Question

Two steel wires are connected together, end to end, and attached to a wall. The two wires have the same length and elastic modulus, but the ratio of the radius of the first wire ?1 to the radius of the second wire ?2 is 5:4. 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 3.350 mm while the two wires stay connected together. After the wires are stretched, what is ?, the magnitude of the distance from the midpoint to the connection point?

Answer 1

Ratio of the radius of the first wire r₁ to the radius of the second wire r₂ = 5:4. applied force then stretches the combination by 3.350 mm

The thicker wire stretches less. Let's say it stretches "d" and the thinner wire stretches "D."

d + D = 3.350 mm

D = d*(5/4)²

D = 1.5625*d

so

d + 1.5625*d = 3.350 mm

2.5625*d = 3.350 mm

d = 1.307 mm

D = 2.042 mm

Let's say each was originally length L.

The total length is 2L + 3.350mm,

so

midpoint = L + 1.675 mm from each end.

But the connection point is only L + 1.307 mm from one of the ends, so

= (1.675 - 1.307)mm

= 0.368 mm