homework25 - Rodriguez, Brandon – Homework 25 – Due:...

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Unformatted text preview: Rodriguez, Brandon – Homework 25 – Due: Nov 16 2006, 11:00 am – Inst: Andrew J Rader 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Please notice that for your homework to be considered towards your grade, it needs to be submitted one hour before the corresponding recitation starts. Work submitted after this time, but before the DUE DATE on top of this page, will be accepted but not graded. PLEASE REMEMBER THAT YOU MUST CARRY OUT YOUR CALCULA- TIONS TO AT LEAST THREE SIGNIFI- CANT FIGURES. YOUR ANSWER MUST BE WITHIN ONE PERCENT OF THE CORRECT RESULT TO BE MARKED AS CORRECT BY THE SERVER. 001 (part 1 of 2) 4 points At 18 ◦ C, an aluminum ring has an inner di- ameter of 2 cm and a brass rod has a diameter of 2 . 03 cm. If the temperature coefficient of expansion for brass is α b = 1 . 9 × 10- 5 ( ◦ C)- 1 and the temperature coefficient of expansion for alu- minum is α a = 2 . 4 × 10- 5 ( ◦ C)- 1 , to what temperature must the ring be heated so that it will just slip over the rod? Correct answer: 643 ◦ C. Explanation: Given : T = 18 ◦ C , d a = 2 cm , d b = 2 . 03 cm , α b = 1 . 9 × 10- 5 ( ◦ C)- 1 , and α a = 2 . 4 × 10- 5 ( ◦ C)- 1 . The new length will be d b = d a (1 + α Δ T ) d b = d a + d a α Δ T T 1 = T + Δ T = T + d b- d a d a α a = 18 ◦ C + 2 . 03 cm- 2 cm (2 cm)(2 . 4 × 10- 5 ( ◦ C)- 1 ) = 643 ◦ C . 002 (part 2 of 2) 4 points To what temperature must both be heated so that the ring just slips over the rod? Correct answer: 3199 . 34 ◦ C. Explanation: We need L Al = L brass for some Δ T . Using the same law, L Al (1 + α a Δ T ) = L brass (1 + α b Δ T ) d a + d a α a Δ T = d b + d b α b Δ T Δ T = T + d b- d a α a d a- α b d b α a d a- α b d b = £ 2 . 4 × 10- 5 ( ◦ C)- 1 / (2 cm)- £ 1 . 9 × 10- 5 ( ◦ C)- 1 / (2 . 03 cm) = 9 . 43 × 10- 6 m / ◦ C so Δ T = T 2- T T 2 = T + Δ T = T + d b- d a α a d...
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This note was uploaded on 10/18/2010 for the course PHYSICS 251 taught by Professor Pedon during the Spring '08 term at IUPUI.

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homework25 - Rodriguez, Brandon – Homework 25 – Due:...

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