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 CONTENTS Introduction Fermi's Piano Tuner Problem How Old is Old? If the Terrestrial Poles were to Melt... Sunlight Exerts Pressure Falling Eastward What if an Asteroid Hit the Earth Using a Jeep to Estimate the Energy in Gasoline How do Police Radars really work? How "Fast" is the Speed of Light? How Long is a Light Year? How Big is a Trillion? "Seeing" the Earth, Moon, and Sun to Scale Of Stars and Drops of Water If I Were to Build a Model of the Cosmos... A Number Trick Designing a High Altitude Balloon Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water Calendar Calculations Telling Time by the Stars - Sidereal Time Fields, an Heuristic Approach The Irrationality of The Irrationality of The Number (i)i Estimating the Temperature of a Flat Plate in Low Earth Orbit Proving that (p)1/n is Irrational when p is a Prime and n>1 The Transcendentality of Ideal Gases under Constant Volume, Constant Pressure, Constant Temperature and Adiabatic Conditions Maxwell's Equations: The Vector and Scalar Potentials A Possible Scalar Term Describing Energy Density in the Gravitational Field A Proposed Relativistic, Thermodynamic Four-Vector Motivational Argument for the Expression-eix=cosx+isinx Another Motivational Argument for the Expression-eix=cosx+isinx Calculating the Energy from Sunlight over a 12 hour period Calculating the Energy from Sunlight over actual full day Perfect Numbers-A Case Study Gravitation Inside a Uniform Hollow Sphere Further note on Gravitation Inside a Uniform Hollow Sphere Pythagorean Triples Black Holes and Point Set Topology Additional Notes on Black Holes and Point Set Topology Field Equations and Equations of Motion (General Relativity) The observer in modern physics A Note on the Centrifugal and Coriolis Accelerations as Pseudo Accelerations - PDF File On Expansion of the Universe - PDF File

## How Do Police Radars Really Work?

Problem:
A car, traveling at speed, V, approaches a police radar, scanning for speeders with a frequency, . Calculate the approximate frequency shift of the reflected signal.

Solution:
Consider a single photon from the police radar. The photon must interact with the approaching car for a finite time while it is being reflected. Call this time, t. Let an interaction force, ± f, exist between the photon and the car for the time, t. The force exerted by the photon on the car, +f, acts to remove energy from the car. The force exerted by the car on the photon, -f, acts to add energy to the photon. Therefore, we expect the photon frequency to increase. During the time t, the car travels a distance s = V t. We may now write two equations, one for a change in momentum, p, and one for a change in energy, E:

 Momentum: p = f t 1
 Energy: E = f s = fV t 2

Since the photon energy, E, is equal to hn, where h = Planck's constant = 6.63 X 10-34 j sec, then

 E = h 3

Also, since photon momentum equals h/c, where c is the speed of light, then

 p = 2h/c + h /c 4

where the first term on the RHS represents p for an elastic reflection (i.e., one for which E = 0), and the second term takes into account the change in frequency due to the change in energy.

Dividing eq. 1 by eq. 2, and substituting for E and p from eqs. 3 and 4, we find

 (2h/c + h /c)/(h ) = 1/V 5

This equation may be simplified to read

 / = 2V/(c-V) 2V/c 6

where the final step results from V << c. Now, let V = 60 mph = 27 m/sec, and let = 5 X 108 Hz. Then,

 = 90 Hz 7

The police radar detector easily detects this frequency shift.