A jet aircraft is traveling at 230 m/s in horizontal flight. The engine takes in air at a
rate of 96.7 kg/s and burns fuel at a rate of
3.96 kg/s. The exhaust gases are ejected at
482 m/s relative to the aircraft.
Find the thrust of the jet engine.
Answer in units of N
To find the thrust of the jet engine, we can use the principle of momentum.
The principle of momentum states that the change in momentum of an object is equal to the force applied to it multiplied by the time interval over which the force acts. In this case, the change in momentum of the engine is equal to the thrust force multiplied by the time interval.
The change in momentum of the engine is given by the mass of air intake multiplied by the change in velocity of the exhaust gases.
Change in momentum = (mass of air intake) * (change in velocity of exhaust gases)
We are given the following values:
- Mass of air intake (m_air) = 96.7 kg/s
- Change in velocity of exhaust gases (Δv) = 482 m/s
Now, we need to calculate the change in momentum.
Change in momentum = (96.7 kg/s) * (482 m/s)
Next, we convert the values into the standard SI unit of Newtons (N). Recall that the unit of momentum is kg·m/s, and the unit of force is kg·m/s² (Newton).
Change in momentum = (96.7 kg/s) * (482 m/s) = 46637.4 kg·m/s
Since the change in momentum is equal to the thrust force multiplied by the time interval, we can set up the equation:
Change in momentum = (thrust force) * (time interval)
Since we are not given the time interval, we assume that it is 1 second. Hence, the equation simplifies to:
46637.4 kg·m/s = (thrust force) * (1 s)
Therefore, the thrust force of the jet engine is approximately 46637.4 N.