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)
m = m0/(sqrt (1 - (v^2/c^2)) ---> notice I fixed your mismatched brackets
m(sqrt (1 - (v^2/c^2)) = m0
square both sides
m^2(1 - v^2/c^2) = m0^2
expand
m^2 - m^2 v^2/c^2 = mo^2
multiply each term by c^2
c^2 m^2 - m^2 v^2 = m0^2 c^2
c^2 m^2 - m0^2 c^2 = m^2 v^2
divide by m^2
v^2 = (c^2 m^2 - m0^2)/m^2
v^2 = 1 - m0^2/m^2
v = √(1 - m0^2/m^2)
check my algebra steps, I should have written it out on paper first.
It is easy to make errors when just typing it on here as you go along.
Aside from the typo where the c^2 gets lost, I'd just do it like this:
m^2(1 - v^2/c^2) = m0^2
1 - (v/c)^2 = (m0/m)^2
(v/c)^2 = 1 - (m0/m)^2
v/c = √(1 - (m0/m)^2)
To me, that makes it easier to see how the ratio of v to c is related to the ratio of the masses. Usually in this kind of relativistic stuff, v is expressed as 0.8c or some such value, anyway.
To solve for v in the equation m = m₀ / √(1 - (v²/c²)), where m is the relativistic mass, m₀ is the rest mass, v is the velocity, and c is the speed of light, you can follow these steps:
Step 1: Multiply both sides of the equation by the square root of (1 - (v²/c²)):
m √(1 - (v²/c²)) = m₀
Step 2: Square both sides of the equation to eliminate the square root:
(m √(1 - (v²/c²)))² = m₀²
Step 3: Expand and simplify the equation:
m² (1 - (v²/c²)) = m₀²
Step 4: Distribute the m² on the left side of the equation:
m² - m²(v²/c²) = m₀²
Step 5: Move the m²(v²/c²) term to the right side of the equation:
m² = m₀² + m²(v²/c²)
Step 6: Subtract m²(v²/c²) from both sides:
m² - m²(v²/c²) = m₀²
Step 7: Factor out m² on the left side:
m²(1 - (v²/c²)) = m₀²
Step 8: Divide both sides of the equation by m²:
1 - (v²/c²) = m₀² / m²
Step 9: Subtract 1 from both sides of the equation:
- (v²/c²) = m₀² / m² - 1
Step 10: Multiply both sides of the equation by -c² to isolate v²:
v² = (-c²)(m₀² / m² - 1)
Step 11: Divide both sides of the equation by -c²:
v² / c² = (m₀² / m² - 1)
Step 12: Take the square root of both sides of the equation:
v / c = √((m₀² / m² - 1))
Step 13: Multiply both sides of the equation by c to solve for v:
v = c √((m₀² / m² - 1))
Therefore, the equation to solve for v is v = c √((m₀² / m² - 1)). Note that this equation gives the velocity v as a fraction of the speed of light c.