Question

At 20.0°C, an aluminum ring has an inner diameter of 5.00 cm and a brass rod has a diameter of 5.055 cm. (a)If only the ring is warmed, what temperature must it reach so that it will just slip over the rod? (b) If both the ring and the rod are warmed together, what temperature must they both reach so that the ring barely slips over the rod? (c) Why might the temperature value of part (b)pose problems for this system?ANS = 478.3 °C, 2315.972 °C

I cannot get the anwser for part B, I keep on getting 2901.61 C! Thanks:)

Answer #1

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?

A steel ring with a 2.5000-in. inside diameter at 20.0 ?C is to
be warmed and slipped over a brass shaft with a 2.5020 in. outside
diameter at 20.0 ?C.
Part A)
To what temperature should the ring be warmed?
Part B)
f the ring and the shaft together are cooled by some means such
as liquid air, at what temperature will the ring just slip off the
shaft?

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 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 steel ring with a 2.5000-in. inside diameter at 20.0 ?C is to
be warmed and slipped over a brass shaft with a 2.5030 in. outside
diameter at 20.0 ?C.
A)To what temperature should the ring be warmed?
B)If the ring and the shaft together are cooled by some means
such as liquid air, at what temperature will the ring just slip off
the shaft?

A steel rod is 3.000 cm in diameter at 33.0 °C. A brass ring has
an interior diameter of 2.992 cm at 33.0 °C. At what common
temperature will the ring just slide onto the rod? The coefficients
of linear expansion of steel and brass are 1.100×10-5 , 1.900×10-5
/°C, respectively, answer in °C.

A steel rod is 2.689 cm in diameter at 35.00°C. A brass ring has
an interior diameter of 2.684 cm at 35.00°C. At what common
temperature will the ring just slide onto the rod? The linear
expansion coefficient of steel is 11.00 × 10-6 1/C°. The
linear expansion coefficient of brass is 19.00 × 10-6
1/C°.
4sig figs

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.

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.

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