Physics Exam 3: Problems on Equilibrium, Waves, and Fluids, Exams of Physics

Download Physics Exam 3: Problems on Equilibrium, Waves, and Fluids and more Exams Physics in PDF only on Docsity! First Name: ____________________ Last Name:_____________________ Section: ________ ■ 1 April 23, 2008 Physics 207 EXAM 3 Please print your name and section number (or TA’s name) clearly on the first page. Show all your work in the space immediately below each problem. Your final answer must be placed in the boxes, when provided. Problems will be graded on reasoning and intermediate steps as well as on the final answer. Be sure to include units wherever necessary, and the direction of vectors. Each problem is worth 20 points. Try to be neat! Check your answers to see that they have the correct dimensions (units) and are the right order of magnitude. You are allowed one sheet of notes (8.5” x 11”, 2 sides), a calculator, and the constants in this exam booklet. The exam lasts exactly 90 minutes. Constants: Acceleration due to gravity at the earth’s surface: g = 9.81 m/s2 SCORE: Problem 1: __________ Problem 2: __________ Problem 3: __________ Problem 4: __________ Problem 5: __________ TOTAL: ___________ Don't open the exam until you are instructed to start. "Whatever you dream you can do begin it. Boldness has genius, power and magic in it. Begin it now."………….Goethe First Name: ____________________ Last Name:_____________________ Section: ________ ■ 2 Problem 1 A uniform rectangular beam of length L= 5 m and mass M=40 kg is supported, but not attached, to two posts which are length D=3 m apart. A child of mass W=20 kg starts walking along the beam. a) Assuming infinitely rigid posts, how close can the child get to the right end of the beam without it falling over? [Hint: The upward force exerted by the beam on the left cannot be negative – this is the limiting condition on how far the child can be to the right. Set up the static equilibrium condition with the pivot about the left end of the beam.] (10 pts) First Name: ____________________ Last Name:_____________________ Section: ________ ■ 5 b) Solve the equation for θ(t) if are given as initial conditions (where B and C are positive numbers). (5 pts) c) For the motion given in part b), what is the child’s maximum kinetic energy? (5 pts) First Name: ____________________ Last Name:_____________________ Section: ________ ■ 6 d) Suppose an adult can push the child in the direction of the child’s motion just when the child passes through θ=0. To achieve maximum height for the child, approximately how many times should the adult push the child during a time period Q which is much longer than the natural oscillation period of the swing? [Hint: Think resonance.] (5 pts) First Name: ____________________ Last Name:_____________________ Section: ________ ■ 7 Problem 3 a.) Suppose we have a massive rope attached to the ceiling. The bottom end of the rope dangles in midair. The mass of the rope is 2.7 kg and its length is 4.5 meters. The bottom end of the rope is shaken and then released to produce a pulse that travels up the rope. What is the speed of the pulse when it is halfway up the rope? (6 pts) Here’s a new question. b.) The figure shows a snapshot graph at t = 0 s of a sinusoidal wave traveling to the right along a string at 50 m/s. Write the equation that describe the displacement D(x, t) of this wave. Your equation should have numerical values, including units, for all quantities except x and t. (8 pts) First Name: ____________________ Last Name:_____________________ Section: ________ ■ 10 Here’s a new question: e.) Two loudspeakers are placed 1.8 m apart. They play tones of equal frequency. If you stand 3.0 m in front of the speakers, and exactly between them, you hear a maximum of intensity. As you walk parallel to the plane of the speakers, staying 3.0 m away, the sound intensity decreases until reaching a minimum when you are directly in front of one of the speakers. The speed of sound in the room is 340 m/s. What is the frequency of the sound? (8 pts) First Name: ____________________ Last Name:_____________________ Section: ________ ■ 11 Problem 5 A ball hangs from a balance. When the ball hangs in the air, the balance reads 0.1 N. When the ball is lowered into water, the balance reads 0.07 N. The density of water is 103 kg/m3. a.) What is the ball’s density? (4 pts) b.) What is the radius of the ball? (4 pts) Here’s a new question: c.) Water is flowing at a speed of 4.0 m/s through a 10.0 cm diameter pipe. The pipe branches to form two pipes each of 5.0 cm diameter. Find the flow speed in the 5.0 cm diameter pipes. (4 pts) First Name: ____________________ Last Name:_____________________ Section: ________ ■ 12 d.) A container is filled with oil and fitted on both ends with pistons. The area of the left piston is 10 mm2; that of the right piston 10,000 mm2. What force must be exerted on the left piston to keep the 10,000-N car on the right at the same height? ( 4 pts) Circle the correct answer: 10 N 100 N 10,000 N 106 N 108 N insufficient information e.) A blood platelet drifts along with the flow of blood through an artery that is partially blocked by deposits. As the platelet moves from the narrow region to the wider region, it experiences: ( 4 pts) Circle the correct answer: an increase in pressure. no change in pressure. a decrease in pressure.