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.

Physics for Scientists and Engineers with Modern Physics
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Author:Raymond A. Serway, John W. Jewett
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Chapter7: Energy Of A System
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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.
Transcribed Image Text: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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