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Homework Help: Show that Newton's Second Law is valid?

  1. Jun 17, 2015 #1
    1. The problem statement, all variables and given/known data
    In a laboratory frame of reference, an observer notes that Newton's 2nd Law is valid.
    Show that Newton's 2nd Law is also valid for an observer moving at a constant speed, small compared with the speed of light, relative to the laboratory frame.

    2. Relevant equations
    dx'/dt = dx/dt - v

    3. The attempt at a solution

    d^2 x' / dt^2 = d^2 x/ dt^2 Can someone help me understand this better?
  2. jcsd
  3. Jun 17, 2015 #2
    Which part don't you understand?

  4. Jun 17, 2015 #3
    I don't understand the whole answer. Can you explain what each part means?
  5. Jun 17, 2015 #4
    I know it means derivative but that's it.
  6. Jun 17, 2015 #5
    The velocity is subtracted from the derivative because it has to be smaller than the speed of light? Also, why is the d squared on the second part and why is d^2x` divided by dt/2 and why does this equal: d^2 x/ dt^2??
  7. Jun 17, 2015 #6
    The second derivative of $x$ is the acceleration $a$. Considering that the second Newton's law states that $F=ma$, your acceleration doesn't varies because you have added a constant. So, the second Newton's law is valid in this reference frame.

    Also, you are mistaken with the notation. $d^2x/dt^2$ means "second derivative of x respect to time".
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