Non inertal frame

1. Jan 19, 2005

matpo39

I am a little stuck on this problem :

Be sure you understand why a pendulum in equilibrium hanging in a car that is accelerating foward tilts backward, and then consider the following: A helium balloon is anchoredby a massless string to the floor of a car that is accelerating foward with acceleration A. Explain why the balloon tends to tilt foward.

I think i was able to explain the pendulum tilting backward, because the acceleration is foward the inertial force is -mA which would act in the opposite direction of the acceleration causing the pendulum to tilt backwards.

Then for the balloon I think that it's tilting foward has to have something to do with the buoyant force and gravity, but im not sure how to relate the two and also wouldn't the inertal force still be acting in the opposite of the acceleration A, then why would it tilt foward?

thanks for the help

2. Jan 19, 2005

marlon

Well, here is the common explanation: the air surrounding the ballon is heavier then the helium inside the ballon. Indeed if the acceleration is forward then Newton's third law states that the balloon should move backwards. However this does NOT happen because it is the surrounding air (which is heavier) that will move backwards due to this law of action and reaction. Because the air moves backwards, a region with very little air arises (pressure is also lower there) and therefore the balloon will move towards that region with "less" air. beware that this happens very fast so generally there is not really "a region with less air". Basically it is always the most massive object that will move backwards with respect to lighter objects present because ma is bigger !!! The balloon is NOT pushed foreward but it is attracted forward because of the local pressure gradient

marlon

3. Jan 19, 2005

arildno

In a CLOSED car, it is perfectly reasonable that the air within the car has the same velocity as the car even if the car is accelerating.
There will be a transitory phase in which a sufficient pressure gradient is built up to generate the car's acceleration within the air (the back of the car will slam into to the adjacent air).
Once this has been done, there has been established the sufficient horizontal pressure gradient in the air; this will give rise to a forwards force on the balloon.
Equilibrium of moments with respect to the attachment point of the string (on the car floor), requires that (buouancy-minus balloon weight)-moment acts oppositely of the (horizontal pressure force)-moment, i.e, the balloon must tilt forwards (in the case of helium filling the balloon).