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?

1 Answer
Feb 27, 2016

Answer:

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#