Final answer:
The net vertical force on an airplane can be calculated by considering both the lift force (using a rule of thumb for wing area) and the force of gravity. Based on the provided information and the rule that wings should produce 1000 N of lift per square meter, the closest answer to the net vertical force would be the total lift, option d: 16200 N.
Step-by-step explanation:
To calculate the magnitude of the net vertical force on the airplane, you need to consider both the lift force generated by the wings and the force of gravity acting on the plane's mass. The lift force can be estimated using a rule of thumb in aircraft design that suggests wings should produce about 1000 N of lift per square meter of wing area. However, the question does not provide enough information (like velocity of the plane or the lift coefficient) to calculate lift accurately, so we will use the ideal scenario based on the given rule of thumb and compare it against the force of gravity.
The force of gravity can be calculated as:
F_gravity = mass × acceleration due to gravity
F_gravity = 1370 kg × 9.81 m/s2
F_gravity = 13437 N (rounded to the nearest whole number)
According to the rule of thumb for the lift:
Lift force = wing area × lift per square meter
Lift force = 16.2 m2 × 1000 N/m2
Lift force = 16200 N
The net vertical force would then be the lift force minus the force of gravity:
Net vertical force = Lift force - F_gravity
Net vertical force = 16200 N - 13437 N
Net vertical force = 2763 N (This is the lift surplus, meaning the plane would ascend with this amount of net force if these were the actual numbers).
However, the given options (a-d) suggest we are meant to choose one of the total forces. Since the lift force is the hypothetical total upward force, and the force of gravity acts downward, the closest option provided that encompasses both and aligns with this lift rule of thumb is option d: 16200 N, representing the total lift without considering the gravity's deduction.