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accountkiller
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Homework Statement
Find the speed of a particle whose relativistic kinetic energy is 40% greater than the Newtonian value for the same speed.
Krel = relativistic kinetic energy
Knew = Newtonian kinetic energy
Homework Equations
Krel = (gamma - 1)mc^2
Knew = 0.5mv^2
gamma = 1/sqrt(1-x)
x = v^2 / c^2
The Attempt at a Solution
So I set it up as K(relativistic) = 1.4K(Newton).. because my problem was 40%.
So (gamma - 1)mc^2 = 1.4 (0.5mv^2) and..
(gamma - 1) = (0.7mv^2)/mc^2
... m's on top and bottom cancel out, then I replaced v^2/c^2 by x...
(gamma - 1) = 0.7x
1/sqrt(1-x) = 0.7x + 1
1/(1-x) = (0.7x+1)^2
1 = 0.49x^2 + 14x + 1 - 0.49x^3 - 1.4x^2 - x
0 = x(-0.49x^2 - 1.09x + 0.4)
Using the quadratic formula, I get either x = -3.12 or x = 0.9
Since x = v^2 / c^2,
v = sqrt(x)*c
So I get v = 0.9c
But the answer is 0.61c.
Where did I go wrong?