Answer:
Fraction of engine is 0.23
Explanation:
Given Data
m=700 kg
v=2.5 m/s
Fraction=?
Solution
Work done against gravity is given as
P=Fv
where F=mg
So
P=mgv
P=(700kg)×(9.8m/[tex]s^{2}[/tex])×(2.5m/s)
P=17.15 kW
To find Fraction
[tex]\frac{17.5}{75}=0.23[/tex]
The fraction of the engine power which is used to make the airplane climb is 0.23 or 23%.
Mechanical power is the power or energy required to perform a particular work. The mechanic power is the product of force and the displacement.
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.
The mass of the single engine airplane is 700 kg. Thus, the force applied by this is,
[tex]F=mg\\F=700\times9.81\\F=6867\rm N[/tex]
Now, the power is the product of force required to the speed of the engine. The speed of the engine is 2.5 m/s. Therefore, power is,
[tex]P=6867\times2.5\\P=17167.5\rm W\\P=17.1675 kW[/tex]
Now, the engine can generate 75 kW power at its full power. Thus, the fraction of the engine power is being used to make the airplane climb, due to its weight is,
[tex]P_f=\dfrac{17.1675}{75}\\P_f\cong 0.23\\P_f=23\%[/tex]
Thus, the fraction of the engine power which is used to make the airplane climb is 0.23 or 23%.
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