Length contraction -- numerical problem

Thread starter Pushoam
Start date Jul 11, 2017
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Contraction Length Length contraction Numerical

In summary, length contraction is a phenomenon in Einstein's theory of relativity where the length of an object appears shorter when it is moving at high speeds due to the distortion of space and time. It is calculated using the formula L = L<sub>0</sub>/γ, and a common numerical problem is calculating the contracted length at a given velocity. Length contraction affects measurements by making objects appear shorter, as seen in the "twin paradox" experiment. However, it is not observable in everyday life as it only becomes significant at speeds close to the speed of light.

Jul 11, 2017

Pushoam

Homework Statement

Homework Equations

The Attempt at a Solution

a) t' = l₀/c

b) ct₁ = l₀ /ϒ - vt₁
t₁ = l₀ /ϒ(c + v)

c) t₂ = l₀ / (ϒ v)

Is this correct?

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Jul 11, 2017

TSny

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I believe your answers are correct.

Jul 11, 2017

Pushoam

Thanks

1. What is length contraction?

Length contraction is a phenomenon in Einstein's theory of relativity where the length of an object appears shorter when it is moving at high speeds. This is due to the distortion of space and time caused by the object's high velocity.

2. How is length contraction calculated?

The formula for calculating length contraction is L = L₀/γ, where L is the contracted length, L₀ is the rest length of the object, and γ is the Lorentz factor, which is dependent on the object's velocity.

3. What is a numerical problem related to length contraction?

A common numerical problem related to length contraction is calculating the contracted length of an object when it is moving at a given velocity. This involves using the formula mentioned above and plugging in the appropriate values.

4. How does length contraction affect measurements?

Length contraction affects measurements by making objects appear shorter when they are moving at high speeds. This can be observed in experiments such as the famous "twin paradox" where one twin ages slower than the other due to their different velocities causing different amounts of length contraction.

5. Is length contraction observable in everyday life?

No, length contraction is not observable in everyday life as it only becomes significant at speeds close to the speed of light. In our daily lives, objects are moving at much lower speeds and the effects of length contraction are too small to be noticeable.