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captain.joco
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Homework Statement
A particle of mass m is tied to a string which goes through a hole in a smooth horizontal table. The particle moves in uniform circular motion with speed v0. The radius of the cricle is R0. By puling the string very slowly, the radius of the circular motion is reduced tao R1.
Show that the work done by the string force is equal to the change of Kinetic energy.
Homework Equations
F=Tension(T) = mv^2 /R
K ( kinetic energy ) =1/2mv^2
K1-K0 ( final - initial kinetic energy ) = 1/2m ( v1^2 - v0^2 )
where v1 = R0*v0/R1 ( using angular momentum conservation ).
The Attempt at a Solution
W=∆K ( work energy theorem )
W = ∫Fdr , where F = m*v*v / r ( centripetal force )
I think I need some substitution to get the integral to give the ∆E...