Suppose two highly precise, identical clocks are synchronized and one clock is placed at the North...

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Suppose two highly precise, identical clocks are synchronizedand one clock is placed at the North Pole and one clock is placedat the equator. After 100 years, how much will the clocks differ intime? You can assume Earth is a perfect sphere of radius 6.37 x10⁶ m and makes one revolution in exactly 24 hours.
(You will have to use a spreadsheet program that holds a lot ofdecimal places rather than your calculator to find youranswer.)

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4.1 Ratings (452 Votes)

at first, find the speed of the second clock:

v = r_e ?_e

Â Â = r_e * ((2?/T))

= 6.37e6 * (2*3.14/(24*60*60))

= 463.00463 m/s

-----------------------------------------

?t = ? ?t_p

Â Â Â = 1/(?(1-(v/c)²)) ?t_p

Â Â Â = 1/(?(1-(463.00463/3e8)²)) * (100)

Â Â Â = 100.0000000003572888 yrs

------------------------------------------

the clocks difference = 100.0000000003572888 - 100

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 3.57288812336366443e-10 years

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 3.57288812336366443e-10 *365.25*24*60*60

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 1.13 * 10^-2 s

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Suppose two highly precise, identical clocks are synchronized and one clock is placed at the North...

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Physics

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