Simple Harmonic Motion of Inverted Simple Pendulum with a Helium Balloon

In summary, a light balloon filled with helium is tied to a light string and forms an inverted simple pendulum. If the balloon is displaced slightly from equilibrium, the motion is simple harmonic and the period can be determined using the density of air and helium, the length of the string, and the acceleration due to gravity. Neglecting the resistance of air, the acceleration of the balloon can be calculated and used to find the period using the simple pendulum formula.
  • #1
Touchme
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Homework Statement


A light balloon filled with helium of density 0.175 kg/m3 is tied to a light string of length L = 3.35 m. The string is tied to the ground, forming an "inverted" simple pendulum (Fig. P13.63a). If the balloon is displaced slightly from equilibrium, as in Figure P13.63b, show that the motion is simple harmonic (do this on paper. Your instructor may ask you to turn in this work), and determine the period of the motion. Take the density of air to be 1.29 kg/m3. (Hint: Use an analogy with the simple pendulum discussed in the text, and see Chapter 9.)



Homework Equations


Ft = [-(density of air - density of He)Vg)/L]s
T= 2pi*sq.root of L/g

The Attempt at a Solution


I tried to play around with the formulas, however, I was unsuccessful. I'm not sure if those formulas are relevant to the question. Any suggestion on how to start solving or any hints?
 

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  • #2
Hint: If the balloon were released, what would its acceleration be? I assume you are supposed to neglect the resistance of the air to the motion of the balloon. You can't have the balloon floating without the air, but you can neglect the resistance effect.
 
  • #3
The acceleration would be
a = ((d(air) - d(gas))V - m)g/(m + d(gas)V)
So...
I neglected mass but it says a light balloon...
a = (1.29-0.175)(9.8)V/(0.175V)
a=62.44 m/s

Hmmm... then I use the period formula and...
GOT IT!
thanks OlderDan =D
 

1. What is an inverted simple pendulum?

An inverted simple pendulum is a physical system that consists of a rigid body suspended from a pivot point and is free to swing back and forth under the influence of gravity. In this case, the pivot point is located above the center of mass of the body, causing it to move in an inverted or upside-down motion.

2. How does an inverted simple pendulum differ from a regular pendulum?

The main difference between an inverted simple pendulum and a regular pendulum is the location of the pivot point. In a regular pendulum, the pivot point is located at the bottom of the pendulum, while in an inverted simple pendulum, it is located at the top. This results in different motion patterns and behaviors for the two systems.

3. What factors affect the motion of an inverted simple pendulum?

The motion of an inverted simple pendulum is affected by several factors, including the length of the pendulum, the mass of the body, the angle at which it is released, and the strength of the gravitational force.

4. What is the significance of studying an inverted simple pendulum?

Studying an inverted simple pendulum can provide insights into the behavior of nonlinear systems and chaotic motion. It also has practical applications in fields such as robotics, where inverted pendulums are used to stabilize and control movements.

5. How can the motion of an inverted simple pendulum be controlled?

The motion of an inverted simple pendulum can be controlled through various methods, such as adjusting the length of the pendulum, changing the initial release angle, or implementing external forces to counteract the effects of gravity. Advanced control techniques, such as feedback control systems, can also be used to stabilize the motion of the pendulum.

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