here\'s the text transcript: Two steel wires are connected together, end to end,

Question

here's the text transcript:

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

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 5:2. 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 2.550 mm while the two wires stay connected together. After the wires are stretched, what is , the distance from the midpoint to the connection point? Number r.

Explanation / Answer

here,

Since E = stress/strain,

than

stress1 / strain1 = stress2 / strain2,

or

strain2 / strain1 = stress2 / stress1

we are also applying the same force to each wire, so

stress2 / stress1 = (F/area2) / (F/area1)

stress2 / stress1= area1/area2

Since r1 = 2.5 * r2,

area1 = 6.25 * area2,

and strain2/strain1 is also 6.25,

so strain2 is 6.25/7.25 of the total strain.

If the total elongation was 2.55 mm,

that was 2.2 mm elongation of the 2nd wire and

only 0.35 mm elongation of the 1st wire.

The midpoint of the elongated wire is 1.275 mm from the original midpoint,
but the first wire stretched by only 0.35 mm, so the connection point is (delta = 1.03) mm from the new midpoint.

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