Vertical circular motion in uniform circular motion

[seanpk92]

Homework Statement

A pilot flies an airplane in a vertical circular loop with a radius of R = 1200 m. The plane is gaining speed as the pilot makes a dive, and its speed is measured to be 150 m/s when the plane reaches the bottom of the circle. If the total acceleration of the plane at the bottom is 2.3g, find (a) the tangential acceleration of the plane, (b) the direction of the plane’s acceleration at the bottom of the loop.

Homework Equations

What I can think of doing, is:
a_n=v²/R
and
a = a_n + a_t

The Attempt at a Solution

I tried making a free body diagram with the total force and a_n pointing toward the center, and the v and the a^t point to the right. At the bottom of the circle.
a_n = 150²/1200 = 18.75m/s²
a = 2.3g = 2.3/9.8m/s² = 0.2346m/s²

but this doesn't give me my answer. The answer is (a) 12.5 m/s² and (b) beta = 56.3^o

(i don't know how to do a, so I can't start b)

 

[PhanthomJay]

Homework Statement

A pilot flies an airplane in a vertical circular loop with a radius of R = 1200 m. The plane is gaining speed as the pilot makes a dive, and its speed is measured to be 150 m/s when the plane reaches the bottom of the circle. If the total acceleration of the plane at the bottom is 2.3g, find (a) the tangential acceleration of the plane, (b) the direction of the plane’s acceleration at the bottom of the loop.

Homework Equations

What I can think of doing, is:
a_n=v²/R

yes, good

and
a = a_n + a_t

the tangential and centripetal acceleration vectors are at right angles to each other, so you need to add them vectorially to get the total acceleartaion.

The Attempt at a Solution

I tried making a free body diagram with the total force and a_n pointing toward the center,

yes

]and the v and the a^t point to the right.

yes, and the tangential force points in the same direction

At the bottom of the circle.
a_n = 150²/1200 = 18.75m/s²
a = 2.3g = 2.3/9.8m/s² = 0.2346m/s²

2.3 g's means the acceleration is 2.3 times the gravitational acceleration

but this doesn't give me my answer. The answer is (a) 12.5 m/s² and (b) beta = 56.3^o

(i don't know how to do a, so I can't start b)

Correct you formula for total acceleration

 

[seanpk92]

Thank you so much PhantomJay!

 

[PhanthomJay]

Thank you so much PhantomJay!

(You're) Welcome to PF!