Question

1. A very fast runner is carrying a pole that is 20m in length when at rest. The runner runs toward a barn that is 10m in length when at rest. We will call event A the time/location where the leading edge pole enters the barn. Event B is when the trailing edge of the pole enters the barn. Event C is when the leading edge of the pole leaves the barn. Event D is when the trailing edge of the pole leaves the barn.
   1. What is the velocity of the runner if an observer at the front door of the barn (and at rest with respect to the barn) “sees” the pole as 10m in length? (to three decimal places please)
   2. Consider the runner. What is the length of the barn as seen by the runner?
   3. Staying with the runner, Event A is 0m time and 0m location (0,0). Event B has coordinates (23.09,-20), (the time is length traveled divided by the velocity, in units of c, the location is the back of the pole). Using this same logic, find the coordinates of events C and D.
   4. Now consider the observer at the front of the barn. Event A is still (0,0). Event B is measured at (11.55,0). Note the interval is conserved (23.09² – 20² = 11.55²). Find the observers coordinate for events C and D.
   5. What is the temporal order of the events as seen by the runner, and by the observer?

Answer 1

20 2 2 I- 41/4- 1-62 (2 ca 1-62 0.866c (2 16) dunner sm (२ 1C) . Ans. last length of pole Ans. Length of pole at rest, L,= Length of barn at rest La = lom Apparent length of pole , Li = lom Using length contraction, L, 금ㅋ 3 c Apparent Length of barn seen by La' = 4 VI-02 Jo VI-60-268] PT? Event A = (0,0) B = ( 23.09,+20) = (,x) C: (5.71 ,+5) (28-87,25) At point c; he of barn (2om bole + sm barn). From barn observen : A = (0,0) B - (11.55,0) (10.41,10) Peckovo D = (17.56,10) of barn at D at ci pole + interval lom barn) and also ensure is conserved (c) Chronological orden is BD Art, B Runner - barn observer » A, B, C, D crosses sm and at D he crosses ; (d) C = b) D=(17. (10.41, 10) and lom runner crosse runner crosse tom