Date | May 2011 | Marks available | 2 | Reference code | 11M.3.HL.TZ1.17 |
Level | Higher level | Paper | Paper 3 | Time zone | Time zone 1 |
Command term | Determine | Question number | 17 | Adapted from | N/A |
Question
This question is about relative velocities and energy at relativistic speeds.
Two identical rockets are moving along the same straight line as viewed from Earth. Rocket 1 is moving away from the Earth at speed 0.80 c relative to the Earth and rocket 2 is moving away from rocket 1 at speed 0.60 c relative to rocket 1.
Calculate the velocity of rocket 2 relative to the Earth, using the
(i) Galilean transformation equation.
(ii) relativistic transformation equation.
Comment on your answers in (a).
The rest mass of rocket 1 is 1.0×103kg. Determine the relativistic kinetic energy of rocket 1, as measured by an observer on Earth.
Markscheme
(i) u'x= ux + v = 0.60c + 0.80c = 1.40c;
(ii) ux′(=ux+v1+uxvc2)=0.60c+0.80c1+0.60c×0.80cc2;
(=1.40c1.48)=0.95c;
Award [1] for answers that use v = –0.80 c to get an answer of –0.38 c.
the answer to (a)(i) exceeds c / the answer to (a)(ii) does not exceed c;
hence the Galilean transformation is not valid / the relativistic transformation must be used / OWTTE;
γ=1√1−v2c2=1√1=0.802c2c2=1.7;
EK=[γ−1]m0c2=[1.667−1]×1.0×103×[3.0×108]2;
=6.0×1019J
Award [0] for answers that use Ek = ½ mv2 to get an answer of 2.9×1019 J.