Acceleration due to gravity in a plane?

Question

An accelerometer ( a device to measure acceleration) can be as simple as a small pendulum. Suppose you are flying a small plane in a straight horizontal line and your accelerometer hangs 12 degrees behind the vertical. What is your acceleration?

Answer 1

Let us examine the "accelerometer". One consideration---there are two forces acting on it, the net resulting force would then provide the force needed for acceleration. The gravity: mg, and the string pulling force, at an angle of 12 degrees from the norm. Another consideration---there are three forces acting on it: the gravity: mg; the string pulling force, at an angle of 12 degrees from the norm; and the reaction force to the plane's accelaration, according to Newton's action-reaction (second) Law. Both considerations are equivalent.
Since the gravity is mg, the string pulling force must be mg/cos(12°) to avoid the "pendulum" to move up/ down. Thus the accelaration force must be {mg/cos(12°)}*sin(12°) = mg*tan(12°), to avoid the "pendulum" to move left/ right. According to Newton's third Law F = ma, the accelaration a = g*tan(12°) = 2.09 (m/s^2).

Answer 2

F = M x A (force = mass x acceleration)

A = F/M

the question is how much force is needed to move the pendulum 12 degrees.

http://www.nd.edu/~pdunn/www.ame250/muPENDho.pdf