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Calculating normal force in a loop-the-loop situation

  • Thread starter jeanjacket
  • Start date
1. The problem statement, all variables and given/known data

Here's the situation:

A jet pilot puts an aircraft with a constant speed into a vertical circular loop. If the speed of the aircraft is 700 km/h and the radius of the circle is 2.0 km, calculate the normal forces exerted on the seat by the pilot at the bottom and top of the loop. Express your answer in terms of the pilot's weight mg.

a) at the bottom
b) at the top

I actually have the answers to the problem, but of course it doesn't help me understand the problem nor the process in getting there. Not sure which angular motion/centripetal force equations to use. But if it helps ya verify results, here are the answers:

At bottom: 2.93*mg
At the top: .929*mg

I would really appreciate any help, even if it's just pointing me in the right direction as far as which equation to use, I'm not necessarily asking anyone to work it out. Thanks in advance!!!

2. Relevant equations

Not necessarily sure which to use, here's some conversions just for quick reference:
700 km/h = 194.444 m/s
2.0 km = 2000 m

Possible eqns:

Angular Velocity = [tex]\omega[/tex] = [tex]\Delta[/tex][tex]\theta[/tex]/[tex]\Delta[/tex]t
Angular Acceleration = [tex]\alpha[/tex] = [tex]\Delta[/tex][tex]\omega[/tex]/[tex]\Delta[/tex]t
[tex]\textbf{F}[/tex][tex]_{centripetal}[/tex] = mass x accel(centrip) = m[tex]v^{2}/r[/tex]
[tex]\textbf{F}[/tex][tex]_{gravity}[/tex] = mg

3. The attempt at a solution

Can't quite figure out where to start...
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
Start with 2 free-body diagrams, 1 for the forces on the pilot at the top of the loop and one for the bottom. Keep in mind what force(s) provide the centripetal acceleration for the pilot at those points.
At all times the centrifugal acceleration pushes the pilot onto the seat. The difference is the direction of the weight of the pilot, which is always the directed towards the centre of the earth. So at the bottom force = centrifugal + weight, at top its centrifugal - weight.

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