solutions_PHY132_midterm_2081

solutions_PHY132_midterm_2081 - PHY 132 Midterm Exam NAME:...

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Unformatted text preview: PHY 132 Midterm Exam NAME: Tuesday, February 5, 2008 Directions: You have 75 minutes. Support your answers. Correct answers with no or unsatisfactory explanation, or supporting calculations (whatever is applicable) will not receive any credit. You are allowed to use one page (front and back) formula sheet, and a calculator. Solve the questions on the same page. If necessary, you can use the back of the page as well. 0.1 Pressure in a fluid at rest expression P = P0 + pgh (l) 0.2 Bernoulli Eqn P + pgh + gm}2 = constant (2) 0.3 Mass—spring system with no friction dga: cit2 Where w = (I i, and $(t) 2 mm” sin(wt + ¢) Mg (4) 0.5 Wavelength and frequency v = A f (5) 1)=\/T/# (5) +w211: = 0 (3) 0.4 Simple pendulum 1 Water level and weight[15 pts] Two cups are filled to the same level with water. One of the two cups has plastic balls floating in it. If the density of the plastic balls is less than that of ice, which of the two cups weighs more? > Figure 1: , 2 An irrigation system [15 pts] Water flows through the pipes shown in the figure. The water’s speed through the lower pipe is 5.0 m/ S and a pressure gauge reads 75 kPa. What is the reading : ” j} of the pressure gauge on the upper pipe? (1 Pa=1 N/m2) «/ [ OQQ L6 /W\ Prim/k“ 3 A person swings on a swing [15 pts] A person swings on a swing. When the person sits still, the swing oscillates back and forth at its natural frequency. (a) If, instead, two people sit on the swing, how does the natural frequency change? (b) If, instead, the person stands on the swing, how does the natural fre— quency change? ((3) If someone on the ground pushes the person on the swing at almost the same frequency with the natural frequency, what do you expect to observe? Explain. 4 Measuring mass on the Moon [20 pts] You have been asked to evaluate the design for a simple device to measure the mass of small rocks on the Moon. The rock is attached to the free end of a lightweight spring which is horizontal. The surface on Which the rock slides is almost frictionless. You are worried that the kinetic energy of the rock may make this device dangerous in some situations. The device specifications state that a 150 gram rock will execute harmonic motion, with a frequency of 0.32 Hz, described by 11:05) 2 Asin(bt — 35°) When the rock has an initial speed of 1.2 cm/s. What is the max kinetic energy of the mass? —> Fixed end Figure 2: . 5 Pulses moving on strings [20 pts] A pulse is moving to the right on a long thin Wire. (The left end of the wire is not shown, which extends at least 50 meters to the left of 55:0) Another thick wire, fixed at the right end, is attached to the thin wire. The diameter of the thick wire is 2.2 times that of the thin one. Both wires are made of the same material. We know that the pulse reaches the junction of the two wires in 1.50 r seconds. QM rfi QULTFEJW‘S‘ (a) What will be the speed of the pulse on the thick wire?(pm3~ W/g) ()0 e (b) Pulse is at X20 at t=0. Draw the pulses (main and reflected) at t=4.00 E‘seconds. Indicate the direction of motion for each pulse. 6 Mathematical description of a wave[15 pts] A traveling wave moving along a string is described by y(m, t) 2 (1.OO><10—2 cos(1.20m+ 10.5t). All quantities are given in SI units. (a) What is the wavelength of the wave? (b) What is the frequency of the wave? (c) What is the speed of the wave? (d) What direction is the wave moving? ) (e Draw the the snapshot of the wave at t=1.00 second. (Plot y(x,l.00) vs X) (A) break/icy (lax +59 2U . a ' k” if :11 (Z //" /'O A Figure 3: . 7 Force on a dam[Emtra Credit: 20 pts] As the reservoir behind a dam is filled with water, the pressure that the water exerts on the darn increases. Eventually, the force on the dam becomes sub- stantial, and it could cause the dam to collapse. To study this phenomenon, consider the simple model of a dam depicted in the diagram. View the figure: the reservoir of water (density p) behind the dam is filled to a height h. Assume that the width of the dam (the dimension pointing into the screen) is L. (a) Consider a horizontal layer of the dam wall of thickness dx located a distance it above the reservoir floor. What is the magnitude dF of the force on.) 7:, r .. I this layer due to the water in the reservoir? _ (b) The force of the water produces a torque on the dam. In a simple model, if the torque due to the water were enough to cause the dam to break free from its foundation, the dam would pivot about its base (point P). What is the ’ magnitude ’7' of the torque about the point P due to the water in the reservoir? dz: JFK ...
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solutions_PHY132_midterm_2081 - PHY 132 Midterm Exam NAME:...

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