# What would be the force required to accelerate 1 gram to 20% of the speed of light?

Asked by: Homer Connor### Answer

It is not just a question of 'how much force' is needed, but rather a combination of a given force for a given length of time. In other words, a small force for a long time can result in the same velocity as a large force for a short time. This combination of force and time is called IMPULSE, and equals the change in momentum given to any mass. Momentum is simply mass x velocity.20% of the speed of light is about 6 x 10

^{7}meters/second. Since the relativistic effects at that velocity are small (only about 2%), let's ignore them and just find the impulse needed in non-relativistic terms. A velocity increase given to 1 gm from 0 to 6 x 10

^{7}m/sec means its momentum would have to change by: 0.001 kg x 6x10

^{7}m/sec = 60,000 kg m/sec

So the IMPULSE needed is the equivalent of 60,000 kg m/sec. In the metric system, a NEWTON is 1 kg m/sec

^{2}, so any combination of newtons x seconds giving a product of 60,000 would do the job. [The units of newtons x seconds = kg m/sec

^{2}x sec = kg m/sec = momentum units]

A force of 60,000 Newtons for 1 second, for example, would provide the impulse needed, as would a force of 1000 Netwons for 60 seconds.

Answered by: Paul Walorski, B.A., Part-time Physics Instructor

'The strength and weakness of physicists is that we believe in what we can measure. And if we can't measure it, then we say it probably doesn't exist. And that closes us off to an enormous amount of phenomena that we may not be able to measure because they only happened once. For example, the Big Bang. ... That's one reason why they scoffed at higher dimensions for so many years. Now we realize that there's no alternative... '

(

**Michio Kaku**(

*1947-*)