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Constant Acceleration Problem

  1. Sep 2, 2013 #1
    1. The problem statement, all variables and given/known data

    I am about to start AS Level Physics and have been given some questions/problems to solve as introductory homework. However, I am stuck on one and cannot seem to get the answer specified as the correct one.

    An electron of mass 9.11x10-31kg is accelerated by a positive charge such that the electron experiences a constant force of 8.5x10-29N. The electron, which was already moving, then travels 45mm in 35microseconds. By first determining the acceleration of the electron, calculate its initial velocity.

    2. Relevant equations


    F = ma
    s = ut + 1/2at2

    F = Force (N)
    m = mass (kg)
    a = acceleration (ms-2)
    s = distance travelled (m)
    u = initial velocity (ms-1)
    t = time (s)

    3. The attempt at a solution

    Converting Units

    45mm = 0.045m
    35microseconds = 0.000035s


    Working Out Acceleration

    F =ma
    8.5x10-29 = 9.11x10-31 x a
    8.5x10-29 / 9.11x10-31 = a
    a = 93 + 277/911

    Check: 9.11x10-31 x (93 + 277/911) = 8.5x10-29

    Working Out Initial Velocity

    Rearranging the Equation:

    s = ut + 1/2at2
    ut = s - 1/2at2
    u = (s-1/2at2) / t

    Putting in the Values

    u = (0.045 - 1/2(93+277/911) x 0.0000352) / 0.000035
    u = (0.045 - (1.142974755x10-7 x 1/2)) / 0.000035
    u = (0.045 - 5.714873765x10-8) / 0.000035
    u = 0.04499994285 / 0.000035
    u = 1285.712653

    According to the booklet, the answer should be 4290ms-1 and not the value I got.
    I have been working at this for hours and cannot seem to find where I am going wrong. Help me out?
     
  2. jcsd
  3. Sep 2, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    Your work looks fine. Could be the booklet has a misprint: 4290 → 1290.

    With the given force the acceleration is on the order of 100m/s2. Over 35 microseconds that can only change the speed by a few thousandths of a meter per second (a*t). It won't significantly affect the initial velocity over that time period so a good approximation for the initial velocity is just Δs/Δt which is about 1290 m/s
     
  4. Sep 2, 2013 #3
    That is definitely a possibility gneill. I never tried rounding the numbers so never spotted how similar they actually could be. Thanks!
     
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