Relativity (lorentz contraction)

In summary, the length of the spacecraft runway as measured by the pilot flying over it at a speed of 4.00 x10^7 m/s relative to the earth is 3351m, calculated using the equation L= Lnot/γ. This takes into account the phenomenon of length contraction due to the pilot being in motion while the runway is at rest relative to him.
  • #1
Allein
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Homework Statement


As measured by an observer on earth, a spacecraft runway has a length of 3.6km. What is the length of the runway as measured by the pilot of a spacecraft flying directly over the runway at a speed 4.00 x10^7 m/s relative to the earth?

Homework Equations


L= Lnot/γ

The Attempt at a Solution


I inserted 3.6km as the Lnot and got 3351m as the answer by using the equation.
L= 3600/ (1/sqrt(1-4.0E7/3.0E8))
= 3351m
Is this true? Or i have confused the L as Lnot? I got the answer as i figure the pilot is in rest and the runway is moving relative to him.
 
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FAQ: Relativity (lorentz contraction)

1. What is Lorentz contraction?

The Lorentz contraction, also known as length contraction, is a phenomenon described by the theory of relativity where objects in motion appear shorter in the direction of motion when observed from a stationary reference frame.

2. How does Lorentz contraction relate to Einstein's theory of relativity?

Lorentz contraction is a consequence of Einstein's theory of special relativity, which states that the laws of physics are the same for all observers in uniform motion. It is a result of the time and space dilation effects described in the theory.

3. Can Lorentz contraction be observed in everyday life?

Yes, Lorentz contraction can be observed in everyday life. For example, when an object moves at high speeds, such as a speeding train or a plane, it appears shorter in the direction of motion to an observer on the ground. However, the effect is only noticeable at speeds close to the speed of light.

4. How is Lorentz contraction calculated?

Lorentz contraction is calculated using the Lorentz factor, which is a mathematical expression that takes into account the speed of the object and the speed of light. The contraction factor is equal to the square root of 1 minus the square of the ratio of the object's speed to the speed of light.

5. Does Lorentz contraction have any practical applications?

Yes, Lorentz contraction has practical applications in various fields, such as particle accelerators and space travel. It is also used in the design and functioning of devices such as particle detectors and GPS systems, which rely on precise timing and measurement of distances.

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