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?

1 Answer
Mar 11, 2016

Answer:

#=0.33#

Explanation:

slant height of the ramp# l=5m#
Angle of inclination of the ramp #theta = 3pi/8#
Length of horizontal floor #s=12m#
vertical height of the ramp #h =l*sintheta#
Mass of the object = m
Now applying conservation of energy

Initial PE = work done against friction
#mgh=mumgcostheta xxl+mumg xxs#
#=>h=mucostheta xxl+mu xxs#
#=>mu=h/(lcostheta+s)=(lsintheta)/(lcostheta+s)=(5xxsin(3pi/8))/(5cos(3pi/8)+12)=4.62/13.9=0.33#