A jet aircraft is traveling at 241 m/s in horizontal flight. The engine takes in air at a rate of 34.9 kg/s and burns fuel at a rate of 3.75 kg/s. The exhaust gases are ejected at
566 m/s relative to the aircraft.
Find the thrust of the jet engine.
Answer in units of N.
The thrust of the jet engine can be calculated using Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In the case of a jet engine, the action is the ejection of exhaust gases at a certain velocity, and the reaction is the forward thrust of the engine.
The thrust of the jet engine can be calculated using the formula:
thrust = (mass flow rate of exhaust gases) x (exhaust velocity) - (mass flow rate of air) x (velocity of air)
Given:
mass flow rate of exhaust gases = 34.9 kg/s
exhaust velocity = 566 m/s
mass flow rate of air = 3.75 kg/s
velocity of air = 241 m/s
Using the formula, we can substitute the given values into the equation to find the thrust:
thrust = (34.9 kg/s) x (566 m/s) - (3.75 kg/s) x (241 m/s)
thrust = (19728.4 kg•m/s) - (902.25 kg•m/s)
thrust = 18826.15 kg•m/s
Since force is equal to mass times acceleration, we can convert the force to newtons by dividing the value by the acceleration due to gravity.
thrust in newtons = (18826.15 kg•m/s) / (9.8 m/s^2)
thrust in newtons = 1920.66 N
Therefore, the thrust of the jet engine is 1920.66 N.