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sp09final

sp09final - Final Exam NAME Units must be included in final...

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Final Exam, May 13, 2009 NAME: Units must be included in final answers, where appropriate. You must show your work! Gravitational acceleration at Earth’s surface, g = -9.8 m/s 2 . Leave the gravitational constant, G , in symbolic form. Problem 1 On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to a maximum rotational speed of 1.4 rad/s. The seats are then allowed to coast at 1.4 rad/s for 42 seconds; after which they are brought to rest in another 7 seconds. a.) What is the tangential acceleration of the passengers during the first 21 s of the ride? b.) Make two sketches, one of the time dependence of the rotational velocity, and one of the time dependence of the tangential acceleration. Sketch from 0-70 seconds. (Be sure to label both axes on each plot.)

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Problem 2 4 m v=5 m/s 3 m A box of mass 30.0 kg slides down a ramp. It starts from rest and reaches a speed of 5 m/s at the bottom. In that time it moves down a vertical distance of 3.0 m and across a horizontal distance of 4.0 m. a.) Find the work done by the frictional force. b.) Find the magnitude of the force of friction between the ramp and the box.
Problem 3 1 x y I II P 1 A particle is subjected to a force that depends on position as follows: ~ F = 2 y ˆ i + 5 ˆ j , where the force is measured in Newtons and the distance in meters. a.) Calculate the work done by this force as the particle moves from the origin to the point P at x = 1 . 0 m, y = 1 . 0 m along the straight path I as shown in the figure. b.) Calculate the work done by this force if the particle returns from the point x = 1 . 0

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