physics
posted by help .
a slide loving pig slides down a certain 44° slide in twice the time it would take to slide down a frictionless 44° slide. What is the coefficient of kinetic friction between the pig and the slide?

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...
mgSinThetamg*mu*Costheta=m Vf/time
=m 1/2 V'/2 t' where the ' means no friction.
g sinThetag*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 sinThetamu*g*CosTheta=g sinTheta/4
dividing both sides by g cosTheta
tanThetamu=tantheta /4
mu=3/4 tanTheta
check that.