Using the angle of a pendulum to measure the acceleration of a plane.

[Ashleydenee]

Homework Statement

An accelerometer—a device to measure acceleration—can be as simple as a small pendulum hanging in the cockpit. Suppose you are flying a small plane in a straight, horizontal line and your accelerometer hangs 12° behind the vertical, as shown in the figure. What is the magnitude of your acceleration at that time?

Homework Equations

Thought SumF = ma, but I have no idea.

The Attempt at a Solution

Ok so I did the FBD for this, but I really have no idea how to go about this. I've tried angular acceleration formulas, etc, but the answer has been wrong. I've been working on Physics HW now for 4 hours and this is the final one, but I really have no idea how to go about this.

http://img87.imageshack.us/img87/1759/fbdam1.jpg

 

[skand]

hello,

I'ld advise you to check for http://en.wikipedia.org/wiki/Fictitious_force" as you are in Accelerated frame of reference.

Here the forces acting on the bob are tension,weight and pseudo force(if you write equation in aeroplane frame of reference).Break Tension in horizontal and vertical components.Vertical component balances weight and horizontal balances Pseudo forces(or alternatively,provide acceleration,if you are looking from ground frame of reference).

note that in non inertial frame,the bob is in rest whereas it is moving with acceleration(equal to that of aeroplane)