Posted by help on Monday, December 15, 2008 at 5:03pm.
The force of friction on the slide is
mg*mu*cosTheta, and the component of gravity down the slide is mgsinTheta
F=ma=m(vf/time) but vf with friction is 1/2 that of no friction (why? average velocity is 1/2 that of no friction).
so, with friction...
mgSinTheta-mg*mu*Costheta=m Vf/time
=m 1/2 V'/2 t' where the ' means no friction.
g sinTheta-g*mu*cosTheta=V'/4t'
now without friction..
mg sinTheta -nofriction=m v'/t'
or v'/t'=g sinTheta
now back into the friction equation.
g sinTheta-mu*g*CosTheta=g sinTheta/4
dividing both sides by g cosTheta
tanTheta-mu=tantheta /4
mu=3/4 tanTheta
check that.
cool
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