Relativistic mass/length contraction problem

In summary: You have two equations with two unknowns: the velocity of A and the velocity of B. Solve for both variables using the two equations. Then you can plug in the velocity of B into the equations for b) and c) to find the length and mass of ship B relative to the observer on Earth. In summary, 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. Using the equations for length contraction and relativistic mass, it can be determined that the length of spaceship A relative
  • #1
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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 length of spaceship A, relative to an observer on earth

b) The length of spaceship B, relative to an observer on earth

c) The mass of spaceship A, relative to an observer on earth.


Homework Equations


Lm = Ls √(1- v2 / c2

mm = ms / √(1- v2 / c2

The Attempt at a Solution

Since both ships appear to have the same length to the observer on earth, ship A must be traveling faster than ship B as length contraction becomes more apparent with an increase in speed: In order for the two uneven length ships to appear the same, they must be moving at different speeds, and B must be the slower ship, therefore the velocity of B is 0.70c.
a) Lm = Ls √(1- v2 / c2

Lm = 60.0m √(1- 0.70c2 / c2

Lm = 60.0m √ (1- 0.49)

Lm = 42.85

Lm = 43m

The length of spaceship A, relative to an observer on Earth is 43m.

For a), I am unsure how to determine the velocity of ship B, other than trying multiple values until ship B's length matches that of ship A. I know there must be some way to determine the velocity of B, I just can't think of it. That value is also required to determine the relativistic mass of spaceship B, so any help on how to determine that value would be great.
 
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  • #2
chef99 said:

Homework Statement



The proper length of spaceship A is 60.0m and the proper length of spaceship B is 60.0m.

Are the spaceships supposed to have the same length of ##60m##?
 
  • #3
PeroK said:
Are the spaceships supposed to have the same length of ##60m##?
Opps. my mistake. I have fixed the problem now, as you can see B is, in fact, the longer ship at 120m, and ship A is 60m. So my first answer is really of A, and I need to determine the velocity of ship B, which must be faster than A, as ship B is longer. I can also determine the relativistic mass of ship A now, as I have its velocity. As for my answer posted above, everything is correct? Sorry about all that.
 
  • #4
chef99 said:
For a), I am unsure how to determine the velocity of ship B, other than trying multiple values until ship B's length matches that of ship A. I know there must be some way to determine the velocity of B, I just can't think of it.

Algebra, perhaps?
 
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1. What is the concept of relativistic mass?

The concept of relativistic mass is a result of Einstein's theory of relativity, which states that the mass of an object increases as its velocity approaches the speed of light. This is in contrast to classical physics, where mass is considered a constant value.

2. How does the mass of an object change according to its velocity?

As an object's velocity increases, its mass also increases according to the equation m = m0/√(1-(v2/c2)), where m0 is the rest mass of the object, v is its velocity, and c is the speed of light.

3. What is the difference between relativistic mass and rest mass?

The rest mass of an object is its mass when it is at rest, while the relativistic mass takes into account the increase in mass as the object's velocity approaches the speed of light. Therefore, the relativistic mass is always greater than or equal to the rest mass.

4. How does the length of an object change according to its velocity?

The length of an object decreases as its velocity increases, a phenomenon known as length contraction. The equation for length contraction is L = L0√(1-(v2/c2)), where L0 is the rest length of the object, v is its velocity, and c is the speed of light.

5. What is the significance of the relativistic mass/length contraction problem?

The relativistic mass/length contraction problem highlights the fundamental differences between classical and relativistic physics. It also has important implications in fields such as particle physics, where the mass and length of subatomic particles are affected by their high velocities. It also helps us better understand the nature of space and time and the concept of simultaneity.

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