Question

Need help on number 3. Have already had 2 tutors not be able to answer

Answer 1

When talking about the stress and strain of a material, the behavior can be very diverse. When the exercise gives us the Modulus, it refers to Young's modulus, which is the slope where the curve strain-stress is linear. On this part of the curve, we have the following equation:

`\sigma=E\epsilon`

Where sigma is the tension, E is Young's modulus and epsilon is the change in length. Considering the data from our problem, we need first to calculate the area of the wire. It is:

`A=\pi r^2\Rightarrow A=\pi0.0035^2=3.848*10^(-5)m^2`

Now we have all the data we need. Considering the tension sigma is force over area, we can write the first equation as:

`(80)/(3.848*10^(-5))=7*10^(10)*\epsilon\Rightarrow\epsilon=(80)/(3.848*10^(-5)*7*10^(10))`
`\epsilon=2.97*10^(-5)`

This value is adimensional. It represents how much of the original length is changed, so we still need to multiply it by the original length, which gives us:

`\Delta l=2.97*10^(-5)*7=20.79*10^(-5)m`

This leaves us with alternative a) 20.788e-5m