Finding the Critical Velocity for Special Relativity Effects

[scurry18]

Homework Statement

For what value of v does Gamma (G) =1.0100? Observe that for speeds lower than this value, time dilationand length contraction are effects amounting to less that 1%

Homework Equations

L=Lp/G=Lp(1-(v^2/c^2))^2

The Attempt at a Solution

I do not know where to start. Is this the correct formula, and then if it is, how would I go about solving for the Velocity?

 

[borgwal]

You seem to have the wrong expression for gamma, unless it's a typo.

 

[jtbell]

The exponent on the right should be 1/2 (square root), not 2. Start with

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

What can you do to simplify this equation a bit, first?

 

[gabbagabbahey]

Why involve any lengths here? You have an equation (rather a definition) for Gamma do you not? Isn't it just

\gamma=\left( \frac{1}{1-\frac{v^2}{c^2}} \right)^{\frac{1}{2}}

If so, try squaring both sides of the equation.

 

[scurry18]

I got it! Thank you!