1. A ball (B) of mass m moves with velocity v relative to an observer (O). The momentum of B relative to O is p=mv according to Newtonian mechanics and p=gamma x mv according to Special Relativity. What do the above two theories predict for B's momentum if its speed equals c, the speed of light?
2. Alice travels from Earth to a distant star that is 25 light years away. One light year is the distance that light propagates in one year. Bob stays at home on Earth. Alice moves at v=0.9998c relative to Bob. The gamma factor is 50. How far has Alice traveled according to (i) her measurements and (ii) those of Bob?© BrainMass Inc. brainmass.com December 24, 2021, 6:57 pm ad1c9bdddf
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Newtonian Mechanics predicts that the momentum = mc (finite) where as Special theory of relativity predicts that the momentum = γmc = 1/sqrt(c^2-c^2) * mc = mc/0 = α (infinite) where γ= 1/sqrt(v^2-c^2).
For the person who is moving with a velocity comparable to the velocity of light, length seems contracted by a factor of γ. Hence, for Alice the distance of 25 light years is contracted by a factor of gamma.
(i) For her distance = 25 ly/ γ = 25/50 = 0.5 light years.
(ii) For Bob the distance = 25 light years. (distance as measured by a stationary observer)© BrainMass Inc. brainmass.com December 24, 2021, 6:57 pm ad1c9bdddf>