Question

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?

Answer 1

`=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`