Calculating Maximum Force in Periodic Motion: Airplane in a Storm

[buffgilville]

1) An airplane caught in a storm, is forced into a vertical periodic motion of period 30.2 seconds and amplitude 17.1 meters. The maximum force (in Newtons) acting on a passenger of mass {M} kG is?

T=2pi/[sqrt of (max a*gravity)/A)] ---> max a = 0.07545 m/s^2 and F=ma but the mass of the passenger is not given. Can someone please help? Thanks.

 

[quantumdude]

F=ma but the mass of the passenger is not given. Can someone please help? Thanks.

It looks to me like your answer is supposed to be in terms of M.

 

[buffgilville]

If the answer is in terms of m than the force is 0.07545M, where M=mass, right? but the correct answer is 976 Newtons.

 

[quantumdude]

If the answer is in terms of m than the force is 0.07545M, where M=mass, right?

Right, but there doesn't seem to be enough information to get a single numerical value for the force. You can do an analysis on an individual passenger (Since you were asked for the force "on a passenger", I'm taking it to mean that you are looking for the normal force N):

N-mg=ma
N=mg+ma

so...

N_max=mg+ma_max.

Then you can do an analysis on the airplane. I model it as a mass on a spring.

kx-Mg=Ma
(4π²M/T²)x-Mg=Ma

so...

a_max=(4π²/T²)x_max

You can substitute that expression for a_max into the equation for N_max, but without knowing the mass m of the passenger you can't get a numerical result.

 

[buffgilville]

I don't get it either. There must be a way to find the force...