Question

a) The speed of an aeroplane is .ms12001− The engines take in 80 kg of air per second and mix it with 40 kg of fuel. This mixture is expelled after it ignites and it moves at a velocity of 1ms3000−relative to the aeroplane. Calculate the thrust of the engine

Answer 1

Answer on Question #39994, Physics, Mechanics | Kinematics | Dynamics

The speed of an airplane is .ms12001– The engines take in 80 kg of air per second and mix it with 40 kg of fuel. This mixture is expelled after it ignites and it moves at a velocity of 1ms3000–relative to the airplane. Calculate the thrust of the engine

Solution

Thrust is a reaction force described quantitatively by Newton's second and third laws. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction on that system.

From Newton's second law of motion a force $F$ on an object is equal to the rate of change of its momentum

$$F = \frac {d p}{d t} = \frac {d (m v)}{d t}.$$

We can find this force using mass that enters the airplane and mass that comes out of it:

$$F = \frac {d m _ {\mathrm {o u t}}}{d t} \cdot v _ {\mathrm {o u t}} - \frac {d m _ {i n}}{d t} \cdot v _ {i n},$$

where $\frac{dm_{in}}{dt}$ - the rate of change of mass that enters the airplane, $\frac{dm_{out}}{dt}$ - the rate of change of mass that comes out of airplane, $v_{in} = 1200\frac{m}{s}$ - velocity of an air which enters the airplane, $v_{out} = 3000\frac{m}{s}$ - velocity of a fuel and an air that comes out of the airplane.

$$\frac {d m _ {i n}}{d t} = 8 0 \frac {k g}{s}; \frac {d m _ {o u t}}{d t} = (8 0 + 4 0) \frac {k g}{s} = 1 2 0 \frac {k g}{s}.$$

The thrust of the engine:

$$F = 1 2 0 \frac {k g}{s} \cdot 3 0 0 0 \frac {m}{s} - 8 0 \frac {k g}{s} \cdot 1 2 0 0 \frac {m}{s} = 2 6 4 0 0 0 \frac {k g \cdot m}{s ^ {2}} = 2 6 4 k N.$$

Answer: 264 kN.