3 years, 1 month ago
physics problem help?!
A brass ring of diameter 10.00 cm at 20 degrees Celsius is heated and slipped over an aluminum rod of diameter 10.01cm at 20 degree Celsius. Assuming the average coefficients of linear expansion are constant,
a. to what temperature must this combination be cooled to separate them? is this attainable?
b. What if the aluminum rod were 10.02 cm in diameter?
a. to what temperature must this combination be cooled to separate them? is this attainable?
b. What if the aluminum rod were 10.02 cm in diameter?
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M$1 Answer
Well the equation you need to use is:
(change in length)/(initial length) = (linear thermal expansion coefficient)*(change in temperature)
These are the expansion coeffiecients:
Brass 18.7*10^-6
Aluminum 22.2*10^-6
So for part a we need to find a change in T so the the diameters are equal. (the length in the equation is the diameter in this problem)
so for the brass ring:
x / 0.1 m = 18.7*10^-6 * (change in T)
for the aluminum rod
(x - .0001 m)/ 0.1001m = 22.2*10^-6 * (change in T)
Solving these equations my answer was:
x = -0.0005309 m or -0.053 cm
change in T = -283.9 C
So at a temperature of -263.9 C both diameters will be 9.947 cm,
which is attainable because absolute zero is -273.15 C
I'm not entirely sure this is right but I hope it helps.
Also I don't have time to work out b right now . but I might get to it tonight.
(change in length)/(initial length) = (linear thermal expansion coefficient)*(change in temperature)
These are the expansion coeffiecients:
Brass 18.7*10^-6
Aluminum 22.2*10^-6
So for part a we need to find a change in T so the the diameters are equal. (the length in the equation is the diameter in this problem)
so for the brass ring:
x / 0.1 m = 18.7*10^-6 * (change in T)
for the aluminum rod
(x - .0001 m)/ 0.1001m = 22.2*10^-6 * (change in T)
Solving these equations my answer was:
x = -0.0005309 m or -0.053 cm
change in T = -283.9 C
So at a temperature of -263.9 C both diameters will be 9.947 cm,
which is attainable because absolute zero is -273.15 C
I'm not entirely sure this is right but I hope it helps.
Also I don't have time to work out b right now . but I might get to it tonight.
You can leave an optional "tip" with Mahalo's virtual currency, Mahalo Dollars. If you are asking a difficult question that might require some research, or if you'd like a wide variety of feedback, a higher tip often leads to more answers to your question.
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