Question

A meter stick is place in a very high-speed spaceship. What length would the astronauts say the meter stick was? What would the length of the meter stick be as measured by stationary observers watching the spaceship and meter stick travel past them?

Answer 1

Answer:

a) The astronauts would see the real length of the meter stick, i.e.  L₀

b) The length of the meter stick as measured by the stationary observer will be $L = L_{0} }{\sqrt{(1-(\frac{v}{c} )^{2} } }$

Explanation:

a) Let the proper length of the meter stick be L₀

The meter stick and the astronauts on the on the space ship are on the same moving frame, therefore, they will see the exact length of the meter stick, that is, L₀

b) A stationary observer watching the space ship and meter stick travel past them will see a contracted length of the meter stick

The original length = L₀

Let the speed of the space ship = v

The contracted length, L, is related to the original length in the frame of rest by

L = L₀/γ......................(1)

Where γ = $\frac{1}{\sqrt{(1-(\frac{v}{c} )^{2} } }$ ....................(2)

Substituting equation (2) into (1)

$L = L_{0} }{\sqrt{(1-(\frac{v}{c} )^{2} } }$