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?

Answer 1

I will be happy to critique your thinking. Set the linear expansion equation equal to the HookÃ©s law expansion.

Answer 2

To calculate Young's modulus, we need to use the formula:

Young's modulus (Y) = Stress / Strain

First, let's calculate the stress applied to the ruler. Stress is defined as the force divided by the cross-sectional area:

Stress = Force / Cross-sectional area

Given:
Force = 1.2 * 10^3 N
Cross-sectional area = 1.50 * 10^-5 m^2

Substituting these values into the formula, we find:

Stress = (1.2 * 10^3 N) / (1.50 * 10^-5 m^2)

Next, we need to calculate the strain. Strain is defined as the change in length divided by the original length:

Strain = Change in length / Original length

For the ruler to stretch back to its original length, the change in length is equal to the amount it shrunk due to the temperature change. The coefficient of linear expansion tells us the proportional change in length per degree Celsius change in temperature. So, the change in length is given by:

Change in length = coefficient of linear expansion * temperature change * original length

Given:
Coefficient of linear expansion = 2.10 * 10^-5 (C°)^-1
Temperature change = 25°C - (-16°C) = 41°C (change in temperature from 25°C to -16°C)
Original length = We don't have the original length of the ruler mentioned in the question, so we cannot directly calculate the strain.

Now, we can substitute the values into the formula for strain:

Strain = (2.10 * 10^-5 (C°)^-1) * (41°C) * original length

Since we don't have the original length, we cannot directly calculate the strain and proceed to find Young's modulus.