3. As we discussed in the class, if we put unequal masses connected by a wire on

Question

3. As we discussed in the class, if we put unequal masses connected by a wire on the two sides of an inclined plane the system will start moving, generically along the direction of the heavier mass. Let us then consider an arrangement of fourteen spheroids slipped around a hanging inclined plane in the following fashion: The bottom droops as a garland, which is in fact in a state of balance. However on one side of the plane there are four spheroids, while the other side has only two spheroids. Thus there seems to be an imbalance of force, and from our analysis it would seem that the system will start moving. If there is no friction, this motion should continue forever, and we have thus succeeded in constructing a perpetual machine! Is it true? Give quantitative reasons

Explanation / Answer

let tension in the left end of the garland just above the first hanging ball be T1
tension in the right end of the garland, just above the first hanging ball be T2

now, as the left and the right angles of the wedge are different
the angle made by T1 and T2 with the horizontal must be same though ( as the hanging part of garland shall form an arc with cord passing through it)

hence
as the angles are the same

now if the tensions are also the same on the both sides, then the side having more mass must start falling perpetually
but this never happens, because first of all, the friction stops the beads from moving perpetually
secondly, values of T1 and T2 are also differnt to keep the garland in static equilibrium so tghat seocnd law of thermodynamics is not violated

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