3. (a) A wire that is 1.50 m long at 20.0 is found to increase in length by 1.90 cm when wamed to 420.0. The average coefficient of linear expansion for wire is 3.2 x10$ (C):'). (b) The wire is stretched just taut (zero tension) at 420.0. Find the stress in the wire if it is cooled to without being allowed to contract. Young's modulus for the wire is 2.0x 10''Pa.
Answers
Answer:
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Given: A wire 1.5 m long at 20 K is found to increase in length by 1.9 cm when warned to 420K. It is also stretched at 420 K. Young's Modulus is 2*10^11
To find: Average coefficient of linear expansion and stress in wire
Explanation: Let the coefficient of linear expansion be a. Now, when wire is heated the length increases by 1.9 cm or 0.019 m.
Temperature change(T)= 420-20= 400 K
Formula used : Change in length= Original length* coefficient of expansion* T
=> 0.019= 1.5*a* 400
=> a= 0.019/600
= 3.1* 10^-5
Now, Young's modulus= Stress/ Strain
where formula of strain= a* T
= 3.1* 10^-5* 400
= 0.0126
Stress= Young's modulus* 0.0126
= 2*10^11*0.0126
= 0.025* 10^11
= 25* 10^8 Pa
Therefore, the coefficient of linear expansion is 3.1* 10^-5 and stress in the wire is 25* 10^8 Pa.