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 true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.'