Pilot problem dealing with weight and magnitude of force exerted on pilot's body

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SUMMARY

The discussion focuses on calculating the apparent weight of a pilot during a loop-the-loop maneuver in an airplane, specifically at the highest and lowest points of the loop. The pilot's true weight is 160 lb, and the airplane's speeds are 300 mi/h at the top and 450 mi/h at the bottom of the loop, with a radius of 1200 ft. The correct equation to determine the normal force (apparent weight) is Fn = -mg + mv²/r, where m is the mass, g is the acceleration due to gravity (32 ft/s²), and v is the velocity at the respective points.

PREREQUISITES
  • Understanding of forces in circular motion
  • Knowledge of gravitational force calculations
  • Familiarity with free body diagrams (FBD)
  • Basic proficiency in converting units (e.g., mi/h to ft/s)
NEXT STEPS
  • Learn how to convert speeds from miles per hour to feet per second for accurate calculations
  • Study the principles of centripetal force in circular motion
  • Explore the concept of apparent weight in varying gravitational contexts
  • Practice solving similar physics problems involving forces and motion
USEFUL FOR

Physics students, aerospace engineering students, and anyone interested in understanding the dynamics of forces acting on pilots during flight maneuvers.

dgibbs
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Homework Statement


The Pilot of an airplane executes a loop-the-loop manuever in a vertical circle. The airplane's speed is 300 mi/h at the top of the loop and 450 mi/h at the bottom. The radius of the circle is 1200 ft. Use American Engineering units in this problem.

A) The pilot's apparent weight is equal to the magnitude of the force exeted by the seat on his body. What is the pilot's weight at the circle's highest point if his true weight is 160 lb?

B) What is the pilot's apparent weight at the circle's lowest point?

Homework Equations


I know I have to find the some of forces and solve for his weight.


The Attempt at a Solution



I know the first step is to draw a FBD and label the forces acting on the pilot.
At the top of the look, with the pilot traveling 300 mi/hr the forces acting are...

Gravitational Force = mg = 32 ft/s^2
w/Pilot's weight = 32 x 160lb = - 5120
Normal Force of seat = Fn = Fg = 5120 ??

I know I have to factor in the velocity but I am not sure what the equation is that i have to use...
Please help thanks
 
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Is the right equation...

Fn = -mg + mv^2/r ??
 
any help please?
 

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