## Centripetal acceleration on a airplane in a circle

gtaletkirk
Posts: 1
Joined: Thu Aug 30, 2018 12:16 pm

### Centripetal acceleration on a airplane in a circle

A 74.4-kg airplane pilot pulls out of a dive by following, at a constant speed of 184 km/h, the arc of a circle whose radius is 282.0 m.
(a) At the bottom of the circle, what are the direction and magnitude of his acceleration?

(b) What is the net force acting on him at the bottom of the circle?

(c) What is the force exerted on the pilot by the airplane seat?

I'm on part a.so does it equal v^2/r
v is speed, r is radius

v=184 and r=282 here, Intuitively the force will be up along the radius and that's right. I get 129 but that's wrong. I'd appreciate some help, thank you

jeff
Posts: 39
Joined: Mon Mar 05, 2018 11:54 pm

### Re: Centripetal acceleration on a airplane in a circle

Hi gtaletkirk ,
gtaletkirk wrote:
Thu Aug 30, 2018 12:16 pm
A 74.4-kg airplane pilot pulls out of a dive by following, at a constant speed of 184 km/h, the arc of a circle whose radius is 282.0 m.
(a) At the bottom of the circle, what are the direction and magnitude of his acceleration?

(b) What is the net force acting on him at the bottom of the circle?

(c) What is the force exerted on the pilot by the airplane seat?

I'm on part a.so does it equal v^2/r
v is speed, r is radius

v=184 and r=282 here, Intuitively the force will be up along the radius and that's right. I get 129 but that's wrong. I'd appreciate some help, thank you
You did not mention what units you are using or what units they are wanting, but I believe that is the problem. The speed they give is in km/hr, so you need to change that to m/s if you want your final answer to be in m/s^2. But yes, once you convert that, you do use v^2/r to get the centripetal acceleration. What do you get for that?

BiancaTex
Posts: 2
Joined: Tue Sep 11, 2018 12:37 am

### Re: Centripetal acceleration on a airplane in a circle

Hey, how do you know if the a is centripetal or not? I tried a=v^2/r for some circular motion problem and get it wrong because there is a tangential as well. This doesn't make any sense, how can you sometimes have it and sometimes not? I know this is likely meaning something easy but I don't know?

jeff
Posts: 39
Joined: Mon Mar 05, 2018 11:54 pm

### Re: Centripetal acceleration on a airplane in a circle

Hi BiancaTex,
BiancaTex wrote:
Tue Sep 11, 2018 2:36 pm
Hey, how do you know if the a is centripetal or not? I tried a=v^2/r for some circular motion problem and get it wrong because there is a tangential as well. This doesn't make any sense, how can you sometimes have it and sometimes not? I know this is likely meaning something easy but I don't know?
That's an important question! Here's the logic behind it all for circular motion:

Acceleration is the rate at which velocity changes.

However, velocity is a vector, with magnitude and direction, so there are two ways that it can change. It change change in magnitude, and it can change in direction. Centripetal acceleration has to do with changes in velocity direction, and tangential acceleration (some books call it linear accleration) has to do with changes in velocity magnitude.

So if something is going in a circle, it automatically has centripetal acceleration towards the center of the circle. If in addition, it is speeding up or slowing down as it goes around the circle, it will have tangential acceleration.

So that's the idea! Many problems, like the one at the top of this thread, will mention that the object is "moving in a circular path at constant speed" so then you know there is centripetal acceleration only. But if the object is not going at constant speed, it will also have tangential acceleration in the forward or backward direction.