(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A light baloon filled wiht helium and with a density of 0.180kg/m^3 is tied to a light string of lenght L= 3.00m. The string is tied to the ground, forming an "inverted" simple pendulum. The balloon is displaced slightly from it's equillibrium position, as shown in picture.

a) show that the balloon executes simple harmonic motion when it is released, i.e., show that the restoring force is a Hooke's law force.

b) What is the period of the motion?

Ignore energy lost due to air friction and take the density of air to be 1.29kg/m^3

http://img212.imageshack.us/img212/9724/58435914sp1.th.jpg [Broken]

2. Relevant equations????

3. The attempt at a solution

a) show that the balloon executes simple harmonic motion when it is released, i.e., show that the restoring force is a Hooke's law force.

not sure how to prove this and how it should look if I do prove it when I do.

in the begining position a):

balloon has:

buoyant force: up

gravity: down

tension: down

position b:

balloon

buoyant force: up

gravity: down?

tension: at an angle

forces on balloon

[tex]\Sum F= B-mg -T= 0 [/tex]

[tex]\Sum F'= B-mg- Tsin \theta [/tex]

I realy don't know... do I combine them??

b) period of the motion

don't know how to find this as well...

please help me on this.

Thank you

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# Homework Help: Helium balloon and simple harmonic motion

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