2006 Final Solutions

2006 Final Solutions - McGill University PHYS...

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Phys 101 Final, Dec 12 th , 2006 Page 1 McGill University PHYS 101 (Introduction to Mechanics for the Life Sciences) FINAL EXAM SOLUTIONS 2006 PHYS 101 Final exam Examiner: K.J. Ragan x6518 Short answer questions (answer all) : you should not need to do any calculations for these questions , and should answer in a few words, a few short phrases, or a simple sketch. In some cases you might find it useful to quote an appropriate formula. 1) [2 pts] Tarzan is perfecting the timing of his vine-swinging, hoping to be able to impress Jane. He wonders if he has to change his timing when he has Jane on the vine with him. Assuming that the vine length is the same, what can you say about the period of the swing of the vine when he is alone, or with Jane? Assume small amplitude swings. Solution : The period of a pendulum is independent of mass, for small amplitude swings: Tarzan doesn’t have to worry about his timing (at least, not his pendulum timing!).
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2) [2 pts] For the two plots of velocity vs. time (v vs. t) shown below, which, if any, best represents the motion of a ball thrown vertically up in the air and caught some time T later? Solution : b). The velocity starts as a large positive number (upwards moving), and ends as a large negative number (downwards going). The slope of a velocity vs. time graph is the acceleration, and we know that this motion is characterized by constant a (at -9.8 m/s 2 ). So b) correctly describes the motion. a) describes a motion with NET displacement (the area under the curve), velocity ALWAYS positive, and acceleration ALWAYS changing. 3) [2 pts] Would you expect sound waves, or light waves, to diffract more (ie, have a larger diffraction angle) when they pass through the same opening such as a doorway? Why? Solution : You would expect sounds waves to diffract more (ie, have a larger characteristic diffraction angle). That angle is θ = λ /D where D is the opening (doorway) size. Since λ sound >> λ light , θ sound >> θ light . 4) [2 pts] Two balls of different mass (but equal size) are thrown vertically upwards into the air, with the same initial velocity. They do not collide. Which ball, if any, reaches the greatest height ? Solution : They reach the same height. The initial velocity is the same, and the final height is given by d = v o 2 /2g, independent of mass. 5) [2 pts] A physics student plays with two examples of simple harmonic motion: a mass on a spring and a simple pendulum. She finds that each of the two has a period of 1.0 sec. She’s an astronaut, and on her next trip to the moon takes each along and measures the
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2006 Final Solutions - McGill University PHYS...

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