phy140_final_may07 - UNIVERSITY OF TORONTO Faculty of Arts...

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Unformatted text preview: UNIVERSITY OF TORONTO Faculty of Arts and Science April/May EXAMINATIONS 2007 PHY 140Y Duration - 3 hours Write your name, student number, and TA’s name on ALL examination booklets used. The only allowed aids are hand-held calculators and the attached appendix of formulae (last page). Answer BOTH Parts A and B. Part A is worth 60% and Part B is worth 40% of the total. For each question, the mark breakdown for each subsection is listed in the right-hand margin in square brackets. Show all derivations, and justify each significant step in your answer. This exam has ?? pages. PART A (60%) Answer SIX of the following eight questions. Each question is worth 10 points. If you answer more than six questions, then only the first six to be encountered will be graded. If you work on more than six questions, explicitly state which ones you would like graded. 1. A block of mass m sits on an inclined plane of angle θ as shown in Figure ?? . The coefficient of kinetic friction of the plane is μ k . Ignore static friction in this problem. A force F A = Bmt where B is a constant and t is time, is applied to the block as shown in Figure ?? . The block is released, causing it to begin accelerating down the plane, starting from rest at t = 0 . Express your answers to the following questions in terms of the variables m,g,μ k ,θ,B and t only, where g is the gravitational acceleration. (a) What is the acceleration of the block down the plane? [2] (b) At what time t 1 is the applied force F A large enough to start slowing down the block? [1] (c) Find an expression for the block’s velocity as a function of time t . [2] (d) At what time t 2 will the block change its direction and start moving up the ramp? [1] (e) If θ = π/ 4 ,μ k = 0 . 50 ,B = 1 . m/s 3 ,m = 1 . kg and g = 9 . 8 m/s 2 , how much work is [4] done on the block in the time interval from t = 0 to t = t 2 by each of the following forces (keep 2 significant figures): (i) gravity, (ii) friction, (iii) normal force? PHY140Y - Foundations of Physics 2006-2007 Final Exam, page 1 of ?? m F A θ g FIG. 1: Question ?? . 2. A pendulum consisting of a ball of mass m at the end of a massless string of length L is released from rest at an angle θ to the vertical as shown in Figure ?? (A). Express your answers to the following questions in terms of the variables g,L,a and θ only. (a) What is the ball’s speed when it reaches its lowest point? [2] (b) At its lowest point the string catches a nail located a distance a above the bottom of the [3] string as shown in Figure ?? (B). Assuming the string stays taut (i.e. in tension), what is the maximum angle θ 1 that the string makes with the vertical? (c) Now don’t assume the string always stays taut. What is the angle θ 2 at which the string [5] will cease to be taut (i.e. when there is no tension left in the string)?...
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phy140_final_may07 - UNIVERSITY OF TORONTO Faculty of Arts...

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