# Relative momentum formula or not?

1. Jan 26, 2010

### leejqs

1. The problem statement, all variables and given/known data
In which of these situations is it reasonable to use the approximate formula for the momentum of an object, instead of the full relativistically correct formula?
A car traveling on the interstate.
A proton in outer space traveling at 2×108 m/s.
A commercial jet plane flying between New York and Seattle.
An electron in a vacuum tube traveling 6×106 m/s.
A neutron traveling at 3600 meters per second.

2. Relevant equations
Velocities closer to the speed of light require a relativistic formula for momentum.

3. The attempt at a solutionA car traveling on the interstate.
A proton in outer space traveling at 2×108 m/s. (Relativistic)
A commercial jet plane flying between New York and Seattle. (Approximate)
An electron in a vacuum tube traveling 6×106 m/s. (Relativistic)
A neutron traveling at 3600 meters per second. (Approximate)

I am incorrect in these answers... however, what makes a velocity "close" to the speed of light. Would a neutron traveling 3600 m/s require a relativistic formula? 3600 m/s isn't very close to 3E8 m/s.

Any help or insight would be greatly appreciated! Thanks!

2. Jan 26, 2010

### Andrew Mason

The electron in vacuum tube travelling at 6 x 10^6 m/s is travelling at .02c. So the relativistic calculation differs from the approximate by a factor of 1.0002. There is no need to use the relativistic calculation.

To determine whether the relativistic calculation is needed you have to evaluate:

$$\frac{1}{\sqrt{1 - v^2/c^2}}$$

AM