Question

a jets engine takes in 20 kilograms of air per second. the air is compressed, heated, and discharged at a rate of 500 m/s². what force is exerted by the jet engine? 10,000 n 2500 n 15,000 n 1000 n

Explanation:

Step1: Recall Newton's second - law

$F = ma$, where $F$ is force, $m$ is mass, and $a$ is acceleration. Here, we have the rate of mass intake $\frac{dm}{dt}=20\ kg/s$ and the acceleration of the discharged air $a = 500\ m/s^{2}$. The force exerted by the jet engine can be calculated using the formula $F=\frac{dm}{dt}v$ (derived from the more general form of Newton's second - law for variable mass systems, and when considering the change in momentum of the air per second, $F=\frac{d(mv)}{dt}=v\frac{dm}{dt}$ since the air starts from rest relative to the engine in the intake and gains velocity $v$ at the discharge). In this case, we can also think of it in terms of the impulse - momentum theorem. The force is equal to the rate of change of momentum. The mass of air processed per second is $m = 20\ kg$ and the acceleration of the air is $a=500\ m/s^{2}$.
$F = ma$

Step2: Substitute values

Substitute $m = 20\ kg$ and $a = 500\ m/s^{2}$ into the formula $F=ma$.
$F=20\times500$
$F = 10000\ N$

Answer:

10,000 N