A small ball of mass m is suspended from a string of length L. The ball revolves with constant speed v in a horizontal circle of radius r as shown in Figure 2. Find an expression for kinetic energy in terms of the length of the string and the r radius. LA

An expression for kinetic energy in terms of the length of the string and the r radius.given,length=Lradius=rmass=mspeed=vDrawing free body diagram,From free body diagram,We have,Writing force equations in y-direction,Tcosθ-mg=0or, Tcosθ=mg ...1stalso, Writing force equations in x-direction,Tsinθ=macwhere, ac is centripetal force,ac=v2rSubstituting above,Tsinθ=mv2r ..2nddividing 2nd from 1st,TsinθTcosθ=mv2rmg tanθ=v2rgor, v2=rgtanθwhere, r=Lsinθso, v2=LsinθgtanθSo, kinetic energy(K.E.)=12mv2=12mLsinθgtanθ=12mLgsinθtanθSo, kinetic energy(K.E.)=12mLgsinθtanθ.

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University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 24CQ: What is the dot product of a vector with the cross product that this vector has with another vector?

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A small ball of mass m is suspended from a string of length L. The ball revolves with constant speed v in a horizontal circle of radius r as shown in Figure 2. Find an expression for kinetic energy in terms of the length of the string and the r radius.

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