Uniform circular motion problems

1. Jan 23, 2008

smally

[SOLVED] Uniform circular motion problems

1. The problem statement, all variables and given/known data
A pilot of mass 50kg comes out of a vertical dive in a circular arc such that his upward acceleration is 8.5g

2. Relevant equations
a) What is the magnitude of the force exerted by the airplane seat on the pilot at the bottom of the arc?
b) If the speed of the plane is 345 km/h, what is the radius of the circular arc?

3. The attempt at a solution
I've done $$F = ma$$, so 50 x 8.5 = 425, which is massively as the answer is 4659.75N

At the bottom of the ark the upward acceleration is the same as the magnitude of its centripetal acceleration (I think) therefore $$r = v^{2} / a$$, which comes to 14002.94, which is also massively wrong as the answer provided is 110m

I tried alsorts of other ways too but they never match the answers provided, what am I missing.

2. Jan 23, 2008

blochwave

You're not too far off

So draw the plane and all the forces acting on the poor pilot(who is pulling nearly 9 Gs and probably about to black out or rip his plane apart)

The centripetal FORCE acting on him is his mass times the centripetal acceleration(which is given in the problem as you correctly saw). What is the CAUSE of the centripetal force? ie what is pushing on him that hard? The seat. So the centripetal force is part of the answer. Is that all?

Also just good 'ol gravity is acting on him, pushing him straight down. That means the seat is exerting an equal normal force

3. Jan 23, 2008

smally

Ok so I've now done:
50 x 9.81 x 8.5 = 4169.25
50 x 9.81 = 490.5
4169.25 + 490.5 = 4659.75

but I'm a bit confused as to why I times gravity for when working out Fcent.

I also assumed that the answer to a, would help me with b; but I'm still getting the answer wrong

4. Jan 23, 2008

blochwave

g represents an acceleration, it's in units of acceleration. A plain old unitless number(8.5) times g is also gonna be an acceleration

It is customary to say the acceleration in terms of g, they could say "oh it's 83.3 m/s^2" or they could say "oh it's 8.5 times the acceleration caused by gravity" which immediately tells you he's being pushed into his seat with 8.5 times more force than normal, and pilots normally have a good sense of what the human body can stand(even trained fighter pilots don't pull more than 7 or 8 gs for just seconds)and their plane can stand

For b)You found the centripetal acceleration as PART of a(it wasn't the final answer!), and you're given v, and you know r=v^2/a

5. Jan 23, 2008

smally

Oh right, the "he's being pushed into his seat 8.5 times more force than normal" got lightbulb above my head appear then thanks.

and for b)
r = 95.83^2 / (9.81 x 8.5)
r = 110.13

correct, thank you