Question

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?

Answer 1

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.