# Special Relativity and Gamma

## 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?

mishelly

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

jtbell
Mentor
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
Homework Helper
Gold Member
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.

I got it! Thank you!