A=1 м/c² v0=2% v=10% L-?

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вопрос

To find the value of L, we first need to determine the Lorentz factor (γ) using the formula:

γ = 1 / √(1 - v^2/c^2)

where:
v = velocity of the object = 10% of the speed of light = 0.1c
c = speed of light = 1 m/s

Plugging in the values, we get:

γ = 1 / √(1 - 0.1^2)
γ = 1 / √(1 - 0.01)
γ = 1 / √(0.99)
γ ≈ 1.00502513

Next, we can calculate the contracted length (L) using the formula for length contraction:

L = L0 / γ

where:
L0 = proper length of the object at rest = L
γ = Lorentz factor = 1.00502513

Given that the initial proper length (L0) is equal to the final length (L), we can directly substitute this value into the formula:

L = L / 1.00502513

Solving for L,

L ≈ L / 1.00502513
1.00502513L ≈ L
L ≈ L / 1.00502513

Therefore, in this scenario, the length L will remain approximately the same due to the negligible effect of length contraction given the slow velocities involved.