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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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You are working during the summer at a company that builds theme parks. The company is designing an electromagnetic propulsion system for a new roller coaster. A model of a substructure of the device appears in the figure below.

Two parallel, horizontal rails extend from left to right, with one rail behind the other. A cylindrical rod rests on top of and perpendicular to the rails at their left ends. The distance between the rails is d and the length of the rails is L. The magnetic field vector B points vertically down, perpendicular to the rails. Within the rod, the current I flows out of the page, from the rail in the back toward the rail in the front.

The rod is of length d = 1.00 m and mass m = 0.600 kg. The rod carries a current I = 100 A in the direction shown and rolls along the rails of length L = 20.0 m without slipping. The entire system of rod and rails is immersed in a uniform downward-directed magnetic field with magnitude B = 2.00 T. The electromagnetic force on the rod is parallel to the rails, causing the rod to roll to the right in the figure. When a full-scale device is produced, this rod will represent the axle of wheels on which the car and its passengers ride. The electromagnetic force on the axle will provide the motion of the car at the beginning of the roller-coaster ride. Your supervisor wants to test the substructure in the figure in a flat outdoor area on the grounds of the company. By projecting the rod from the rails in a horizontal direction from a height h = 2.00 m, the projection speed can be determined from how far from the ends of the rails the rod hits the ground. Your supervisor asks you to determine the length of the outdoor area needed to test the device. (Determine the total horizontal distance, in m, from the initial position of the rod on the tracks to the final position of the rod where it lands on the ground.)

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