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When its 75-kW (100-hp) engine is generating full power, a small single-engine airplane with mass 700 kg gains altitude at a rate of 2.5 m/s(150 m/min or 500ft/min). What fraction of the engine power is being used to make the airplane climb? (The remainder is used to overcome the effects of air resistance and of inefficiencies in the propeller and engine.)

Short Answer

Expert verified

The fraction of engine power used to lift the airplane is 23%.

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The power of the engine is, P=75kW
  • The mass of the airplane is, m=700kg
  • The velocity of the airplane is,2.5m/s
02

Concept/Significance of power

The amount of work done by the engine in unit time, gives the power of the engine. Its unit is Watts (W) .

03

Determination of the fraction of the engine power is used to make the airplane climb

The power of the single-engine use to lift the plane-

P=Fv=mgv

Here, m is the mass of the airplane, g is the acceleration due to gravity, and v is the speed of the airplane.

Substitute all the values in the above,

P=700kg9.8m/s22.5s=17.15kW

This is the part of power used by plane to climb so the fraction of power used is given by,

Pf=17.15kW75kW=0.23=23%

Thus, the fraction of engine power used by airplanes to climb is 23%.

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