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

Answer:

The difference in the length of the two rods when compressed is $5.4\times10^{-5}\ m$.

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

$Y=2\times10^{11}$

Using formula of young modulus

$e_{s}=\dfrac{Fl}{AY}$

$e_{s}=\dfrac{4350\times0.780}{3.14\times(0.75\times10^{-2})^2\times2\times10^{11}}$

$e_{s}=9.6\times10^{-5}\ m$

(b). For copper rod

We know ,

The young modulus for steel rod

$Y=1.1\times10^{11}$

Using formula of young modulus

$e_{c}=\dfrac{Fl}{AY}$

$e_{c}=\dfrac{4350\times0.780}{3.14\times(0.75\times10^{-2})^2\times1.1\times10^{11}}$

$e_{c}=1.5\times10^{-4}\ m$

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

$difference\ in\ length=e_{c}-e_{s}$

$difference\ in\ length=1.5\times10^{-4}-9.6\times10^{-5}$

$difference\ in\ length =5.4\times10^{-5}\ m$

Hence, The difference in the length of the two rods when compressed is $5.4\times10^{-5}\ m$.