# Length Contraction/Relativistic mass question

• chef99

## Homework Statement

The proper length of spaceship A is 60.0m and the proper length of spaceship B is 120.0m. The proper mass of spaceship A is 15000 kg. An observer on Earth watches the two spaceships fly past at a constant speed and determines that they have the same length. If the speed of the slower ship is 0.70c, find:

a-The speed of spaceship B, relative to an observer on earth

b- The mass of spaceship A, relative to an observer on earth

2. Homework Equations

γ = 1/ √1- v2 / c2

mm = ms / √ 1- v2 / c2

## The Attempt at a Solution

a)

Use the Lorentz factor to determine the velocity of ship B

γ = proper length B/ contracted length A

γ = 120m /42.8m

γ = 2.8

γ = 1/ √1- v2 / c2

rearrange to solve for v.

γ2 = 1/ √1- v2 / c2

1 - v2 / c2 = 1/γ2

v2 / c2 = 1 - 1/γ2

v/c = √1- 1/2.82

v/c = √1- 1/7.84

v = 0.934

The speed of spaceship B, relative to an observer on Earth will be 0.934c.

b) The mass of spaceship A, relative to an observer on earth. 3mk

mm = ms / √ 1- v2 / c2

mm = 15000kg / √1- 0.70c2 / c2

mm = 15000kg / √1- 0.49

mm =2100.4
https://www.physicsforums.com/file://localhost/Users/jefferyhewitt/Library/Group%20Containers/UBF8T346G9.Office/msoclip1/01/clip_image016.png

The mass of spaceship A, relative to an observer on Earth, is 2100kg.

The main part I am unsure of is question a, I hadn't specifically been taught about the Lorentz Factor, but this is all I could find that seemed to be able to determine the answer. As such I am not sure if I applied it correctly. If someone could give a few pointers that would be great.

The answer to (a) is correct. The Lorentz factor ##\gamma=\frac{1}{\sqrt{1-v^2/c^2}}## is greater than 1 when ##v\neq 0##. The contracted length would be ##L=L_0/\gamma##. Your answer to (b) is missing a zero, probably a typo. The mass of the moving rocket must be greater than its rest mass, not less.

The answer to (a) is correct. The Lorentz factor ##\gamma=\frac{1}{\sqrt{1-v^2/c^2}}## is greater than 1 when ##v\neq 0##. The contracted length would be ##L=L_0/\gamma##. Your answer to (b) is missing a zero, probably a typo. The mass of the moving rocket must be greater than its rest mass, not less.
Yes it is missing a 0, thanks for the explanation