A pig enjoys sliding down a ramp. The farmer who owns the pig discovers that if he greases the pig, there is no fiction and the pig enjoys the slide more (happy pig, better bacon). The time required for the pig to reach the bottom of the slide with friction is twice the time without friction. Assumed the pig starts from rest. Derive an expression for the coefficient of friction. (

Explanation:

Acceleration without friction on an inclined plane = g sinθ

Acceleration with friction on inclined plane = g sinθ - μ g cosθ

s = 1/2 a t²

For motion on friction-less surface

s = 1/2 g sinθ t₁²

For motion on frictional surface

s = 1/2( g sinθ - μ g cosθ)  t₂²

t₂ = 2t₁

(  sinθ - μ  cosθ)  t₂² =  sinθ t₁²

(  sinθ - μ  cosθ)  4t₁² =  sinθ t₁²

(  sinθ - μ  cosθ)  4 =  sinθ

4sinθ - sinθ = 4μ  cosθ

3sinθ = 4μ  cosθ

3 / 4 tanθ =μ  

μ  = .75  tanθ