Question

A slide loving pig slides down a certain 28° slide in three times the time it would take to slide down a frictionless 28° slide. What is the coefficient of kinetic friction between the pig and the slide?

Answer 1

let k be the coefficient of kinetic friction between the pig and the slide

m be mass of pig

friction force

= k * mg cos 28

force // to slope due to weight

= mg sin 28

Net force down the slope

= mg sin 28 - k * mg cos 28

= mass * acc

= m * a

a= g sin 28 - k * g cos 28

without friction

ma' = mg sin 28

a' = g sin 28

s= ut + 0.5 a' t^2

s = 0 + 0.5 * g sin 28 t^2

with friction

s = 0 + 0.5 * [g sin 28 - k * g cos 28] (2t)^2

0.5 * g sin 28 t^2 = 0.5 * [g sin 28 - k * g cos 28] (2t)^2

0.5 * g sin 28 t^2 = 2 g sin 28 t^2 - 2k * g cos 28 * t^2

2k * g cos 28 * t^2 = 1.5 * g sin 28 t^2

2k * cos 28 = 1.5 * sin 28

k = 0.75 tan 28

k = 0.39878 ---answer