Calculating Minimum Radius for Circular Motion in a Vertical Loop

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Homework Help Overview

The discussion revolves around calculating the minimum radius required for a plane to complete a vertical loop without exceeding a specified acceleration limit for the pilot. The problem involves concepts from circular motion and forces acting on the pilot during the maneuver.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to analyze forces using a free body diagram but expresses confusion about the setup of equations related to forces. Some participants question the interpretation of g-forces experienced by the pilot and suggest that the centripetal acceleration should account for the existing gravitational force. Others propose using conservation of energy to relate velocities at different points in the loop.

Discussion Status

The discussion is active, with participants exploring different interpretations of the forces involved and the implications for the radius calculation. There is acknowledgment of the need for a larger radius based on the revised understanding of the forces. Guidance has been offered regarding the application of conservation of energy, but no consensus has been reached on the final approach.

Contextual Notes

Participants are navigating through the complexities of the problem, including the effects of gravitational force on the pilot and the assumptions about acceleration limits. There is an indication of confusion regarding the setup of equations and the variables involved in the free body diagram.

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Homework Statement


A plane pilot takes his aircraft in a vertical loop. If the plane is moving at a speed of 700km/h at the lowest point of the loop:
a) Determine the minimum radius of the circle so the pilots acceleration does not exceed 6 g's
b) What is the pilot's effective weight at the bottom of the loop if her mass is 60.0kg?

Homework Equations


Fc=mv^2/r
Ac=v^2/r

The Attempt at a Solution



I have a free body diagram with force centripetal going up towards center, and the normal force going up as well. I also have mg going down, but i feel like I am missing something and I am confused about how to setup the EFy=? EFx=? or EF=?

I think I got a) with 6(9.81)=(194)^2/r
"R= 639m
 
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When the plane is at the lowest part of the loop the downward force on the pilot is already 1g. If he is not to experience greater than 6g the centripetal acceleration shouldn't be greater than 5g right?
 
Thanks Pion :). So therefore the radius is actually larger. I'm still confused about the free body diagram because I feel like i am missing a variable and don't know how to set it up.
 
Last edited:
Apply the conservation of energy and find the relation between velocity at the bottom, velocity at the top and distance between top to bottom.
At the top, v^2/R - g = 6g.
Can you proceed now?
 

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