First slide
Work
Question

A square carpet of a mass of 20 kg is dragged from one room into another as shown in the figure. The width of the corridor and the carpet is the same, i.e., 2 m. The friction coefficient is 0.1 at the end of the first room and 0.2 at the other end, in the corridor it changes linearly from 0.1 to 0.2. The carpet presses the floor uniformly. Find the amount of work (in J) that must be done to drag the carpet slowly from the first room to the other.

Moderate
Solution

Let the coefficient of friction for the corridor is given as
μ(x)=0.1+(0.20.1)x2
Let us divide the carpet into infinitesimally thin vertical strips. The mass per unit width of the carpet be
λ=20 kg2 m=10 kg m
Work done in moving each strip (dl) through a distance dx is μ(λdl)gdx. Total work done in moving each strip from one end to the other
=020.1+0.12xλdlgdx=(0.3)λdlg
Total work done in moving the carpet =020.3λgdl
0.6×λg=60 J

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