A ruler is accurate when the temperature is 25°C. When the temperature drops to -16°C, the ruler shrinks and no longer measures distances accurately. However, the ruler can be made to read correctly if a force of magnitude 1.2 103 N is applied to each end so as to stretch it back to its original length. The ruler has a cross-sectional area of 1.50 10-5 m2, and it is made from a material whose coefficient of linear expansion is 2.10 10-5 (C°)-1. What is Young's modulus for the material from which the ruler is made?

Question

A ruler is accurate when the temperature is 25°C. When the temperature drops to -16°C, the ruler shrinks and no longer measures distances accurately. However, the ruler can be made to read correctly if a force of magnitude 1.2  103 N is applied to each end so as to stretch it back to its original length. The ruler has a cross-sectional area of 1.50  10-5 m2, and it is made from a material whose coefficient of linear expansion is 2.10  10-5 (C°)-1. What is Young's modulus for the material from which the ruler is made?

drwls · Accepted Answer

Set the (negative) thermal expansion equal per unit length to the strain due to tension.
alpha*(delta T) = (F/A)/Y

Y = (F/A)/[(delta T)*alpha]
Y is Young's modulus
A is the cross sectional area, 1.5*10^-5 m^2
delta T = 41 C
F = 1200 N
alpha = 2.1*10^-5 C^-1 is the coefficient of thermal expansion
Solve for Y

Johnson · Answer

that's what I have been working and keep coming up with either two answers 9.29 or 9.29 * 10 ^10 and the computer is telling me its wrong I don't know what else to do. Maybe I'm computing the number wrong.

drwls · Answer

I also get 9.29*10^10 N/m^2. That is a typical value for a metal.