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An iron ring of diameter 15.00 cm must be slipped (shrink-fitted) onto a pulley of diameter 15.05 cm; all measurements are at 20 deg C. Taking the linear expansion coefficient of iron as 12 x 10⁻⁶ per deg C, to what minimum temperature must the ring be heated to just fit, and what strain will exist in the ring after it cools back to 20 deg C?

1. minimum temperature about 298 deg C
2. minimum temperature about 278 deg C
3. strain about 3.33 x 10⁻³
4. strain about 6.67 x 10⁻³

Correct answer: minimum temperature about 298 deg C

Solution

The fractional increase needed is 0.05/15.00 = 3.33e-3, requiring a temperature rise of about 278 deg C, i.e. a final temperature near 298 deg C; the residual strain on cooling is 3.33e-3.

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