Two stiff parallel wires a distance d apart in a horizontal plane act as rails t

Question

Two stiff parallel wires a distance d apart in a horizontal plane act as rails to support a light metal rod of mass m(perpendicular to each rail), see the figure.(Figure 1) A magnetic field B? , directed vertically upward (outward in diagram), acts throughout. At t = 0, a constant current Ibegins to flow through the system.

Determine the speed of the rod, which starts from rest at t = 0, as a function of time assuming no friction between the rod and the rails.

Express your answer in terms of the variables I, d, B, m, and t.

Determine the speed of the rod, which starts from rest at t = 0, as a function of time if the coefficient of friction is ?k.

Express your answer in terms of the variables I, d, B, m, ?k, t, and acceleration due to gravity g.

In which direction does the rod move, east or west, if the current through it heads north?

Explanation / Answer

if there is no friction, the force, F = BIL = ma

acceleration is, a = BIL/m

Then using v = v0 + at, when the rod starts from rest shows that

thus the speed is, v = BILt/m

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the friction force opposes the relative motion of the object.

its defined as,e Ff = Fn = kmg

thus, the net force is,

F = BIL - kmg = ma

thus, the acceleration, a = (BIL- kmg)/m

therefore, the velocity is,

v = (BIL- kmg)t/m= BILt/m - kgt

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from the right hand rule, the rod is moving along the east.

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