Question

Please explain, DON'T give me the answer.
An airplane has a mass of 3.1x 10^4 kg and takes off under the influence of a constant net force of 3.7x 10 ^4 N. What is the net force that acts on the plane’s 78-kg pilot?

The professor solved this as a proportion, however, I am having issues understanding why?
p= pilot & a=airplane

mp/ ma = Fp/ Fa

My theories: I now that the Forces can't be same because Force depends on the mass, therefore, the airplane's force would be higher. I know that they are both accelerating at the same rate, the pilot in reference to the airplane.

Answer 1

So why setting this up as a proportion solves the problem?

Answer 2

F=m*a
both the airplane and the pilot have the same acceleration "a"
Fp = mp*a
Fa = ma*a

dividing the two equations we get
Fp/Fa = mp/ma
so Fp = Fa*mp/ma
we have Fa= 3.7x 10 ^4 N
ma= 3.1x 10^4 kg
mp= 78 kg
so we can get Fp

Answer 3

Is there any other way of solving it?
Or a theory behind it?

Answer 4

Maybe I'm thinking too much into it.

Answer 5

I don't think there is a special theory for this case
and this formula is the only one that relates the masses and forces (as far as i know :P)
I think it's the only way to solve it.

Answer 6

Relates masses and forces!!! Thank you!!! Sometimes the small things make it click!!! Thanks again!!

Answer 7

yeah when you are approaching to solve a problem you must keep in consideration the given you have, you may find lots of ways to find the unknown you need but not all the ways are applicable with your few given values

Answer 8

Thank you again.