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1 I. A mechanical device shakes a ballspring system vertically at its natural frequency. The ball is attached to a string, sending a harmonic wave in the positive xdirection. +x a) The ball, of mass M, moves up and down 80 cm from its equilibrium position 2 times each second, and the wave travels down the string 1.2 m in each period of the oscillator. Write a function that describes the vertical displacement along the string for any time t. Include numeric values in your expression for all of the quantities that you know, and explain your reasoning. y(x,t) = b) The ball in part (a) is replaced by a ball of mass 4M which is attached to the string, and the mechanical device is tuned to the natural frequency of the new ballspring system. What will the period, frequency and wavelength of the travelling wave be in this case? period = frequency = wavelength = c) Use a dashed line to draw the traveling wave that generated by the 4M oscillation on the axes below. The wave generated with the 1M mass is shown for reference. +x
2 II. A pipe of length 0.5 m is closed at one end and open at the other. Sound is created in the pipe at four different frequencies. The diagram shows the location of nodes (N) and antinodes (A) in the pipe for the four different modes. The table to the right has an entry for wave speed of the fifth harmonic. requency Wavelength Wave speed 340 m/s 0.5 m a) Complete the table, and please explain your reasoning in the space below. b) Write a function that describes the wave pattern of the third harmonic. Assume that the origin is at the left side of the tube and that the wave has an amplitude of 0.1 m. Include numeric values in your expression for all of the quantities that you know, and please explain your reasoning. y(x,t) =
3 III. A constant force of 1.5 N is exerted perpendicular to the edge (pointing into the paper on the diagram below) of a 5kgdisk (r=0.3 m) causing it to rotate about its fixed axis. The steady force is applied when the disk is at rest, and removed after 9.0 s. a) ind the angular momentum of the disk after 9.0 s. b) How much work was done by this force on the disk as the disk was sped up from rest to its final angular velocity? c) A 0.4 kg lump of clay is dropped straight down on the spinning disk halfway between the center and the edge. How fast does the disk spin after the clay has been dropped?
4 4) A rod is bent into an L shape and attached at one point to a pivot. The rod sits on a frictionless table and the diagram to the right is a view from above. What does the magnitude of have to be so that the rod is in rotational equilibrium? a) 2.0 N b) 2.5 N c) 2.3 N d) 4.0 N e) 4.6 N 30 5) Six identical 2meter massless rods are supporting identical 12Newton weights. In each case, a vertical A B C force is holding the rods and the D E weights at rest. The left end of each rod is held in place by a frictionless pin. The rods are marked at halfmeter intervals. Rank the magnitude of the vertical force applied to the rods, from GREATEST to LEAST. a) > C > A=E > B=D b) E > D= > A=B=C c) A=B=C=D=E= d) E= > C > D=A > B e) B=D > A=E > C > 6) Wood blocks that have different masses and different volumes are floating in water. On top of these blocks are additional masses as shown. Rank the buoyancy force exerted by the water on the wood blocks, from GREATEST to LEAST. a) D > A=C > B b) D > A=B=C c) B=D > A=C d) C > D > A=B e) D > A=B > C
5 7) Consider the portion of a flow tube shown in the figure. Point 1 and point 2 are at the same height and point 1 is open to the air (point 2 is not open to the air and is connected to more pipe which is not shown here). The water has a speed of v 1 at point 1 and moves steadily toward point 2 where it has speed v 2. The cross section of the flow tube at point 1 is greater than that at point 2. The density of water ρ w =1000 kg/m 3. Which of the following is closest to the pressure P 2 at point 2 if v 1 = 1.0 m/s, v 2 = 5.0 m/s, P 1 = 1.0 atm = 10 5 Pa? a) 9.8 x10 4 Pa b) 9.2 x10 4 Pa c) 1.0 x10 5 Pa d) 1.1 x10 5 Pa e) 8.8 x10 4 Pa 8) Two different glasses contain different amounts of water. Glass A contains 300 g of water and Glass B contains 750 g of water. The water in glass B has twice the internal energy as the water in Glass A. Compare the temperatures of the water in Glass A and Glass B. a) T A > T B b) T A = T B c) T A < T B d) It is impossible to say without knowing the number of moles of water in each cup. e) It is impossible to know without knowing the pressure in each cup. 9) A gas process is described by the 1st law of thermodynamics (ΔU = Q + W) as follows:  2P o V o = Q 3P o V o where P o and V o represent a particular value of pressure and volume. Which of the following statements could be TRUE? a) The gas expands and is cooled. b) The gas expands and is heated. c) The gas is condensed and is cooled. d) The gas is condensed and is heated. e) The gas is cooled at a constant volume.
6 10) Two moles of an ideal gas are compressed isothermally. During the compression, 328 J of work is done on the gas and no work is done by the gas. Which of the following statements is TRUE? a) More than 328 J of energy must leave the gas through cooling. b) Exactly 328 J of energy leaves the gas through cooling. c) The compression is isothermal so there is no heating or cooling. d) Exactly 328 J of energy enters the gas through heating. e) More than 328 J of energy must enter the gas through heating. 11) A heat engine takes 3 moles of an ideal gas through a reversible cycle 1!2!3!1 etc. The path 2!3 is an isothermal process. The temperature at 3 is 680 K and the volumes V 1 = 0.02 m 3 and V 3 = 0.06 m 3. The net energy transferred to the gas during heating/cooling in one complete cycle is closest to P (P 2, V 2 ) (P 1, V 1 ) (P 3, V 3 ) a) 7.3 kj b) 18 kj c) 0 kj d) 11 kj e) 25 kj V 12) A real heat engine operates between the temperatures of 45 C and 525 C. Which of the following is a TRUE statement? a) The ratio of (Work done/heat taken in) is almost exactly 90% for this engine. b) The ratio of (Work done/heat taken in) is almost exactly 60% for this engine. c) The ratio of (Work done/heat taken in) could be slightly less than 90% for this engine. d) The ratio of (Work done/heat taken in) is definitely less than 60% for this engine. e) There is not enough information given to comment on the ratio of (Work done/heat taken in).
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