Unformatted text preview: Physics 2750 FS 2007 (white version) Exam 3 Last Name______________________________ First Name_____________________________ ID # ___________________ This is a closed book exam. I understand, pursuant to University Regulations on academic honesty, that I am not to use any notes or information other than what is in the official, non‐ annotated formula sheet. Signature_______________________________________ For multiple choice questions, please make sure that you circle the letter for the answer which you believe to be correct and only that answer. If more than one answer is circled for the same problem, you will not receive credit for it. Don’t get hung up on questions. They should take only one or two minutes each. If you find yourself spending more than a few minutes on a multiple choice question you are probably looking at it the wrong way. You should skip it for now and come back to it later. For full credit show your work for solutions to questions that require calculations. Explain from where you start to solve the problem and show your math flowing from it for full credit. No shown work, no credit! Relax, read carefully, think – and then read everything again. During the exam, if you have questions please raise your hand and the TA or the instructor will come to you and provide help. 1. (5 points) A wheel of radius R rotates about a fixed axis. When a point at distance R from the center is moving with angular speed ω, a point located at a distance R/2 from the center is moving with angular speed a ω/4 b) ω/3 c) ω/2 d) ω e) 2ω 2. A primitive yo‐yo is made by wrapping a string several times around a solid cylinder with mass M = 200 g and radius R = 10 cm. You hold the end of the string stationary while releasing the cylinder with no initial velocity. The string unwinds but does not slip or stretch as the cylinder drops and rotates. In all calculations take g = 10 m/s2. The moment of inertia for a cylinder is ½ MR2. a) Find the speed of the center of mass of the cylinder after it has dropped a distance h = 1.2 m. (10 points) b) Find the tension in the string and the acceleration of the cylinder. (15 points) 3. In the figure below the three identical yo‐yos are all initially at rest on a horizontal surface. For each yo‐yo, the string is pulled in the direction shown and as a result it moves. In each case there is sufficient friction for the yo‐yo to roll without slipping. Draw the force of friction acting on each yo‐yo (on the figures provided) and clearly state in which direction it will roll: clockwise or counterclockwise. (3 points) Direction: (2 points) (3 points) Direction: (2 points) (3 points) Direction: (2 points) 4. (5 points) A particle located at the position vector r = −2i + j has a force F = − j + 3k (in N) acting on it. The torque about the origin is: a) 3i − 6 j + 2k Nm c) 3i + 6 j + 2k Nm e) −3i + 6 j + 2k Nm b) 3i − 6 j − 2k Nm d) 0 Nm 5. (5 points) A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a torque of 0.80 N∙m on the saw blade. If the blade rotates with a constant angular velocity of 10 rad/s the work done on the blade by the motor in 1.0 min is: a) 0 b) 480 J c) 960 J d) 1400 J e) 1800 J 6. (5 points) An object weighs 10 N on the earth's surface. What is the weight of the object on a planet that has one tenth the earth's mass and one half the earth's radius? a) 4 N b) 1 N c) 20 N d) 2 N e) 10 N 7. The horizontal beam in the figure below weights 150 N and its center of gravity is at its center. a) On the figure provided clearly draw all the forces that act on the horizontal beam. Make sure to draw the forces with their point of application exactly where they act. (5 points) b) Find the tension in the string (9 points) c) Find the horizontal and vertical components of the force exerted on the beam at the wall. (16 points) 8. A projectile of mass m = 0.1 kg moves to the right with speed v = 2 m/s. The projectile strikes and sticks to the end of a stationary rod of mass M = 0.5 kg and length d = 1 m that is pivoted about a 1 frictionless axle through its center. The moment of inertia of the rod is Md 2 . 12 a) Find the angular speed of the system right after the collision. (10 points) b) Determine the change in kinetic energy of the system due to the collision. (6 points) c) What happened to the energy? (4 points) MC 20/ Q2 25/ Q3 15/ Q7 30/ Q8 20/ Total 110/ ...
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 Spring '10
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