# Magnitude of Acceleration given a pendulum equilibrium

## Homework Statement

A pendulum has a length L = 1.36m. 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 = 0.410m. Calculate the magnitude of the plane's acceleration.

## The Attempt at a Solution

I have attempted this many ways. First of all I found the angle that the pendulum swung by using the length of the pendulum rope as two sides of an isosceles triangle. Then placing D = .410 m at the base of this triangle. Then splitting the triangle in half, creating two right triangles. Solving for the top angle and timesing it by two to get the angle of the pendulum swing. I then used gravity, 9.8 m/s/s and found an acceleration of 169.9 m/s/s but this was wrong. I have no idea anymore... anything would help.

tiny-tim
Homework Helper
welcome to pf!

hi joejoemickgo! welcome to pf! … 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 = 0.410m.

First of all I found the angle that the pendulum swung by using the length of the pendulum rope as two sides of an isosceles triangle. Then placing D = .410 m at the base of this triangle. Then splitting the triangle in half, creating two right triangles. Solving for the top angle and timesing it by two to get the angle of the pendulum swing. I then used gravity, 9.8 m/s/s and found an acceleration of 169.9 m/s/s but this was wrong. I have no idea anymore... anything would help.

ah, nooo … "equilibrium" means when the pendulum is in the middle of the swing (zero angular acceleration, maximum angular speed), not when it's stationary at the ends of the swing

"equilibrium" refers to the position at which the pendulum would remain stationary if you held it there and then let go 