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237HW1sol - Physics 237 Solution to Homework Assignment#1...

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Physics 237 Solution to Homework Assignment #1 1-8. (a) This will not yield the same result since distance measured depends on the relative motion of the frames (Lorentz transformation). (b) As we saw in class, this will yield the same result if we define mass as “invariant mass.” The result will be different if we define momentum = mv (then mass becomes frame dependent.) (c) This will yield the same result (2 nd postulate). (d) This will not yield the same result since time interval depends on the relative motion of the frames (Lorentz transformation). (e) Newton’s first law states that a body stays at rest or in a state of uniform motion unless acted upon by an external force. This is a fundamental Law that cannot change as we go from one inertial frame to another. (f) This should not depend on the reference frame because it depends on fundamental quantities such as charge and mass. (g) The charge is an intrinsic property of the electron, a fundamental constant, and will not change with reference frames. 1.10. In frame S’ , we define the co-ordinates for the points A, B, and C as – L , 0, + L . In this reference frame, the light flash occurs with spacetime coordinates (0,0). (a) If an observer is at rest in S ’, the wavefronts clearly arrive at A and C simultaneously. The spacetime coordinates for these events are ( -L , ( L/c )) and (+ L , ( L/c )). (b) In frame S , we figure out the time coordinates for these two events: Arrival at A: t A = γ t A ' + β c x A ' = γ L c β c L = γ 1 β ( ) L c Arrival at C: t C = γ t C ' + β c x C ' = γ L c + β c L = γ 1 + β ( ) L c So clearly, according to an observer at rest in S , the wavefronts do not reach A and C simultaneously.
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