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

• Ashleydenee
In summary, the conversation discusses how an accelerometer can be used to measure acceleration in a small plane. The person is struggling to find the magnitude of their acceleration in a specific scenario and has been working on the problem for several hours. They are advised to consider fictitious forces in a non-inertial frame of reference.
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

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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)

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I would recommend using the equation for the period of a pendulum to calculate the acceleration of the plane. The period of a pendulum is given by T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. In this case, the pendulum is hanging at an angle of 12°, so the length of the pendulum can be calculated as L = Lcos(12°). The acceleration due to gravity can be approximated as 9.8 m/s^2. Therefore, the period of the pendulum would be T = 2π√(Lcos(12°)/9.8). From this, the acceleration of the plane can be calculated using the equation a = 4π^2Lcos(12°)/T^2. This would give the magnitude of the acceleration of the plane at that time.

## 1. How does using the angle of a pendulum help in measuring the acceleration of a plane?

The angle of a pendulum is directly proportional to the acceleration of the plane. By measuring the angle of the pendulum, we can determine the acceleration of the plane.

## 2. What is the relationship between the angle of a pendulum and the acceleration of a plane?

The angle of a pendulum is directly proportional to the acceleration of the plane. This means that as the angle of the pendulum increases, the acceleration of the plane also increases.

## 3. What factors can affect the accuracy of using a pendulum to measure the acceleration of a plane?

The accuracy of using a pendulum to measure the acceleration of a plane can be affected by factors such as air resistance, friction in the pendulum's pivot point, and the precision of the measuring instrument used.

## 4. How can the angle of a pendulum be measured accurately?

The angle of a pendulum can be measured accurately using a protractor or an inclinometer. It is important to ensure that the pendulum is hanging freely and the measuring instrument is precisely aligned with the pendulum's motion.

## 5. What are the practical applications of using the angle of a pendulum to measure the acceleration of a plane?

Using the angle of a pendulum to measure the acceleration of a plane can be useful in experiments or simulations involving motion and acceleration, as well as in the design and testing of aircraft and other vehicles that require precise acceleration measurements.

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