Question

1. During take-off, an aircraft accelerates at 3.4 m/s2. The total mass of the aircraft is 8.0 × 103 kg. Calculate:

a) the net force acting on the aircraft during the acceleration.

b) the speed of the aircraft after 5.0 seconds of acceleration.

I need a free body diagram for the following question

Answer 1

The free body diagram is shown on the picture below.

Here $\mathbf{F_{res}}$ is the force due to the air resistance, $\mathbf{mg}$ is the gravity force, $\mathbf{F_{e}}$ is the engine force and $\mathbf{F_{net}}$ is the net force.

According to the Newton's second law:

$$F_{net} = ma$$

where $a = 3.4m/s^2$ is the acceleration of the aircraft and $m = 8\times 10^3 kg$ is its mass. Thus:

$$F_{net} = 8\times10^3\cdot 3.4 = 27.2\times 10^3N = 27.2kN$$

If the aircraft starts from the rest, then the speed after 5 sec will be:

$$v = at = 3.4m/s^2\cdot 5s = 17 m/s$$

Answer. a) 27.2 kN, b) 17 m/s.