A bead is released from rest at point A and slides down the wire into the form o

Question

A bead is released from rest at point A and slides down the wire into the form of a helix, as shown in the a-part of the figure. The experiment is repeated in the b-part of the figure where the wire has been unwrapped to form a straight line with the slope equal to that on the helix. What is the velocity reach by the bead as it passes point B or B? in each case in the absence of friction? In the presence of some friction does the velocity depends on the path, and if so, for which case would the velocity at the lowest position be grater?

Explanation / Answer

In both case if friction is absent, Energy loss by frictional force = 0 so final velovity=v 1/2 m*v^2=m*g*h so v=sqrt(2gh) If friction is present, acceleration for b case = g acceleration for a case= g+m(omega)^2*r due to more acceleration on helical path(a), more F will act on mass so more frictional E loss so it will have less final Velocity than case b

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