Question

In the theory of relativity, the mass of a particle with speed v

is m=f(v)=m01−v2/c2√
, where m0
is the rest mass of the particle and c
is the speed of light in a vacuum. Letting m0=1
, find f−1(10)
.

f−1(10)=

Answer 1

To find the inverse f-1(10) for the relativistic mass function f(v), we solve for the speed v when the mass m is 10, resulting in v being slightly less than the speed of light.

The calculation involves setting m to 10, rearranging the equation, and solving for v, which yields the result as a fraction of the speed of light, will get f−1(10) = c √(99/100).

Step-by-step explanation:

The question is asking how to find the inverse of the function defining the relativistic mass of a particle in terms of its speed.

Given the function f(v) = m0 / √(1 - v2/c2), with m0 = 1 and f-1(10), we need to find the speed v when the mass m equals 10.

To find f-1(10), we set m equal to 10 and solve for v:

m = 10 = 1 / √(1 - v2/c2)

Squaring both sides, we get:

100 = 1 / (1 - v2/c2)

Therefore, 1 - v2/c2 = 1/100

v2/c2 = 1 - 1/100

= 99/100

v2 = (99/100)c2

v = c √(99/100)

Thus, f-1(10) = c √(99/100), which means the speed v is slightly less than the speed of light c.