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 5 : 3. 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 2.500 mm while the two wires stay connected together. After the wires are stretched, what is 6, the distance from the midpoint to the connection point?

Explanation / Answer

let e1 be the extension of the first wire, and e2 that of the second. let L be the unextended length of each wire.

e1 = ?
e2 = (5/4)^2 *e1
e1 + e2 = 4.05 mm
e1 ( 1 + 2.5^2)= 4.05 mm -------> e1 = 0.558 mm, and e2 = 3.4913 mm.
Now after extention, mid point at (2*L + 4.05 mm)/2 = L + 2.025 mm
= (L + 2.025 mm) - the extended length of the first wire.
= (L + 2.025 mm) - (L + 0.558 mm) = 1.467 mm

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