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?

Question

Charles Aeschliman · Accepted Answer

0.64

The application of mechanical energy conservation can solve the problem. 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#

Xavier Adame · Answer

undefined To find the coefficient of kinetic friction, you can use the formula:

μ = tan(θ)

where θ is the angle of the incline. Since the incline has an angle of π/3, substitute this value into the formula:

μ = tan(π/3)

μ ≈ √3

So, the coefficient of kinetic friction for the material is approximately √3.