The aircraft carrier USS George Washington has mass 1.0 ×108kg. When its engines are developing their full power of 260,000 hp, the George Washington travels at its top speed of 35 knots ( 65 km/h). If 68 % of the power output of the engines is applied to pushing the ship through the water, what is the magnitude of the force of water resistance that opposes the carrier’s motion at this speed?

Question
Asked Nov 10, 2019
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The aircraft carrier USS George Washington has mass 1.0 ×108kg. When its engines are developing their full power of 260,000 hp, the George Washington travels at its top speed of 35 knots ( 65 km/h).

 

If 68 % of the power output of the engines is applied to pushing the ship through the water, what is the magnitude of the force of water resistance that opposes the carrier’s motion at this speed?

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Expert Answer

Step 1

Let Pout be the total power output of the engines, P is the power used to push the ship through the water, F is the force applied by the water in the opposite direction, v be the speed of the ship.

Write the given values of question.

P 260000 hp
out
749.65 W
(260000 hp)
hp
=19.49x 10 w
v 65 km/h
103 m
1
=(65 km/h)
km
3600 s
=18.05 m/s
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P 260000 hp out 749.65 W (260000 hp) hp =19.49x 10 w v 65 km/h 103 m 1 =(65 km/h) km 3600 s =18.05 m/s

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Step 2

Write the expression for power P supplied by the engine to push the ship through the water.

68
P P
out
100
68
(19.49x10' w)
100
13.25 x10 w
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68 P P out 100 68 (19.49x10' w) 100 13.25 x10 w

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Step 3

Write the expression for the resistance for...

F
13.25x 107 W
18.05 m/s
= 7.34 x 106 N
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F 13.25x 107 W 18.05 m/s = 7.34 x 106 N

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