Home
Science
Next
Email
harry@chaospark.com

### E = MC
^{2
}

We've all seen it but what does it really mean? Atomic reactions create energy by making matter disappear. The amount of matter that disappears to make a lot of energy is amazingly small. In E = MC
^{2
} E is energy, M is mass, and C is the speed of light so (energy) = (mass)x(the speed of light)
^{2
}.

Energy, mass, and speed seem unrelated; how can you calculate with things that are so different?

The word "energy" is defined in physics as a force applied through a distance. The energy it takes to lift a one pound weight one foot upward is one foot-pound (ft-lb) of energy. But this force (measured in pounds) isn't the same as mass (measured in pounds). Force is defined in physics as (mass)x(acceleration). What acceleration? The acceleration of gravity; without gravity the pound(mass) would exert no force at all.

The acceleration of gravity here on Earth is 32 ft/sec
^{2
}. What sort of units are (ft/sec
^{2
})? Acceleration is the rate of change of speed. A car that accelerates to 60 (miles/hour) in 10 seconds has an average acceleration of 6(miles/hour)/sec. When we measure speed in ft/sec acceleration is (ft/sec)/sec. The rules of algebra say (a/b)/b = a/b
^{2
} so (ft/sec)/sec = ft/sec
^{2
}.

Energy is (force)x(distance). Force is (mass)x(acceleration). So energy is (mass)x(acceleration)x(distance) or (pounds)x(32 ft/sec
^{2
})x(ft) or (pounds)x(32 ft
^{2
}/sec
^{2
}). This is (mass)x(speed)
^{2
}just like the right hand side of E = MC
^{2
}.

The speed of light is 186,000 miles/sec. We want ft/sec so (186,000)x(5,280(ft/mile)) = 984,000,000 ft/sec. Now this enormous number must be squared! The result is around 967,000,000,000,000,000. To get energy in ft-lb we must divide by the acceleration of gravity (32) to get 30,000,000,000,000,000.

Electric energy is measured in kilowatt-hours (1000 x watts x hours) or kwh. One kwh will light a 100 watt bulb for 10 hours. One kwh is 2,660,000 ft-lb. Dividing 30,000,000,000,000,000 by 2,660,000 we get one pound mass equal to 11,300,000,000 kwh. Let's divide by 16 to get one ounce of mass equal to 700,000,000 kwh. If electricity costs ten cents per kwh this becomes $70,000,000.

According to E = MC
^{2
} a single ounce of matter is equal to $70 million dollars worth of energy in the form of electric power.