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 10⁷ 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 10⁷ m/sec means its momentum would have to change by: 0.001 kg x 6x10⁷ 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/sec², 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/sec² 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