Question

Consider a steel rod of diameter 1.4 cm and length 1.0 m. If the temperature of this rod is increased by 22

Answer 1

You will need two equations for this question:
1. Young's Modulus
2. Thermal Expansion

Thermal Expansion for Steel / Fe:
- 11.8e-6

You need to calculate the ?L first:
- ?L = L * a * ?T
- ?L = 1 * 11.8e-6 x 22
- ?L = 2.596e-4 m

Then plugin to Young's Modulus:
- F/A = Y * (?L / L)
- F = A * Y * (?L / L)
*where A = pi * r^2 = 3.14*[1.4/(2*100)]² =1.5386e-4 m²

-F = 1.5386*10^-4 * 2.0 10¹¹*(-2.596*10^-4/1) N

or F = 7.988*10³ N

Answer 2

Change in lenght for a increase of temperature by 22⁰C,

$\Delta L=L_{0}\alpha _{steel}\Delta T=1\times 13\times 10^{-6}\times22=2.86\times10^{-4}m$

Young's modulus,

$Y=\frac{\frac{F}{A_{0}}}{\frac{\Delta L}{L_{0}}}=\frac{FL_{0}}{A_{0}\Delta L}$

$F=\frac{YA_{0}\Delta L}{L_{0}}=2\times 10^{11}\times \pi 0.007^{2}\times 2.86\times10^{-4}=8800.792N$ ...Which is the required force