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15 Physics 153 Assignment 1a
Due the day of your Tutorial in the week of September 2529, 2010
Useful constants:
αaluminum = 2.8×10−5 K −1 , αsteel = 1.3×10−5 K −1 , αbrass = 1.9×10−5 K −1 , Yaluminum =
8 × 1010 P a, Ysteel = 21 × 1010 P a, βwater = 2.07 × 10−4 K −1 1. The ampliﬁcation or gain of a transistor ampliﬁer may depend on the temperature. The
gain for a certain ampliﬁer at room temperature ( 20.0◦ C ) is 30.0, where as at 55.0◦ C it
is 35.2. What would be the gain at 30.0◦ C if the gains depends linearly, over a limited
range?
2. The length of a mercury column of a thermometer is 4.0 cm long when immersed in ice
water and 24 cm long when immersed in boiling water. (a) What would be the length at
22◦ C? (b) When immersed in a solution the length is 25.4 cm. What is the temperature
of the solution? 3. Wheels for railway cars are made of a disk shaped cast iron body of outer diameter
930.0 mm and a steel rim of inner diameter 927.0 mm at 20◦ C. To what temperature must
the steel rim be heated so that it will just slip over the cast iron body?
4. A composite bar of length L = L1 + L2 is made from a bar of material 1 and length L1
attached to a bar of material 2 and length L2 , as shown.
(a) Show the eﬀective coeﬃcient of linear expansion is (α1 L1 + α2 L2 )
.
L
(b) Using steel and brass, design such a composite bar whose length is 52.4 cm and
whose eﬀective coeﬃcient of linear expansion is 16.0 × 10−6 K −1 .
α= material 2 BC material 1 L 1 UB
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15 5. A thick aluminum rod and thin steel wire is attached in parallel, as shown. The
temperature is 12.0◦ C. Both the rod and wire are 95.0cm long and neither is under stress.
The system is heated to 100◦ C. Calculate the resulting stress in the wire, assuming that
the rod expands freely. wire BC aluminum rod 2 UB
Ph C
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20 ics
10
15 Physics 153 Assignment 1b
Due the day of your Tutorial in the week of September 2529, 2010
Useful constants: αaluminum = 2.8×10−5 K −1 , αsteel = 1.3×10−5 K −1 , αbrass = 1.9×10−5 K −1 , Yaluminum =
8 × 1010 P a, Ysteel = 21 × 1010 P a, βwater = 2.07 × 10−4 K −1 1. In the interval between the freezing point of water and 700.0◦ C, a platinum resistance
thermometer (PRT) can be used to measure temperature. The relationship between the
Celsius temperature TC and the resistance R of the PRT is given by the formula
R = R0 (1 + ATC + BTC 2 ) where R0 , A and B are constants. (a) If R equals 10.000 ohms at the freezing point of
water, 13.946 ohms at the boiling point of water, and 24.174 ohms at the melting point
of zinc ( 419.514◦ C ), ﬁnd R0 , A, and B; (b) Plot R versus TC using graph paper in the
range from 0◦ C to 700.0◦ C. 2. A cubical swimming pool is ﬁlled to within 1 cm of the top with water at 21◦ C. On
a very hot summer day, when the water warms to 37◦ C, the pool overﬂows. What is the
depth of the pool?
3. A 1 km steel railroad rail is fastened securely at both ends when the temperature is
20◦ C. With increasing temperature the rail begins to buckle. Assuming the buckle is
triangular, how high is the buckle at 25◦ C? 4. a) The inner diameter of a steel ring is 2.0000 cm, and the diameter of an aluminum
disk is 2.0100 cm. Both are at 430◦ C. At what common temperature will the disk ﬁt
precisely into the hole in the steel ring?
b) If after the aluminum disk is ﬁtted precisely into the hole the two metals are the
temperature is changed to 200 C, what is the stress in the steel ring? BC 5. A grandfather’s clock is calibrated at a temperature of 20◦ C. The pendulum is a thin
brass rod with a heavy mass attached to the end. On a hot day, when the temperature is
30◦ C does the clock “run” fast or slow? How much time does it gain or lose in a 7 day
period? 1 ...
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 Spring '10
 SarahBurke,DonaldWitt,MichaelDHasinoff,AndrzejKotlicki
 Orders of magnitude, Fahrenheit, Celsius, Useful constants, Ysteel

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