2. 2. A small particle of mass m is pulled to the top of a frictionless half-cylinder by a light cord that passes over the top of the cylinder as shown. The particle moves at constant speed. a) Show that T = mgcos(0). (Hint: consider the tangential component of acceleration) b) By integrating S F · dř find the work done by the m cord in moving the particle from the bottom to the top of the half-cylinder. R c) Now integrate f F· dĩ to find the work done by gravity as the particle travels over the same path d) Use the work-kinetic energy theorem to check that your answers to b and c make sense.
2. 2. A small particle of mass m is pulled to the top of a frictionless half-cylinder by a light cord that passes over the top of the cylinder as shown. The particle moves at constant speed. a) Show that T = mgcos(0). (Hint: consider the tangential component of acceleration) b) By integrating S F · dř find the work done by the m cord in moving the particle from the bottom to the top of the half-cylinder. R c) Now integrate f F· dĩ to find the work done by gravity as the particle travels over the same path d) Use the work-kinetic energy theorem to check that your answers to b and c make sense.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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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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Transcribed Image Text:2. 2. A small particle of mass m is pulled to the top of a frictionless half-cylinder by a light cord that
passes over the top of the cylinder as shown. The particle moves at constant speed.
a) Show that T =
mgcos(0). (Hint: consider the
tangential component of acceleration)
b) By integrating S F · dř find the work done by the
m
cord in moving the particle from the bottom to
the top of the half-cylinder.
R
c) Now integrate S F · dĩ to find the work done by
gravity as the particle travels over the same path
d) Use the work-kinetic energy theorem to check that your answers to b and c make sense.
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