Heat and work. Fit ring over rod, remove ring from rod

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SUMMARY

The discussion focuses on the thermal expansion of an aluminum ring intended to fit over a steel bar at specific temperatures. At 7.00° C, the aluminum ring's inside diameter is 4.000 cm, while the steel rod's diameter is 4.080 cm. To fit the ring over the rod, it must be heated to a temperature where the ring expands sufficiently. The second scenario involves a ring at 21° C with an inside diameter of 4.000 cm and a rod diameter of 4.004 cm, requiring the ring to be heated to a specific temperature before it can be removed after cooling.

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  • Understanding of linear thermal expansion principles
  • Knowledge of thermal expansion coefficients for aluminum and steel
  • Familiarity with the formula ΔL/L = αΔT
  • Basic skills in algebra for solving equations
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nicoleb14
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It is desired to slip an aluminum ring over a steel bar. At 7.00° C the inside diameter of the ring is 4.000 cm and the diameter of the rod is 4.080 cm.

(b) Find the temperature of the ring at which it fits over the bar. The bar remains at 7.00° C.
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It is desired to slip an aluminum ring over a steel bar. At 21° C the inside diameter of a ring is 4.000 cm and the diameter of a rod is 4.004 cm. By heating the ring, it expands so that it can slip over the bar, after which time they both are allowed to cool to the same temperature, so that the ring is now stuck on the bar.

(b) Find the temperature at which the ring can be removed. Express your answer to the nearest whole degree.


Attempt:
i don't know even know where to start.
i tried (kAdeltaT)/L
but i don't know what A is!
 
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nicoleb14 said:
i don't know even know where to start.
i tried (kAdeltaT)/L
but i don't know what A is!
What's the formula describing linear thermal expansion? ΔL/L = ?

You should be able to look up the expansion coefficients for aluminum and steel in your text.
 

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