# Homework Help: Spacetime Interval Problem

1. Dec 12, 2011

### ssmfour

1. The problem statement, all variables and given/known data
Two friends with super-synchronized clocks. One goes on merry-go-round the other stands outside at the same point. The merry-go-round has a constant v of 45 m/s and takes 300s to go around. Find dt, ds, and dτ.

2. Relevant equations
v=dx/dt
v=2πR/p using p=period
ds^2=dt^2-dx^2
dτab=(1-v^2)^1/2 x dtab
dt≥ds≥dτ

3. The attempt at a solution
Put into SR Units first:
45 m/s (1 s/3x10^8m)=1.5 x 10^-7
300 s (1 x 10^9 ns/1 s)=3 x 10^11 ns

v=dx/dt
1.5 x 10^-7=(3.0 x 10^11 ns)/dt
dx= (1.5 x 10^-7)(3.0 x 10^11 ns)
dx=45000 ns

ds=√(3.0 x 10^11)^2 - (45000 ns)^2
ds=√9.0 x 10^22
ds= 3.0 x 10^11

v=2πR/p
1.5 x 10^-7= 6.28R/(3.0 x 10^11 ns)
R=7165 ns

dtab=2πR/v
=2π(7165 ns)/(1.5 x 10^-7)
=3.0 x 10^11

dτab=(1+(-v^2))^1/2 x dtab
= (1-1/2(v^2)) x dtab
= (1-1/2(2.25 x 10^-14)) x dtab
because v ≪ 1:
dτab=dtab

My answer fits the equation dt≥ds≥dτ but it seems wrong that they're all the same. Never had any examples before where this has happened. Was hoping someone can just check to see if I made any mistakes.

Thanks