Help please. I know how to compute for the rest mass but how can you solve this problem. Solve for v in m = m0/(sqrt of 1 - (v^2/c^2)
something wrong with Reiny's previous solution?
http://www.jiskha.com/display.cgi?id=1459772906
I did this in a rather lengthy series of steps here.
Steve has a more simplified version and also found an typo in mine
http://www.jiskha.com/display.cgi?id=1459772906
my last 3 lines should have been
v^2 = (c^2 m^2 - m0^2c^2)/m^2
v^2 = c^2 - m0^2c^2/m^2
v = c√(1 - m0^2/m^2)
which matches his last line
To solve for v in the equation m = m0/(sqrt(1 - (v^2/c^2))), where m is the relativistic mass, m0 is the rest mass, c is the speed of light, and v is the velocity, you can follow these steps:
1. Start by rearranging the equation to isolate the term containing v:
m * sqrt(1 - (v^2/c^2)) = m0
2. Square both sides of the equation to eliminate the square root:
(m * sqrt(1 - (v^2/c^2)))^2 = m0^2
m^2 * (1 - (v^2/c^2)) = m0^2
3. Expand the left side of the equation by multiplying m^2 with each term:
m^2 - (m^2 * (v^2/c^2)) = m0^2
4. Move the term involving v to the right side of the equation:
m^2 = m0^2 + (m^2 * (v^2/c^2))
5. Subtract m0^2 from both sides of the equation:
m^2 - m0^2 = m^2 * (v^2/c^2)
6. Divide both sides of the equation by m^2:
(m^2 - m0^2) / m^2 = v^2/c^2
7. Take the square root of both sides of the equation:
sqrt((m^2 - m0^2) / m^2) = v/c
8. Multiply both sides of the equation by c:
v = c * sqrt((m^2 - m0^2) / m^2)
And that's the solution for v in terms of m, m0, and c. You can now substitute the values of m, m0, and c into the equation to find the value of v.