Airplane diving with a circle radius

[Robertoalva]

1. A 55 kg airplane pilot pulls out of a dive by following, at constant speed, the arc of a circle whose radius is 320 m. At the bottom of the circle, where her speed is 230 km/h, what is the magnitude of her acceleration?

Homework Equations

v^2= vi^2 +2a(x-xi)

The Attempt at a Solution

i suppose that the plane has a height of the radius and the initial velocity would be 0. Am I wrong? if I am, please tell me!

 

[nil1996]

i think only acceleration will be of gravity.

 

[CWatters]

The equation you cite isn't relevant. Hint: centripetal acceleration.

 

[CWatters]

i think only acceleration will be of gravity.

No. It's moving in a circle.

 

[nil1996]

No. It's moving in a circle.

I first saw at the eqn he has given and so declared as the acceleration is of gravity.
I think you are right it is centripetal acceleration.

 

[Robertoalva]

oh! that's true! i totally forgot about centripetal forces!

 

[dreamLord]

You are visualizing the question wrongly I believe. The aeroplane is in the air, and is heading down towards the Earth. The pilot then pulls out of the dive - he will not go vertically up straight away, rather, he will move along a curved arc upwards. You have the radius of this arc, you have the velocity, and you have the mass. This is a straightforward formula application question.

 

[Robertoalva]

if centripetal force is Fc= m(v^2/r)
then
the centripetal acceleration formula can be derived from the circular acceleration right? a=v^2 /r ,right?

 

[dreamLord]

Yes. All you need to do is divide the force by the object's mass to get it's acceleration.

 

[Robertoalva]

really? so i just do:

Fc=m (v^2/r)
Fc/m=a ? i already got confused!

they are giving me:
m=55kg
r=320m
v=230km/h

and a=v^2/r, wouldn't it be easier to just substitute the values in this formula?

 

[dreamLord]

You don't need the mass to calculate the acceleration. You may use the formula in the last line. All the same thing really.

 

[CWatters]

The answer is not just the centripetal acceleration :-)

 

[Robertoalva]

they want me to find the magnitude of her acceleration, which tells me that they only want a numerical value without a direction, so if they are not asking only for centripetal acceleration then what is it!?

 

[CWatters]

In level flight a pilot experiences 1g.

 

[dreamLord]

The answer is not just the centripetal acceleration :-)

Why do you say that?

 

[CWatters]

I take it back. She feels like she is accelerating at v^2/r + g but is actually only accelerating at v^2/r.

 

[Robertoalva]

so how this affects the acceleration? would it be a=(centripetal accel.)(gravity) ??

 

[haruspex]

so how this affects the acceleration? would it be a=(centripetal accel.)(gravity) ??

No, you already have the answer in the last line of your post #10.
Acceleration is completely determinable by knowing the position as a function of time. With that information, the forces that led to that pattern of movement become irrelevant.