Problem 3: A mass m is thrown from the origin att = 0 with initial three-momentum po in the y direction. If it is subject to a constant force Fo in the x direction, find its velocity v as a function of t, and by integrating v find its trajectory. Check that in the non-relativistic limit the trajectory is the expected parabola. Hint: The relationship F = P is still true in relativistic mechanics, but now p = ymv instead of p = mv. To find the non-relativistic limit, treat c as a very large quantity and use the Taylor approximation (1+ x)" = 1 + nx when a is small.
Problem 3: A mass m is thrown from the origin att = 0 with initial three-momentum po in the y direction. If it is subject to a constant force Fo in the x direction, find its velocity v as a function of t, and by integrating v find its trajectory. Check that in the non-relativistic limit the trajectory is the expected parabola. Hint: The relationship F = P is still true in relativistic mechanics, but now p = ymv instead of p = mv. To find the non-relativistic limit, treat c as a very large quantity and use the Taylor approximation (1+ x)" = 1 + nx when a is small.
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Transcribed Image Text:Problem 3:
A mass m is thrown from the origin att = 0 with initial three-momentum po in the y direction. If it is
subject to a constant force F, in the x direction, find its velocity v as a function of t, and by integrating v
find its trajectory. Check that in the non-relativistic limit the trajectory is the expected parabola.
Hint: The relationship F = P is still true in relativistic mechanics, but now p = ymv instead of
p = mv. To find the non-relativistic limit, treat c as a very large quantity and use the Taylor approximation
(1+ x)" = 1 + nx when a is small.
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