Magnitude of Acceleration given a pendulum equilibrium

In summary, a pendulum with a length of 1.36m hangs in a jet plane about to take off. As the plane accelerates uniformly, the equilibrium position of the pendulum shifts to a distance of 0.410m from the starting position. The magnitude of the plane's acceleration can be calculated by using the definition of acceleration and the pendulum
  • #1
joejoemickgo
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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.

http://capa-new.colorado.edu/msuphysicslib/Graphics/Gtype09/prob48_sidepend.gif


Homework Equations





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.
 
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welcome to pf!

hi joejoemickgo! welcome to pf! :smile:
joejoemickgo said:
… 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 :redface: … "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 :biggrin:
 

Related to Magnitude of Acceleration given a pendulum equilibrium

1. What is the magnitude of acceleration in a pendulum equilibrium?

The magnitude of acceleration in a pendulum equilibrium depends on the length of the pendulum and the strength of the gravitational force. In general, the magnitude of acceleration is equal to the square of the velocity divided by the length of the pendulum.

2. How does the length of the pendulum affect the magnitude of acceleration?

The length of the pendulum has a direct effect on the magnitude of acceleration. As the length of the pendulum increases, the magnitude of acceleration decreases. This is because a longer pendulum has a slower velocity, resulting in a smaller magnitude of acceleration.

3. What is the relationship between the magnitude of acceleration and the gravitational force?

The magnitude of acceleration is directly proportional to the gravitational force. This means that as the gravitational force increases, the magnitude of acceleration also increases. This is because a stronger gravitational force causes the pendulum to move faster, resulting in a larger magnitude of acceleration.

4. Can the magnitude of acceleration change in a pendulum equilibrium?

In a simple pendulum, the magnitude of acceleration remains constant in a state of equilibrium. However, in a compound pendulum or a pendulum with a non-uniform mass distribution, the magnitude of acceleration can change as the pendulum swings back and forth.

5. How can the magnitude of acceleration be calculated for a pendulum equilibrium?

The magnitude of acceleration can be calculated using the formula a = (v^2)/L, where a is acceleration, v is velocity, and L is the length of the pendulum. This formula applies to simple pendulums and compound pendulums with small amplitudes. For more complex pendulums, other equations may need to be used.

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