Question

A certain wire, 3 m long, stretches by 1.2 mm when under tension of 200 N. By how much does an equally thick wire 6 m long, made of the same material and under the same tension, stretch?

Answer 1

Answer:

2.4 mm

Explanation:

Given that:

Initial Original length of the wire L = 3 mm

The stretch  of the first wire  ΔL= 1. 2 mm

The length of the second wire L'' = 6 mm

The stretch of the second wire ΔL'' = ???

Considering the Tension of the system; the Young modulus and the cross sectional remains constant ; as such:

$\frac{Y}{Y''} = \frac{FL}{A \Delta L} *\frac{A \Delta L''}{FL''}$

$1= \frac{L \Delta L''}{L'' \Delta L}$

$\Delta L''= \frac{L'' \Delta L }{L}$

$\Delta L''= \frac{6 \ m * 1.2 \ mm }{3 \ m}$

$\Delta L''=2.4 \ mm$

Thus, the same material under the same tension stretches 2.4 mm

Answer 2

Answer:

2.4 mm

Explanation:

Given that

Length of the wire, L = 3 m

Extensión of the wire, ΔL = 1.2 mm = 1.2*10^-3 m

Tensión of wire, T = 200 N

We use the formula

Y = TL/ΔLA

Since both wires material is same that makes the value of young's modulus the same in both the cases

hence equating

[200 * 3 / 1.2*10^-3 * A] = [200 * 6 / ΔL * A]

ΔL = 2.4*10^-3 m = 2.4 mm