Question

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).
A. If 69 % of the power output of the engines is applied to pushing the ship through the water?B. what is the magnitude of the force of water resistance that opposes the carrier’s motion at this speed?

Answer 1

Answer:

7409092.8223 N

Explanation:

$p_f$ = Full power = 260000 hp

$1\ hp=745.7\ W$

$\eta$ = Efficiency = 69%

Power

$p=\eta p_f\\\Rightarrow p=0.69\times 260000\times 745.7\\\Rightarrow p=133778580$

Velocity of aircraft carrier

$v=65\ km/h$

$1\ km/h=\frac{1}{3.6}\ m/s$

$65\ km/h=65\times \frac{1}{3.6}=18.056\ m/s$

When we multiply force (F) and velocity (v) we get power

$p=Fv\\\Rightarrow F=\frac{p}{v}\\\Rightarrow F=\frac{133778580}{18.056}\\\Rightarrow F=7409092.8223\ N$

The magnitude of the force of water resistance that opposes the carrier’s motion is 7409092.8223 N