Find plane's acceleration from mass on a string

[psal]

Homework Statement

A pendulum has a length L = 1.13m. It hangs straight down in a jet plane about to take off as shown by the dotted line in the figure. The jet then accelerates uniformly, and while the plane is accelerating, the equilibrium position of the pendulum shifts to the position shown by the solid line, with D = 0.370m. Calculate the magnitude of the plane's acceleration.

Homework Equations

Lsinθ = D
a = gsinθ

The Attempt at a Solution

sinθ = 0.37/1.13
θ = 19.11 deg
9.8sin(19.11) = 3.209

I thought that is the correct way to solve it, but I am not getting the correct answer, and I cannot think of another way to go about it.

 

[azizlwl]

I think it is called fictitous force.
You assume there is a force pulling it to the right.

 

[nasu]

Or write Newton's second law for horizontal and vertical directions.

By the way, one can tell that you result is not right without going through the calculations. If it were, you will have a horizontal string (angle=90 degrees) when a=g. There will be no tension component to balance the weight.

 

[psal]

Okay, did I at least calculate the angle correctly?

Edit: Figured it out. Thanks for the help.

 

[Nickie]

I would like to clarify that the given information does not provide enough details to accurately calculate the plane's acceleration. We need to know the mass of the pendulum and the force acting on it in order to calculate the acceleration.

Assuming that the pendulum has a small mass and negligible air resistance, we can use the formula T = 2π√(L/g) to calculate the period of the pendulum, where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

Using the given information, we can calculate the initial period of the pendulum (when the plane is stationary) as T1 = 2π√(1.13/9.8) = 2.4 seconds.

When the plane accelerates, the equilibrium position of the pendulum shifts to D = 0.370m. This means that the new period of the pendulum (when the plane is accelerating) is T2 = 2π√(0.370/9.8) = 0.6 seconds.

The change in period can be calculated as ΔT = T2 - T1 = 0.6 - 2.4 = -1.8 seconds.

Using the formula a = 4π²ΔT/L, we can calculate the acceleration of the plane as a = 4π²(-1.8)/1.13 = -9.8 m/s².

Since the plane is accelerating uniformly, we can assume that the acceleration of the pendulum is equal to the acceleration of the plane. Therefore, the magnitude of the plane's acceleration is 9.8 m/s².

Note: The negative sign in the final answer indicates that the plane is decelerating, not accelerating. This could be due to the fact that the pendulum is experiencing an apparent force due to the acceleration of the plane, known as the Coriolis force.