# Basic question on length contraction.

1. Jun 26, 2008

### pc2-brazil

good night,

this is not actually a homework question, this is just plain curiosity.
we've written a basic problem on length contraction and tried to resolve it ourselves. we just want to know if the concept of the problem is right.

1. The problem statement, all variables and given/known data

a body of length $$L=20m$$ travels from the Earth to the Moon at a speed $$\vec{v}=0.8c$$.
find the apparent length contraction of the body seen from an observer who is at rest in relation to the Earth.
known data: distance from the Earth to the Moon: approx. 480000 km.

2. Relevant equations

Lorentz's length contraction: $$L'=L\gamma^{-1}$$, where $$\gamma=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$.

3. The attempt at a solution

first of all:
c = 300000 km/s;
20m = 0.02 km.
substituting the variables in Lorentz's length contraction,
$$L'=L\sqrt{1-\frac{v^{2}}{c^{2}}}$$
$$L'=0.02\sqrt{1- \frac{(0.8c)^{2}}{c^{2}} } = 0.02\sqrt{1-(0.8)^{2}}$$
$$L'=0.02\sqrt{1-0.64}=0.02\sqrt{0.36}=0.012km$$
$$L'=12m$$
therefore, the apparent length of the body will be 12 meters.

are the concept and calculations right?

2. Jun 26, 2008

### Staff: Mentor

Looks good to me.

3. Jun 29, 2008

### pc2-brazil

very good, thank you for the confirmation.