An object, previously at rest, slides 5 m down a ramp, with an incline of (3pi)/8 , and then slides horizontally on the floor for another 12 m. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Mar 11, 2016

$= 0.33$

Explanation:

slant height of the ramp$l = 5 m$
Angle of inclination of the ramp $\theta = 3 \frac{\pi}{8}$
Length of horizontal floor $s = 12 m$
vertical height of the ramp $h = l \cdot \sin \theta$
Mass of the object = m
Now applying conservation of energy

Initial PE = work done against friction
$m g h = \mu m g \cos \theta \times l + \mu m g \times s$
$\implies h = \mu \cos \theta \times l + \mu \times s$
$\implies \mu = \frac{h}{l \cos \theta + s} = \frac{l \sin \theta}{l \cos \theta + s} = \frac{5 \times \sin \left(3 \frac{\pi}{8}\right)}{5 \cos \left(3 \frac{\pi}{8}\right) + 12} = \frac{4.62}{13.9} = 0.33$