Vertical circular motion in uniform circular motion

seanpk92

1. The problem statement, all variables and given/known data
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.


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

3. 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 dont know how to do a, so I cant start b)

PhanthomJay

yes, good 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. yes yes, and the tangential force points in the same direction 2.3 g's means the acceleration is 2.3 times the gravitational acceleration Correct you formula for total acceleration

seanpk92

Thank you so much PhantomJay!

PhanthomJay

(You're) Welcome to PF!