Question

An object, previously at rest, slides `7 m` down a ramp, with an incline of `(pi)/3`, and then slides horizontally on the floor for another `6 m`. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Answer 1

0.64

Explanation:

It can be solved by applying conservation of mechanical energy.

The initial PE of the body = `mglsintheta`,where m= mass of the object,l is the length of the inclined ramp i.e.7m, `theta=pi/3,`angle of inclination of the ramp.and g = acceleration due to gravity.

The frictional force exerted by the ramp `F_r=mumgcostheta`, where`mu=`coefficient of kinetic friction
Again the frictional force exerted by horizontal floor `F_f=mumg`
By law of conservation of energy
Work done against friction = Initial PE

`:.F_r*7+F_f*6=mglsintheta`
`=>mucancel(mg)cos(pi/3)*7+mucancel(mg)*6=cancel(mg)*7sin(pi/3)`
`=>mu(3.5+6)=7*sqrt3/2`
`mu=7*sqrt3/(9.5*2)=0.64`