Question

A steel wire has a cross sectional area of 1.5 x 10^-4 cm^2 and a length of 10.0 m. By how much will it stretch if a 25 kg weight is hung from it? Please answer in millimeters.

Answer 1

Answer: The steel wire will stretch up to 1837.5 mm

Step-by-step explanation:

We are given:

Mass = 25 kg

Length of wire = 10 m

Area of cross-section of wire =
`1.5* 10^(-4)cm^2=1.5* 10^(-8)m^2` (Conversion factor:
`1cm^2=10^(-4)m^2` )

To calculate the change in stretching, we use the equation:

`E=(Fl)/(A\Delta l)`

where,

E = young modulus of steel =
`20* 10^(10)Pa`

F = force exerted by the weight = m g =
`25kg* 9.8m/s^2`

l = length of wire = 10 m

A = area of cross section =
`1.5* 10^(-8)m^2`

`\Delta l` = change in length = ?

Putting values in above equation, we get:

`20* 10^(10)=(25* 9.8* 10)/(1.5* 10^(-8)* \Delta l)\\\\\Delta l=1.8375m`

Converting above value in mili meters, we use the conversion factor:

1 m = 1000 mm

So, 1.8375 m = 1837.5 mm

Hence, the steel wire will stretch up to 1837.5 mm