How fast should a particle move in order for its mass to increase n-12 times?

univerkov | May 3, 2021 | education

Data: m (final particle mass) = 12m0 (initial particle mass).

Constants: C (speed of light) = 299 792 458 m / s.

The required speed of the particle can be expressed from the equality: P = m * V = m0 * V / √ (1 – V ^ 2 / C ^ 2); m = m0 / √ (1 – V ^ 2 / C ^ 2); m0 / m = √ (1 – V ^ 2 / C ^ 2); 1/12 ^ 2 = 1 – V ^ 2 / C ^ 2; 1 – 1/12 ^ 2 = V ^ 2 / C ^ 2 and V = √ (1 – 1/12 ^ 2) * C.

Calculation: V = √ (1 – 1/12 ^ 2) * 299792458 = 0.9965 * 299792458 = 2.9875 * 10 ^ 8 m / s.

Answer: The particle will have to move at a speed of 2.9875 * 10 ^ 8 m / s.

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