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Proton Bombardment

  1. Mar 2, 2008 #1
    1. The problem statement, all variables and given/known data
    A proton with mass 1.45*10^-27 kg is propelled at an initial speed of 3.99*10^5 m/s directly toward a uranium nucleus 5.16 m away. The proton is repelled by the uranium nucleus with a force of magnitude F = a/x^2 where x is the separation between the two objects and a = 2.12 *10^-26 Nm2. Assume that the uranium nucleus remains at rest. What is the speed of the proton when it is 8.79 *10^-10 m from the nucleus?

    Give your answer in m/s in scientific notation to three significant digits (i.e. 1.15*10^2)

    Note: The numbers given in this problem do not represent actual figures, instead this is to be thought of as a theoretical calculation.

    2. Relevant equations
    F = a/x^2
    W = F*D
    KE = .5*m*Vf^2-.5*m*Vi^2

    3. The attempt at a solution

    F = a/x^2
    F = 2.12 *10^-26/(8.79 *10^-10)^2 = 2.7438*10^-8 N
    W = F*D
    W = 2.7438*10^-8*(5.16 - 8.79 *10^-10) = 1.4158*10^-7 J
    KE = .5*m*Vf^2-.5*m*Vi^2
    1.4158*10^-7 = .5(1.45*10^-27)Vf^2-(.5)(1.45*10^-27)(3.99*10^5)^2
    Vf^2 = 1.95285*10^20
    Vf = 1.397410*10^10 m/s

    The correct answer is supposed to be 3.55*10^5 m/s, no matter how many times I try to work this problem out I cannot every arrive at the correct value for Vf.
  2. jcsd
  3. Mar 2, 2008 #2

    Shooting Star

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    Homework Helper

    You have to integrate the force eqn wrt dist to find the work done. The force is a function of dist, not constant.

    Otherwise, use the concept of PE and KE which you must have learnt in electrostatics.
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