How many times should the power develop by the engine of a ship increases to double is velocity i the resistance of the water to the motion of the ship increases in proportion to the square of the velocity.

Question

Misael Glenn

Physics

4 January, 12:36

How many times should the power develop by the engine of a ship increases to double is velocity i the resistance of the water to the motion of the ship increases in proportion to the square of the velocity.

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Answers (1)

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Ollie · Answer 1

If the ship speed is doubled, then the power developed is 8 times the initial value.

Explanation:

ship power is roughly proportional to the cube of the speed, so

P ∝ v³

If the speed is doubled, then the power developed becomes

P ∝ (2) ³ = 8 times

Therefore, if the ship speed is doubled, then the power developed is 8 times the initial value.