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Basic Physics Sliding Bar on Rails

  1. Jul 22, 2010 #1
    A conducting bar of length L = 21.2 cm and mass M = 60.0 g lies across a pair of conducting rails. The contact friction between the bar and the rails is negligible, but there is a resistor at one end with a value R = 30.0 Ohms. Initially the rod is given an initial speed of v0 = 64.0 meters per second. There is a uniform magnetic field perpendicular to the plane containing the rod and rails of magnitude B = 1.3 T.
    What is the speed of the rod at time t = 26.068 s?

    I know:
    v=v0 + at
    F=ma
    F=iLB
    i=(emf)/R
    emf = dflux/dt
    flux = BA

    I know I need to solve for the area to get the flux and the length (L) is constant while the width is changing but I don't understand how to get the integral or set up the integral for the width. Please help ASAP.
     
  2. jcsd
  3. Jul 22, 2010 #2

    kuruman

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    v = v0+at is out of the picture. This is not a constant acceleration situation. All your other equations are relevant.
    You need to set up a differential equation and solve it. Start with

    F = m (dv/dt)

    Replace F with iLB and then replace i with (1/R)(dΦ/dt). The expression for dΦ/dt is proportional to v. So you end up with the differential equation that is essentially

    dv/dt = (const)v

    You should be able to find what "const" is and to integrate the above equation.
     
  4. Jul 22, 2010 #3
    Okay, so dv/dt = v(const) or dv/dt = v(LB/mR)
    I still don't know how to solve for v.
    When I integrate dv/dt, do I get r(LB/mR)? and if so, what is r?
     
  5. Jul 22, 2010 #4

    kuruman

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    This is incorrect. Please show how you got it, then I can point out where you went wrong.
    Worry about that later. First get the correct expression for dv/dt.
    No, you do not.
    I don't know, but r it appears in your expression above. You made it up so you should know what it represents.
     
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