Question

a metal wire 3.50m long and 0.70mm in diameter was given the following test. a load weight 20N was originally hung from the wire to keep it taut. the position of the lower end of the wire was read on a scale as loads was added. determine young's modulus​

Answer 1

Young-modulus=3.7*10^8N/m^2

Step-by-step explanation:

We are not given the read position on the scale as this value represent the new length, which is needed to compute the change in length "e"

However, let us use a value of 4m to represent the value on the scale

Step one:

given data

original length=3.5m

diameter d= 0.7mm in meters= 7*10^-4m

Area A= πd^2/4

A= 3.142* (7*10^-4)^2/4

A=3.142*4.9*10^-7/4

A= 3.85×10-7m^2

Force F= 20N.

original length =3.5m

change in length = 4-3.5= 0.5m

Step two:

`young-modulus= (stress)/(strain)`

`stress= (F)/(A)`

`strain= (l)/(L)`

l= change in length = 4-3.5= 0.5m

L= original length =3.5m

solving for the stress

`stress= (20)/(3.85*10^-^7)\\\\stress= 5.19*10^7`

stress= 5.19*10^7N/m^2

solving for strain

`strain= (0.5)/(3.5)\\strain= 0.14`

`Young-modulus= (5.19*10^7)/(0.14)\\\\ Young-modulus=3.7*10^8`

Young-modulus=3.7*10^8N/m^2