A disc of mass `m` slides with the zero initial velocity down an inclined plane of inclination `theta` to the harizontal, having traveled the distance `d` along the horizontal plane, the disc stops. Find the work performed by the friction over the whole distance, assuming the friction coefficient `mu` for both the inclined and horizontal planes.

Explanation

Let `h`: Height of the inclined plane
`K_1+U_1=K_2+u_2+W_f`
`mgh=W_f=mumgcosthetaxx(h)/(sintheta)+mumgd`
`h(1-mucottheta)=mudimpliesh=(mud)/(1-mucottheta)`
on the inclined plane
friction `=mumgcostheta`, distance travelled `(h)/(sintheta)`
On the horizontal plane,
Friction `=mumg`, distance travelled d
Work done by frictioni `W_f^(')=-W_f=-mgh=(mumgd)/(1-mucottheta)`