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Relativity Questions (1 Viewer)

jskeza

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Help with these 2 questions please.

I am confused about which term is and , also and

1. There are 1000000 muons formed at an altitude of 15000m, taking time dilation into account find how long it would take the muons to reach the ground if they were travelling the 0.994c .

2. There are 1000000 muons formed at an altitude of 15000m, taking length contraction into account find the contracted length the muons travel.

Thanks
 
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Drdusk

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1.




2.
This one is a bit tricky for some, so I like to explain it like this.
In this case imagine you are on the ground looking up at the muons. Now imagine the distance between you and the muons as a ruler 15000 meters long. The muons are moving with respect to that ruler. We know that when you are moving with respect to something, it will undergo length contraction. So in the reference frame of the muons L_0 is just the normal altitude(15000m) and L_v is the distance when the imaginary 'ruler' contracts.
 

blyatman

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This is a common issue, where students aren't sure where to use the subscript 0 and the v. As a general rule, just remember that moving clocks run slower. In other words, figure out whether the time (or length or whatever) should increase or decrease. If it's dilated such that it results in a larger value, then we need to divide by the sqrt since you'll be dividing by a number less than 1. If you expect it to be a smaller value, then you need to multiply by the sqrt.
 

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