A pilot of mass 65 kg in a jet aircraft makes a complete vertical circle in mid-air. The vertical circle has a radius of 1.70 km at a constant speed of 215 m/s. Determine the force of the seat on the pilot at (a) the bottom of the loop and (b) the top of the loop. (Note that at the top of the loop, the aircraft is upside down.)
Okay, i know that first i will have to use 1700m as my radius.
Also, i know the equations i will have to work with (uniform circular motion
Centripetal Force= mass times velocity squared, all over radius.)
But, am i looking for the Fn (Normal Force) ..
Centripetal force will equal force of gravity plus the normal force in both situations, so how will the situations differ? like, is there something i'm missing?
Please explain, thanks :)
Physics - MathMate, Thursday, October 29, 2009 at 5:58pm
It is very good that you have mentioned what you have already found, and what bothers you.
Basically, the centripetal force Fc=mv²/r will exert extra load on the seat. The extra load is radially outwards.
Therefore, when the pilot is at the bottom of the loop, Fc adds to gravity, which is mg. With the sign convention of positive upwards, it would be -Fc-mg.
When he is at the top of the loop, gravity is -mg (downwards), which is added to Fc. So the total force on the seat is Fc-mg (upwards).
Therefore you see that the two net forces on the seat are different when at the top and at the bottom of the loop.