Question

A cylindrical pin of diameter 20 cm, made of aluminum, does not fit through a 19.97cm circular hole in a copper plate. The pin and the copper plate both are initially at a temperature of 110 degrees C. At what temperature, in degrees C, does the cylindrical pin just fit into the circular hole of the copper plate if both the plate and the pin are cooled together?

Answer #1

At 20∘C, the hole in an aluminum ring is 2.200 cm in diameter.
You need to slip this ring over a steel shaft that has a
room-temperature diameter of 2.204 cm .
To what common temperature should the ring and the shaft be
heated so that the ring will just fit onto the shaft? Coefficients
of linear thermal expansion of steel and aluminum are
12×10-6K-1 and
23×10-6K-1 respectively.
Express your answer in degrees Celsius to two significant
figures.

A brass ring with inner diameter 2.00 cm and outer diameter 3.00
cm needs to fit over a 2.00-cm-diameter steel rod, but at 20
degrees Celsius the hole through the brass ring is 40 μm too small
in diameter.
To what temperature, in degrees Celsius, must the rod and ring
be heated so that the ring just barely slips over the rod?

At 20∘C, the hole in an aluminum ring is 2.100 cm in diameter.
You need to slip this ring over a steel shaft that has a
room-temperature diameter of 2.107 cm To what common temperature
should the ring and the shaft be heated so that the ring will just
fit onto the shaft? Coefficients of linear thermal expansion of
steel and aluminum are 12×10−6 K−1 and 23×10−6 K−1
respectively.

2 parts thx!
1. A flat aluminum plate has a circular hole of diameter 1.739
cm at 0.00 °C.What is the change in its diameter when the
temperature of the plate is increased to 116 °C? For reference, the
coefficient of thermal expansion for aluminum is 2.3 x
10-5/C°. Give at least 2 significant figures in your
answer, which should be in cm.
2. A flat plate made of an unknown metal has a circular hole of
diameter 2.89 cm...

A hole in an Aluminum plate has diameter of 1.235 cm at 200C
[???= 25 × 10−6?0−1, ???= 75 × 10−6?0−1]
i. What is the diameter of the hole at 2000C?
ii. At what temperature is the diameter of the hole equal to 1.176
cm?

A closed and elevated vertical cylindrical tank with diameter 80
cm contains water to a depth of 0.900 m . A worker opens a circular
hole with diameter 12 cm in the bottom of the tank. As the water
drains from the tank, compressed air above the water in the tank
maintains a gauge pressure of 5.00×103Pa at the surface of the
water. Ignore any effects of viscosity ( ½w = 1000 kg=m3 ).
a) (12 points) Just after the...

A brass ring of diameter 10.00 cm at 15.7°C is heated and
slipped over an aluminum rod of diameter 10.01 cm at 15.7°C. Assume
the average coefficients of linear expansion are constant.
(a) To what temperature must the combination be cooled to
separate the two metals?
°C
Is that temperature attainable?
Yes No
(b) What if the aluminum rod were 10.04 cm in diameter?
°C
Is that temperature attainable?

A brass ring of diameter 10.00 cm at 17.8°C is heated and
slipped over an aluminum rod of diameter 10.01 cm at 17.8°C. Assume
the average coefficients of linear expansion are constant.
(a) To what temperature must the combination be cooled to
separate the two metals?
°C
(b) Is that temperature attainable?
Yes or No
(c) What if the aluminum rod were 9.16 cm in diameter?
°C
(d) Is that temperature attainable?
Yes or No

A brass ring of diameter 10.00 cm at 22.0°C is heated and
slipped over an aluminum rod of diameter 10.01 cm at 22.0°C. Assume
the average coefficients of linear expansion are constant.
(a) To what temperature must the combination be cooled to
separate the two metals?
°C
(b) What if the aluminum rod were 10.02 cm in diameter?
°C

A 23.0 g copper ring at 0.000°C has an inner diameter of
D = 2.46000 cm. An aluminum sphere at 100.0°C has a
diameter of d = 2.46507 cm. The sphere is put on top of
the ring, and the two are allowed to come to thermal equilibrium,
with no heat lost to the surroundings. The sphere just passes
through the ring at equilibrium temperature.
What is the mass of the sphere?

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