# Fermilab

## Inquiring Minds

 Questions About Physics

Accelerating massive objects

Dear Mr. Krupa,

To accelerate an object so its mass is increased by 1% then gamma, the "time dilation factor" will be simply 1.01. That is equivalent to accelerating the mass to a velocity of 14% of the speed of light or 42,000 km/sec.

A 10% increase in mass corresponds to a gamma of 1.10 or a velocity of 42% of the speed of light.

The amount of energy required is ENORMOUS! Remember E=mc2. The "exchange rate" between energy and mass is a very large number. So when you turn mass into energy (nuclear reactors, nuclear bombs) you get an enormous amount of energy while using up a small amount of mass.

But that also works in the other direction. To create even a small amount of mass requires a very large amount of energy.

Take your 1 kg mass and increase it by 1%. In other words you want to move it fast (14% of the velocity of light) so that its (relativistic) mass is increased by 1% or 10 grams.

How much energy is required to create 10 grams? Here are a few numbers I worked out:

-- approximately the electrical energy required to run Fermilab for one year -- the kinetic energy of 3 MILLION, 1000 ton freight trains all moving at 50 miles/hour -- the explosion of 300 kilotons of TNT (or about 15 Hiroshima sized bombs).

Let me know if you have further questions.

Sincerely, Dr. Ernest Malamud

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 last modified 2/16/1999   physicsquestions@fnal.gov

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