Question

2- Two materials, A and B, are used to make cables of

identical cross section and length, to lift identical loads.
If A has a greater Young's Modulus than B, which cable
will stretch the most when loaded? Explain why.

Answer 1

Cable B will more stretch the most.

Step-by-step explanation:

Given that,

Length of material A =
`l_(A)`

Length of material B =
`l_(B)`

If A has a greater Young's Modulus than B.

We know that,

The deflection is defined as,

`\delta=(Wl)/(AE)`

For material A,

`\delta_(A)=(W_(A)l_(A))/(A_(A)E_(A))`

`\delta_(A)\propto(1)/(E_(A))`

For material B,

`\delta_(B)=(W_(B)l_(B))/(A_(B)E_(B))`

`\delta_(B)\propto(1)/(E_(B))`

The deflection is inversely proportional to the young's modulus.

We need to find which cable will stretch the most when loaded

Using formula of deflection

`(\delta_(A))/(\delta_(B))=((W_(A)l_(A))/(A_(A)E_(A)))/((W_(B)l_(B))/(A_(B)E_(B)))`

Put the value into the formula

`(\delta_(A))/(\delta_(B))=((Wl)/(AE_(A)))/((Wl)/(AE_(B)))`

`(\delta_(A))/(\delta_(B))=(E_(B))/(E_(A))`

So,
`\delta_(B)>\delta_(A)`

Hence, Cable B will more stretch the most.