Question

Two circular rods, one steel and the other copper, are both 0.780 m long and 1.50 cm in diameter. Each is subjected to a force with magnitude 4350 N that compresses the rod. What is the difference in the length of the two rods when compressed?

Answer 1

The difference in the length of the two rods when compressed is
`5.4*10^(-5)\ m`.

Step-by-step explanation:

Given that,

Length = 0.780 m

Diameter = 1.50 cm

Force = 4350 N

(a). For steel rod

We know ,

The young modulus for steel rod

`Y=2*10^(11)`

Using formula of young modulus

`e_(s)=(Fl)/(AY)`

`e_(s)=(4350*0.780)/(3.14*(0.75*10^(-2))^2*2*10^(11))`

`e_(s)=9.6*10^(-5)\ m`

(b). For copper rod

We know ,

The young modulus for steel rod

`Y=1.1*10^(11)`

Using formula of young modulus

`e_(c)=(Fl)/(AY)`

`e_(c)=(4350*0.780)/(3.14*(0.75*10^(-2))^2*1.1*10^(11))`

`e_(c)=1.5*10^(-4)\ m`

The difference in the length of the two rods when compressed is

`difference\ in\ length=e_(c)-e_(s)`

`difference\ in\ length=1.5*10^(-4)-9.6*10^(-5)`

`difference\ in\ length =5.4*10^(-5)\ m`

Hence, The difference in the length of the two rods when compressed is
`5.4*10^(-5)\ m`.