Question

The parameter γ = 1/(1-v^2/c^2)1/2 can be used to determine how large relativistic effects can be expected to be. When the speed is small compared to the speed of light, γ does not get much larger than 1. As v gets close to the speed of light, γ gets very large.

Required:
At what speed, as a ratio to the speed of light, is γ = 1 + 0.035? This corresponds to a 0.035 times 100 percent relativistic effect.

Answer 1

Answer:

$\frac{v}{c} \approx 0.184$

Explanation:

After some mathematical handling, the ratio of speed to speed of light is:

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

$\frac{v}{c} = \sqrt{1-\frac{1}{1.035} }$

$\frac{v}{c} \approx 0.184$