A solid metal cylinder of mass m rolls down parallel metal rails spaced a distan

Question

A solid metal cylinder of mass m rolls down parallel metal rails spaced a distance L apart with a constant acceleration of magnitude a0 [part (a) of figure]. The rails are inclined at an angle ? to the horizontal. Now the rails are connected electrically at the top and immersed in a magnetic field of magnitude B that is perpendicular to the plane of the rails [part (b) of figure].

(c) Instead of rolling at constant acceleration, the cylinder now approaches a terminal speed vt. Express vt using L, m, R (the total electrical resistance of the circuit consisting of the cylinder, rails, and wire), a0, ?, and B, respectively. Assume R is constant (that is, the resistances of the rails themselves are negligible).

vt=?

Explanation / Answer

terminal velocity is found at the position where net force=0
force due to gravity=ma0
force due to magnetic field=ilB
i=V/R
V=Blv
(Blv/R)lB=ma0
vt=Rma0/(B2l2)

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