E, the bigger cross section be A1, smaller A2,
now we know ?= FL/AE

?1= FL/9E , ?2=FL/2E

?1+?2 = 11FL/18E= 2.750 mm

FL/E = 4.5

now distance of midpoint is (2L+2.75)/2= L+1.375 -----1

distance of joint = L+?1 = L+FL/9E =L+ 4.5/9 = L + 0.5 ----2

?= (1)-(2) = 1.375-0.5 = 0.875 mm

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