An aluminum bar has the desired length when at 20 C. Part A How much stress is r

Question

An aluminum bar has the desired length when at 20 C.

Part A

How much stress is required to keep it at this length if the temperature increases to 30 C? Young's modulus for the aluminum isE = 70×109N/m2 and the coefficient of thermal expansion of aluminium is 25×1061/C

Express your answer using two significant figures.

An aluminum bar has the desired length when at 20 C.

Part A

How much stress is required to keep it at this length if the temperature increases to 30 C? Young's modulus for the aluminum isE = 70×109N/m2 and the coefficient of thermal expansion of aluminium is 25×1061/C

Express your answer using two significant figures.

Explanation / Answer

Let the initial length of the aluminum rod be L

Let E = 70 * 109 N / m2 be the young’s modulus

Let the initial temperature of rod be t1 = 200 C

Let the final temperature of the rod be t2 = 300 C

Change in the temperature of the rod is t = t2 – t1 = 300 – 200 = 100 C

Let = 25 * 10-6 / 0C be the coefficient of linear expansion

The thermal stress required to keep the length same as L even for change in temperature be S

Then stress required is given by

               S = E * * t

                  = 70 * 109 * 25 * 10-6 * 10

                  = 175 * 105 N / m2

So the stress required to keep the length of the aluminum rod same under temperature change is S = 175 * 105 N / m2

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