Circular Motion Help

1. Sep 7, 2015

Jimmy87

1. The problem statement, all variables and given/known data
NASA’s Vomit Comet simulates zero gravity by flying parabolic arcs of radius r and speed v to stimulate free fall. If the pilot flies a parabolic path which has a radius of 1km, calculate the speed (*in km/hr) the plane must travel at in order to stimulate free fall?

2. Relevant equations
a = v^2/r

3. The attempt at a solution
I get the answer as 356km/hr which I think is correct. I solved for v and used 1km for r and plugged in 'a' at 9.81 m/s^2 as freefall is when the only force acting on an object is gravity. However, after thinking about the problem I don't understand how this works in real life at all! I don't understand how you can assume the centripetal acceleration is 9.81m/s^2. If the plane is coasting through the air at any finite speed then surely due to its design if must experience lift so how can you make the only force it experiences gravity when you will always have some lift?

2. Sep 7, 2015

andrewkirk

The answer is that the lift forces operate on the plane, not on the person inside the plane, and it is the latter that experiences weightlessness.

It's an interesting point though. The pilot would have to take the plane's lift into account in tracing out the correct arc. It wouldn't be just a matter of shutting the engines off, as it would be if the plane were a giant cannonball. I imagine it's quite complicated to determine what combination of thrust and elevator settings to use to trace out the required parabola. My guess is that the pilot would have to set elevators down (ie push the yoke forward, which accelerates the plane downwards) and engine thrust above idle, to counteract the lift.

Last edited: Sep 7, 2015