First Name: ____________________ Last Name:_____________________ Section: ________ ■ 1 March 21, 2007 Physics 207 EXAM 2 Please print your name and section number (or TA’s name) clearly on all pages. Show all your work in the space immediately below each problem. Your final answer must be placed in the boxes 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 Avogadro’s Number: NA = 6.02 x 1023 molecules/mole 1 metric ton = 1000 kg Radius of the Earth = 6.4 x 106 m (Do not write below) SCORE: Problem 1: __________ Problem 2: __________ Problem 3: __________ Problem 4: __________ Problem 5: __________ TOTAL: ___________ Don't open the exam until you are instructed to start. “Out of clutter, find simplicity. From discord, find harmony. In the middle of difficulty lies opportunity.” A. EinsteinFirst Name: ____________________ Last Name:_____________________ Section: ________ ■ 2 PROBLEM 1 It’s time for the egg drop at the annual Physics 207 picnic. You are to drop an egg from a bridge. The egg starts at rest and falls a distance H = 7 m before hitting a spring designed to cushion the landing. a.) Given that the maximum force the egg shell can withstand is 5 N and an egg has a mass of 50 g, what is the maximum value of the spring constant, k, that will result in a successful egg drop (i.e. no broken eggs)? Neglect air resistance and assume the spring is long enough that it doesn’t compress all the way to the ground. (12 pts.) b.) What is the magnitude and direction of the impulse of the spring force on the egg between the time the egg first contacts the spring and the time that the spring is compressed? (8 pts.) egg H spring (relaxed)First Name: ____________________ Last Name:_____________________ Section: ________ ■ 3 Problem 2 a.) Two particles move perpendicular to each other until they collide. Particle 1 has mass m and momentum of magnitude 2p, and particle 2 has mass 2m and momentum of magnitude p. Suppose that after the collision, the particles "trade" their momenta, as shown in the figure. That is, particle 1 now has magnitude of momentum p, and particle 2 has magnitude of momentum 2p; furthermore, each particle is now moving in the direction in which the other had been moving. How much kinetic energy, Klost, is lost in the collision? Express your answer in terms of m and p. (12 pts.) b.) Consider an alternative situation: This time the particles collide completely inelastically. How much kinetic energy K is lost is lost in this case? Express your answer in terms of m and p. (8 pts.)First Name: ____________________ Last Name:_____________________ Section: ________ ■ 4 Problem 3 You set out to design a car that stores energy in a spinning flywheel with moment of inertia I. a.) Suppose your car requires E Joules to travel 100 km. You want to be able to travel 100 km between “spinning-up” the flywheel. What is the required angular velocity of the wheel when it is “spun-up?” Express your result in terms of E and I. (8 pts.) b.) You use a motor to spin the wheel from rest to its maximum rotation speed in one minute at constant angular acceleration. How much torque is required from your motor? Express your result in terms of E and I. (8 pts.) c.) How many revolutions of the wheel occur during the “spin-up” process of part b? Let I = 50 kg-m2 and E = 2 x 106 J. (4 pts.)First Name: ____________________ Last Name:_____________________ Section: ________ ■ 5 Problem 4 – Multiple Choice a.) Two people standing on ice (with no friction) throw a ball back and forth. After a couple of throws, they are (ignore friction): (4 pts.) 1. standing where they were initially. 2. standing farther away from each other. 3. standing closer together. 4. moving away from each other. 5. moving toward each other. b.) A ladybug sits at the outer edge of a merry-go-round that is turning and is slowing down. The vector expressing her angular velocity is (4 pts.) 1. in the +x direction. 2. in the –x direction. 3. in the +y direction. 4. in the –y direction. 5. in the +z direction. 6. in the –z direction. 7. zero. c.) What is the net torque exerted by the four forces about the point A? (4 pts.) 1. 80 N m 2. 100 N m 3. 180 N m 4. 200 N m 5. None of the aboveFirst Name: ____________________ Last Name:_____________________ Section: ________ ■ 6 d. Prof. Timbie’s sensible, small car has a mass of 1000 kg and is parked on the street. His neighbor runs into it with his SUV. The force (in kilo-Newtons) exerted on Prof. Timbie’s econo-car during the collision is shown below. What is the final velocity of the econo-car ? (4 pts.) 1. 10 m/s 2. 20 m/s 3. 30 m/s 4. 40 m/s 5. 50 m/s e.) A block of mass m is released from the top of the frictionless track shown. What is its speed v at the top of the loop-the-loop? (4 pts.) 1. 2gh 2. (2gR)1/2 3. [2g(h-R)]1/2 4. [2g(h-2R)]1/2First Name: ____________________ Last Name:_____________________ Section: ________ ■ 7 Problem 5 Suppose you are given the following data points for the measurements of the speed v of a ball (dropped from rest from a height h) when it hits the ground: Trial # v (m/s) 1 1.1 2 1.2 3 1.0 4 1.1 5 1.1 6 0.9 7 1.2 8 1.2 9 1.1 a) Assuming as usual a product of Gaussian probability distribution functions for the likelihood function (denoted as symbol L in lecture), what would you estimate for the true value (or mean value) of v (7 pts.)? b) What would you estimate for the error in each of the measurements of v (7 pts.)? c) What would you estimate for
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