Question

Relativistic Length Measurements 4.7. Compute the contraction in length of a train 1/2 mile long when it is traveling at 100 mi/hr. Ans. 5.58 x 10-15 mi = 3.52 x 10-10 in. 4.8. At what speed must an observer move past the earth so that the earth appears like an ellipse whose major axis is six times its minor axis? Ans. 0.986c 49. An observer O' holds a 1.00 m stick at an angle of 30° with respect to the positive x'-axis. O' is moving in the positive x-x' direction with a velocity 0.8c with respect to observer 0. What are the length and angle of the stick as measured by 0? Ans. 0.721 m; 43.9° Relativistic Time Measurements 5.7. An atom will decay in 2 x 10-6 s. What will be the decay time as measured by an observer in a laboratory when the atom is moving with a speed of 0.8c? Ans. 3.33 X 10-6S 5.8. How fast would a rocket ship have to go if an observer on the rocket ship ages at half the rate of an observer on the earth? Ans. 0.866C 5.10. A particle moving at 0.8c in a laboratory decays after traveling 3 m. How long did it exist as measured by an observer in the laboratory? Ans. 1.25 x 10-85

Answer 1

4.7. og of light length train - speed Train 100 mi/hr. Speed ã 6-71 X 108 miles/hr. we know e le Ji-uz e Observed length the lot proper length contraction in length = lo al Ź [ 104 6-71)31016 |- 2.2X10-14 = £x 1.10X10 -14 a 5.5X10 miles 46 first considering earth as sphere now we have to calculat speed fon which magon axid becomes 6 times minor evcis majan since profes length of minon arca also to an but contracted minon culis = 2r acis = 2 a 2r 6

Page No ar 2 u 11-v² C2 36 36 10.97222 0.986 c XC So observer should move at a speed 0.9866c so that earth's th minan arus seems to be i be thg majan wris. 6.9. Proper length of sticks Im x' lenght along lelyth along (x cos30° lxsin 30 = 0.5m. = 0.866 m. y n anis only. So only length we have velocity vi o.fc along length along or axcid will contract So luright component alory x quis la loi si-v2 a l = 0.866 1-0.64 = 8.5 196 m. length along ly = b = 0.5m. stick in a C2 So length a fram = Ver ty? 0.721 m.

Angle af Stick o So tano = In ao - 43.90 - 0.9622 0.5196 5.7 Decay time in atom's in atom's frame = to = 28106 Speed from time dilution formula atom 0.8c g t = to where to time observed in moving frame So decay time obsewed in laboratory, ta to viny? 3.33X10 sec. 2x10 -6 1-0,64