+ CD Page view | AREau duopen [T) Add text Dra Only muons with a speed of 0.995c are stopped in the detector where they remain until they decay. Muons with less speed are stopped in the iron above the detector. Muons with greater speeds pass through the detector Into Mount Washington below. 1. Calculate the speed (In m/s) of the muons moving at 0.995c 2. What distance do they travel in one microsecond? 3. Mount Washington is about 6,300 feet high. What are the appropriate S.I. units? Show that It takes about 6.4 microseconds for a muon to travel this distance. 4. The physicists counted 568 muons on the top of the mountain. Based on the average life span of a muon in the rest frame, the scientist calculated that 29 should reach the bottom of the mountain. That is, twenty nine of the 568 muons should survive the 6.4 microseconds required to travel the height of Mount Washington. Show that this expectation is correct under classical mechanics. You can use the equation N-N/2" y =t/ty/ N. is the initial count and N is the count after time t where the half-life time is ty When the physicst took the equipment to sea level (to the foot of Mount Washington), 412 muons were counted in a one hour period (and not just 29 as expected III). Clearly, moving clocks do not keep time at the same rate as stationary clocks, or (perhaps) distances are not the same in a fixed or moving frame. We can analyze the results from either frame. EARTH FRAME Here we are at rest alongside the mor and we observe the m speeding towards us at a speed of 0.995 c. 5. Calculate the gamma factor for muons. 6. Calculate the time (in us) for half of the 568 muons to decay 7. Calculate the distance a typical muon travel in 15 us Compare your answer to question (7) with the height of the mountain. Use this to appreciate why so many muons survived to sea level. Muon Reference Frame . Use the gamma factor, y, calculate the ght of the mountain as it is seen to pass by. 10. Compare answer (9] with the beig ribe to Mount Washington. 11. How far does the earth n is in a time of 1.5 us. Comment on how many of the muons should be hit by the earth! 12. Given the experimental fact that 412 muons reach the foot of the mountain, calculate the fraction of one half life that elapsed. and so calculate the elapsed time in us from the muon's reference frame. For us (at nest on the earth) the time & clearly 6.4 us