Atomic Clock Problem: Calculate Nanoseconds Difference

[Tonia]

Homework Statement

An atomic clock moves at 1,000 km/h for 1.00 h as measured by an identical clock on the Earth. At the end of the 1.00 h interval, how many nanseconds slow will the moving clock be compared with the Earth clock?

Homework Equations

(1/ sqr rt 1 - v^2/c^2)

The Attempt at a Solution

1,000 km/h = 278 m/s
Convert the 1,000 km/h to met/sec. first
(1/ sqr rt 1 - v^2/c^2)

= (1/ sqr rt 1 - 278^2/3.00 X 10^8 m/s)

 

[Tonia]

I am not sure how to convert from 1,000 km/h to m/s, I think I divide it by 3600 seconds which would equal 0.277 m/s, so how do I change that to 278 m/s?

 

[ehild]

I am not sure how to convert from 1,000 km/h to m/s, I think I divide it by 3600 seconds which would equal 0.277 km/s, so how do I change that to 278 m/s?

Convert also km-s to meters.

 

[Tonia]

1,000 km/hr to met./sec. = 1,000km X 1,000met. = 1,000,000 met./ hr
1,000,000 met. divided by 3600 seconds = 277.7met./sec. = 278 met./sec.

Equation used: 1/ (squr rt 1 - v^2) = 1/ (squrrt 1 - 278^2/3.00 X 10^8 met./sec. = 1/ 1 - 77284/3.0 E8 = 1/-77283/3.0 E8 = 1/-2.5761e12 The Answer is supposed to be 1.54 Nanoseconds, what am I doing wrong?

 

[ehild]

You

1,000 km/hr to met./sec. = 1,000km X 1,000met. = 1,000,000 met./ hr
1,000,000 met. divided by 3600 seconds = 277.7met./sec. = 278 met./sec.

Equation used: 1/ (squr rt 1 - v^2) = 1/ (squrrt 1 - 278^2/3.00 X 10^8 met./sec. = 1/ 1 - 77284/3.0 E8 = 1/-77283/3.0 E8 = 1/-2.5761e12 The Answer is supposed to be 1.54 Nanoseconds, what am I doing wrong?

You did not write any equation. As I see, you intended to calculate the factor $\sqrt{1-\frac{v^2}{c^2}}$, but you forgot to square c, did not apply parentheses and made some more errors.
Look after Lorentz transformation in your Lecture Notes.

 

[andrevdh]

Multiply with conversion factors do get the values in the correct units eg. 1km = 1000 m
So you can multiply with the conversion factor 1 km / 1000 m and the value will not be
altered since you are multiplying by one . So 35.7 km = 35.7 km x 1000 m / 1 km = 35 700 m
The km units cancel each other out so only the meter units are leftover, which is the units
of the answer.

 

[Tonia]

I figured out the problem but thanks.