Pendulem in an Accelerting Plane

[BrettL789123]

A pendulum has a length L = 1.14 m. It hangs straight down in a jet plane about to take off as shown by the dotted line in the figure. The jet accelerates uniformly, and during that time, the pendulum oscillates about the equilibrium position shown by the solid line, with D = 0.42 m. What is the acceleration of the plane?

 

[tiny-tim]

A pendulum has a length L = 1.14 m. It hangs straight down in a jet plane about to take off as shown by the dotted line in the figure. The jet accelerates uniformly, and during that time, the pendulum oscillates about the equilibrium position shown by the solid line, with D = 0.42 m. What is the acceleration of the plane?

HI BrettL789123!

(ignore the fact that it's a pendulum. … only the angle of the equilibrium position matters )

This is a vector addition problem.

I expect you're used to velocites adding like vectors.

Well, accelerations do also!

 

[baba89]

I would first analyze the given information and determine the variables involved in this scenario. The length of the pendulum (L) and the maximum displacement from equilibrium (D) are provided. I would also consider the acceleration of the plane (a) as the unknown variable.

Next, I would apply the principles of physics, specifically the laws of motion and simple harmonic motion, to solve for the acceleration of the plane. The pendulum's oscillation is affected by the acceleration of the plane, which can be represented by the equation a = -ω^2D, where ω is the angular velocity.

To solve for ω, I would use the equation ω = 2π/T, where T is the period of oscillation. The period can be calculated using the equation T = 2π√(L/g), where g is the acceleration due to gravity.

Substituting the values given in the problem, we get T = 2π√(1.14/9.8) = 1.41 seconds.

Now, we can solve for ω = 2π/1.41 = 4.45 rad/s.

Substituting this value for ω in the initial equation, we get a = -4.45^2(0.42) = -8.87 m/s^2.

Therefore, the acceleration of the plane is -8.87 m/s^2. This negative sign indicates that the acceleration is in the opposite direction of the pendulum's displacement, which is expected as the plane is accelerating forward and the pendulum is swinging backwards.

In conclusion, the acceleration of the plane is -8.87 m/s^2, and this calculation was made possible by applying the principles of physics to the given scenario.