PHYS153assign1a_solution - Don’s Boot Camp for Midterm 1...

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Unformatted text preview: Don’s Boot Camp for Midterm 1 These are problems to help you prepare for midterm 1 UB ys C ics 20 15 10 3 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. To measure temperatures, physicists and astronomers often use the variation of intensity of electromagnetic radiation emitted by an object. The wavelength λmax at which the intensity is greatest is given by the equation λmax T = 0.2898cm K, where T is the object temperature in Kelvins. In 1965, microwave radiation peaking at λmax = 0.107cm was discovered coming in all directions from space. To which temperature does this correspond? What was the 1978 Nobel Prize in Physics give for? What was the 2006 Nobel Prize in Physics give for? 3. In the interval between the freezing point of water and 700.0◦ C, a platinum resistance thermometer is used for interpolating the temperatures on the international scale. The Celsius temperature TC is given by a formula for resistance R with temperature R = R0 (1 + ATC + BTC 2 ) where A and B are constants determined by measurements at the ice point of water, the steam point of water, and the melting point of zinc ( 419.514◦ C ). (a) If R equals 10.000 ohms at the ice point, 13.946 ohms at the steam point, and 24.174 ohms at the melting point of zinc, find R0 , A, and B; (b) Plot R versus TC in the range from 0◦ C to 700.0◦ C. 4. 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? 5. A cubic metal box with sides of length 20 cm contains air at pressure of 1 atm and a temperature of 300K. The box is sealed so that the volume is constant and heated to 400K. What is the net force on each side of the box? 6. 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? Ph For these problems 7-11 use the following 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 7. 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 α= (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 . 1 UB ys C ics 20 15 10 3 material 2 material 1 L 8. 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 aluminum rod Ph 9. A steel ball is 4.000cm in diameter at 28◦ C. A brass ring has an interior diameter of 2.992cm at 30◦ C. At what common temperature will the ball just slide through the ring? 10. 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? 11. 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 2 UB ys C ics 20 15 10 3 Ph UB ys C ics 20 15 10 3 Ph UB ys C ics 20 15 10 3 Ph UB ys C ics 20 15 10 3 Ph UB ys C ics 20 15 10 3 Ph UB ys C ics 20 15 10 3 Ph UB ys C ics 20 15 10 3 Ph UB ys C ics 20 15 10 3 Ph UB ys C ics 20 15 10 3 Ph ...
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This note was uploaded on 11/12/2010 for the course PHYS 153 PHYS 153 taught by Professor Sarahburke,donaldwitt,michaeldhasinoff,andrzejkotlicki during the Spring '10 term at The University of British Columbia.

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