# hw21a - aldawsari(ma28683 – HW21 – Betancourt –(16856...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: aldawsari (ma28683) – HW21 – Betancourt – (16856) 1 This print-out should have 8 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 17.1-17.6 001 (part 1 of 2) 10.0 points At 11 ◦ C, an aluminum ring has an inner di- ameter of 8 cm and a brass rod has a diameter of 8 . 06 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: 323 . 5 ◦ C. Explanation: Given : T = 11 ◦ C , d a = 8 cm , d b = 8 . 06 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 = 11 ◦ C + 8 . 06 cm- 8 cm (8 cm)(2 . 4 × 10 − 5 ( ◦ C) − 1 ) = 323 . 5 ◦ C . 002 (part 2 of 2) 10.0 points To what temperature must both be heated so that the ring just slips over the rod? Correct answer: 1555 ◦ 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 = bracketleftbig 2 . 4 × 10 − 5 ( ◦ C) − 1 bracketrightbig (8 cm)- bracketleftbig 1 . 9 × 10 − 5 ( ◦ C) − 1 bracketrightbig (8 . 06 cm) = 3 . 886 × 10 − 5 m / ◦ C so Δ T = T 2- T T 2 = T + Δ T = T + d b- d a α...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

hw21a - aldawsari(ma28683 – HW21 – Betancourt –(16856...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online