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# Time Dilation Help (page 3)

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By McGraw-Hill Professional
Updated on Sep 12, 2011

## Time Dilation Practice Problems

#### Problem 1

Why don’t we notice relativistic time dilation on short trips by car, train, or airplane? When we land, the clocks are still synchronized (except for time-zone differences in some cases). Why isn’t the traveling clock behind the earthbased ones?

#### Solution 1

Theoretically, they are. However, the difference is too small to be noticed. The time dilation factor is exceedingly small unless a vessel travels at a significant fraction of the speed of light. Its effect at normal speeds can’t be measured unless atomic clocks, accurate to a minuscule fraction of 1 s, are used to measure the time in both reference frames.

#### Problem 2

What speed is necessary to produce a time dilation factor of k = 2.00?

#### Solution 2

Use the formula for time dilation, and let u be the unknown. Then u can be found, step by step, this way:

k = (1 − u 2 ) −1/2

2.00 = (1 − u 2 ) −1/2

0.500 = (1 − u 2 ) 1/2

0.250 = 1 − u 2

−0.750 = − u 2

u 2 = 0.750

u = (0.750) 1/2 = 0.866

That is, the speed is 86.6 percent of the speed of light, or 2.60 × 10 8 m/s.

Practice problems of these concepts can be found at: Relativity Theory Practice Test

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