Centripetal Force: 80kg Pilot in Jet at 305m/s

[electricheart]

Homework Statement

An 80 kg pilot, makes a loop the loop in a jet, the jet maintains a constant speed of 305 m/s and the radius of the loop is 1.900km. What is the apparent weiht that the pilot feels( Force) at the bottom of the loop the loop.

Homework Equations

Acp=w^2/r
w=(v/r)
F= ma or F= mg

The Attempt at a Solution

First I solved for omega w=0.1605, then I solved for Acp=0.0000136
the Force the pilot feels at the bottom of the loop would be
mg+ Acp or is this wrong?

 

[electricheart]

I figured out what I was doing wrong, I calculated the Acp wrong.

 

[nlightner]

I would like to clarify a few things in this scenario. Firstly, it is important to note that the pilot's weight is not changing throughout the loop. The force of gravity, mg, remains constant regardless of the pilot's motion. Therefore, the pilot's apparent weight at the bottom of the loop should be equal to their actual weight, 80 kg.

Now, let's look at the forces acting on the pilot at the bottom of the loop. The pilot is experiencing two forces: the force of gravity, mg, and the centripetal force, Fc. The centripetal force is the force that keeps the pilot moving in a circular path. It is given by Fc = m(v^2/r), where m is the mass of the pilot, v is the velocity, and r is the radius of the loop.

In this case, we have all the necessary values to calculate the centripetal force. Plugging in the values, we get Fc = 80(305^2/1900) = 3,088 N. This is the force that the pilot is feeling at the bottom of the loop.

Now, if we want to calculate the apparent weight of the pilot, we can simply add the force of gravity and the centripetal force. The apparent weight, Fapp, is given by Fapp = mg + Fc. Plugging in the values, we get Fapp = 80(9.8) + 3,088 = 3,868 N. This is the apparent weight that the pilot feels at the bottom of the loop.

In conclusion, the pilot's apparent weight at the bottom of the loop is 3,868 N, which is the sum of their actual weight and the centripetal force acting on them. It is important to note that the pilot's actual weight remains constant throughout the loop, but the apparent weight changes due to the additional centripetal force.