Is it possible to figure out the centripetal acceleration?

Question

Is it possible to figure out the centripetal acceleration when all you know is that a plane is moving with constant speed in a half circle, and the plane is tilted 40 degrees? A passenger on the plane will notice a force pressing him towards his seat, but no force from the side.

Answer 1

Since you know the passenger is not experimenting forces from the side, you know that the resultant of weight and centripetal force is perpendicular to the plane (I mean perpendicular to plane cabin floor). To draw a diagram of both forces, you can draw the forces the passengers exerts on the plane: weight downwards and centripetal force outwards, and since you know that the plane is tilted 40 degrees, you will see that:

$$ \text{centripetal force }=\text{ weight }\times\tan(40º) $$ And since: $$ \text{centripetal force }=\text{ centripetal acceleration }\times\text{ mass } $$ and $$ \text{weight }=g\times\text{ mass } $$ you can see that: $$ \text{centripetal acceleration }=g\times\tan(40º) $$

Then, you can know the centripetal acceleration.