A particle of mass m moves in the XY-plane, and its position vector is given by = a cos wtî + b sin wtĵ where a, b, and w are positive constants, and a > b. Show that a. The particle moves in an ellipse. b. The force acting on the particle is always directed toward the origin. The total work done by the force in moving the particle once around the ellipse is zero c. d. The force is conservative.

A particle of mass m moves in the XY-plane, and its position vector is given by = a cos wtî + b sin wtĵ where a, b, and w are positive constants, and a > b. Show that a. The particle moves in an ellipse. b. The force acting on the particle is always directed toward the origin. The total work done by the force in moving the particle once around the ellipse is zero c. d. The force is conservative.

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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Instantaneous Power

Power is defined in physics as the amount of energy transmitted or transformed per unit time. The watt is the unit of electricity in the International System of Units, equivalent to one joule per second.

Question

A particle of mass m moves in the XY-plane, and its position vector is given by
= a cos wtî + b sin wtĵ
where a, b, and w are positive constants, and a > b. Show that
a. The particle moves in an ellipse.
b. The force acting on the particle is always directed toward the origin.
c. The total work done by the force in moving the particle once around the
ellipse is zero
d. The force is conservative.

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