Centripetal acceleration A jet flies in a vertical circle

[hCornellier]

Homework Statement

A pilot, whose mass is 96.0 kg, makes a loop-the-loop in a fast jet. Assume that the jet maintains a constant speed of 225 m/s and that the radius of the loop-the-loop is 2.064 km.

What is the apparent weight that the pilot feels (i.e., the force with which the pilot presses against the seat) at the bottom of the loop-the-loop?

What is the apparent weight felt at the top of the loop-the-loop?

Homework Equations

ac = v^2/r

The Attempt at a Solution

I've tried finding a solution for the bottom, but have yet to find it. I solved for Fg, (96kg*9.81m/s/s), then I found the centripetal force (point towards center of circle) to be equal to 2354.65N. I read that n-mg=ac?

 

[jtpope2]

you have the correct magnitudes for centripetal and gravitational force. you need to think about the direction of the force vectors and add them.

 

[hCornellier]

So the force exerted on the chair is equal to the centripetal force - Fg?

 

[jtpope2]

the vector for centripetal force always points towards the center and gravity points down, so add the vectors appropriately

 

[Nickie]

First, let's clarify some terminology. The term "apparent weight" refers to the force that a person feels due to the normal force of a surface they are in contact with. In this case, the pilot is feeling a normal force from the seat of the jet. So, we can rephrase the question as "what is the normal force exerted by the seat on the pilot at the bottom and top of the loop-the-loop?"

To solve for this, we can use the equation F = ma, where F is the net force on the pilot, m is their mass, and a is the acceleration they are experiencing. In this case, the acceleration is centripetal acceleration, which we can calculate using the equation ac = v^2/r.

At the bottom of the loop-the-loop, the pilot is experiencing both the acceleration due to gravity (downward) and the centripetal acceleration (upward). So, we can write the equation as:

Fnet = Fg + Fac

Where Fg is the force of gravity (mg) and Fac is the centripetal force (m*v^2/r).

Substituting in the given values, we get:

Fnet = (96 kg)(9.81 m/s^2) + (96 kg)(225 m/s)^2 / (2064 m)

Fnet = 940.8 N + 249.8 N = 1190.6 N

So, at the bottom of the loop-the-loop, the pilot feels a normal force of 1190.6 N from the seat.

At the top of the loop-the-loop, the pilot is still experiencing the acceleration due to gravity (downward), but now the centripetal acceleration is in the opposite direction (downward). So, the equation becomes:

Fnet = Fg - Fac

Substituting in the given values, we get:

Fnet = (96 kg)(9.81 m/s^2) - (96 kg)(225 m/s)^2 / (2064 m)

Fnet = 940.8 N - 249.8 N = 691 N

So, at the top of the loop-the-loop, the pilot feels a normal force of 691 N from the seat.

It's important to note that the pilot's apparent weight (normal force) is changing throughout the loop-the-loop due to the changing direction of the centripetal acceleration. This is why the pilot