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

m_m = m_s / √ 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

m_m = m_s / √ 1- v² / c²

m_m = 15000kg / √1- 0.70c² / c²

m_m = 15000kg / √1- 0.49

m_m =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.

 

[kuruman]

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.

 

[chef99]

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