Relativity Questions (1 Viewer)

jskeza

Member
Help with these 2 questions please.

I am confused about which term is $\bg_white to$ and $\bg_white tv$, also $\bg_white Lv$ and $\bg_white Lo$

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

Last edited:

Drdusk

π
1.
$\bg_white t_v = \frac{t_0}{\sqrt{1-v^2/c^2}}$

$\bg_white \text{t0 is the time the muons take to travel in the rest frame. It is therefore just the altitude divided by the speed. You will obviously need to convert to SI units }$

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

Active Member
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.

jskeza

Member
Thanks for the replies!! I understand it now!!