Solving a Steel Rod Temperature Expansion Problem

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To solve the thermal expansion problem involving a steel rod, the change in temperature needed to achieve the same elongation as a 500 N force must be calculated. The average linear expansion coefficient of the steel is 11x10^(-6), and Young's modulus is 20x10^10. The relationship between force, area, and elongation can be used to determine the elongation caused by the applied force. By equating this elongation to the thermal expansion formula, the required temperature change can be derived. Understanding these principles is crucial for accurately solving the problem.
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Thermal Expansion Problem

i've been working on this problem forever and i don't know what I'm doing wrong!
a steel rod undergoes a stretching force of 500 N. Its cross sectional area is 2.00 cm^2. Find the change in temperature that would elongate the rod by the same amount as the 500-N force does.
here's some info that may be of some use but i don't know how to use it!
average linear expansion coefficient: 11x10^(-6)
young's modulus: 20x10^10
shear modulus: 8.4x10^10
thanks in advance you guys!
 
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