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Hibbeler 13-34

  1. Mar 2, 2014 #1
    1. The problem statement, all variables and given/known data

    In the cathode-ray tube, electrons having a mass m
    are emitted from a source point S and begin to travel
    horizontally with an initial velocity v0. While passing
    between the grid plates a distance l, they are subjected to a
    vertical force having a magnitude eV/w, where e is the
    charge of an electron, V the applied voltage acting across
    the plates, and w the distance between the plates. After
    passing clear of the plates, the electrons then travel in
    straight lines and strike the screen at A. Determine the
    deflection d of the electrons in terms of the dimensions of
    the voltage plate and tube. Neglect gravity which causes a
    slight vertical deflection when the electron travels from S to
    the screen, and the slight deflection between the plates.

    See attachment for picture

    2. Relevant equations

    ∑Fy = may

    vy = ayt

    3. The attempt at a solution

    By Newton's 2nd Law,

    ay = eV/mw from 0 to l

    By kinematics t1 = l/v0
    t2 = t1 + L/v0 = l/v0 + L/v0

    From 0 to l, by kinematics:

    y1 = 1/2*eV/mw*(l/v0^2)
    (v1)y = eV/mw*l/v0

    Hence, from l to L where ay is zero

    y2 = d = 1/2*eV/mw*l^2/v0^2 + eV/mw*L/v0

    It appears the solution is missing the left term I keep getting, any idea why?
     

    Attached Files:

    Last edited: Mar 2, 2014
  2. jcsd
  3. Mar 2, 2014 #2

    Redbelly98

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    The solution is missing that term because they are neglecting the slight deflection between the plates, as mentioned at the end of the problem statement.
     
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