Calculating Maximum Force in Periodic Motion: Airplane in a Storm

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Homework Help Overview

The discussion revolves around calculating the maximum force acting on a passenger in an airplane undergoing vertical periodic motion due to a storm. The problem involves concepts from mechanics, specifically relating to forces and motion, with given parameters such as period and amplitude.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between maximum acceleration, force, and mass, questioning how to express the force in terms of the passenger's mass. There is also discussion about the adequacy of the provided information for deriving a numerical answer.

Discussion Status

Participants are actively engaging with the problem, attempting to derive expressions for the force acting on a passenger. Some have suggested methods for analyzing the forces involved, while others express confusion about the lack of specific mass information needed for a numerical solution. There is no explicit consensus on how to proceed given the constraints.

Contextual Notes

The mass of the passenger is not provided, which is a critical piece of information for calculating the maximum force. Participants are considering the implications of this missing data on their ability to reach a definitive answer.

buffgilville
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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.
 
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buffgilville said:
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.
 
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.
 
buffgilville said:
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...

Nmax=mg+mamax.

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...

amax=(4π2/T2)xmax

You can substitute that expression for amax into the equation for Nmax, but without knowing the mass m of the passenger you can't get a numerical result.
 
I don't get it either. There must be a way to find the force... :cry:
 

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