How much is the mass of an airplane moving at a speed of 965 km / h more than that of a stationary one?

univerkov | May 7, 2021 | education

How much is the mass of an airplane moving at a speed of 965 km / h more than that of a stationary one? The mass of a stationary aircraft is 10 tons.

The mass of a moving aircraft will increase with an increase in its speed:
m = m0 / (√ (1- (V ^ 2 / C ^ 2))), where m0 is the mass of the stationary aircraft (m0 = 10 t = 10000 kg), V is the aircraft speed (V = 965 km / h = 965 * 1000/3600 m / s = 268 m / s), C is the speed of propagation of sunlight in a vacuum (C = 3 * 10 ^ 8 m / s).
Then:
m = m0 / (√ (1- (V ^ 2 / C ^ 2))) = 10000 / (√ (1- (268 ^ 2 / (3 * 10 ^ 8) ^ 2)))) = 10000 / ( √ (1 – 7.98 * 10 ^ -13)) = 10000 / 0.99 = 10000 kg.
Answer. The mass of the aircraft will increase by 4 * 10 ^ -9 kg.

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