Balloon in a car - Solution

Because of buoyancy, the helium balloon on the string will want to move in the direction opposite the effective gravitational field existing in the car.

Thus, when the car turns the corner, the balloon will deflect towards the inside of the turn.

A so-called ‘Nobody‘ has sent in the following on this:

‘The answer you give is incorrect - the balloon will lean opposite the curve, but this has nothing to do with “gravitational fields,” which are always, for the purpose of this sort of problem, directed toward the center of the Earth. The balloon will move because it has mass, and therefore inertia, and will want to resist the pull of the curve.’

I was waiting for a reaction on this one. I completely agreed with Steven White who has sent in the following:

‘Nobody’ is correct about inertia being the key to the problem. He is incorrect about the direction the balloon will go. The key is that air is heavier than the helium, so air is what must be considered. The inertia of the air will move it towards the outside of the car. The pressure is therefore higher in the car at the outside of the curve than at the inside. The balloon, filled with the lighter gas, will move to the area of lower pressure– the inside of the curve.

Untill…

Ian Ellis had sent in the following:

�As a physics teacher, my slant on the answer is this:

Remember the movie 2001? A circular, rotating space station housed a
walkway that appeared to let a person walk with feet to the rim and head
to the centre. That person will experience a comforting contact with the
“ground” with a force similar in feel to gravity (he could drop an apple
to his feet.) How fast the apple would fall would depend on the
measurement of the radius of the walkway and the rotational speed of the
station. These could be designed to simulate the same “feel” as gravity
on earth.

However, the force producing this contact with the “ground” is a
centripetal force related to the circular motion, not the gravitational
attraction between the mass of the person and the hull. “Centripetal” is
a general term for “centre-seeking,” and the actual nature of the force
will depend on the situation. In this case, it is the reaction force of
the hull pressing on the person’s feet.

Bring in Newton’s Laws of Motion. Law (I). An object in motion will
continue to move in a straight line at constant speed unless acted upon
by a net external force. This is the Law of Inertia; inertia is the
reluctance of a body to change its state of motion. A similar statement
applies for rotational motion and a torque. (By the way, Law II covers
what happens when there IS a net force, and ties in with acceleration.
But let’s skip that.) (III) is the often cited “action-reaction” law,
best understood as “when one object pushes on a second object, then the
second object pushes back on the first with a force that is equal in
size and opposite in direction.

Now, if you tend to move in a straight line, while the hull is rotating
to a position in front of you, it is going to be constantly nudging you
towards the centre. That nudge is a force due to contact, and is the
aforementioned “centripetal” force pushing you towards the centre. Which
follows there is a reaction force where you are pushing back against the
hull. That is known as the “centrifugal” or centre-fleeing force.

What does all this mean? Well, to steer a car around a bend is to
produce the above effects, but for only a part a full circle of motion.
And a passenger with closed eyes feels “thrown” towards the outside
door. Change your perspective to a line from the centre of the curve
outwards, and the passenger is “falling” towards the door. (To repeat,
it is in fact due to the passenger’s inertia continuing in straight-line
motion while the car door moves into the curve and passes in front.)

Back to “gravity.” In daily life, “gravity” is superficially regarded as
that comforting clinging to the surface of the earth as it spins,
instead of departing in straight line motion into space (like a stone
rotated on a string over your head when the string breaks.) That
goodness for the gravitational force of attraction between two masses -
you and the earth - which is the centripetal (center-seeking) force
here. Meanwhile, the layman pays no attention to this attraction. Which
is just as well, because even scientists cannot yet explain the basis of
the phenomenon of the mass-to-mass attraction.

By now, you should see the “effective” gravity as experienced by the
person in the car as he “falls” toward the outside door is a direct
analogy. Good enough for the layman. And the puzzle’s answer did say
“effective” - read “pseudo” - gravity. Layman’s gravity is the person
describing his experience from an internal perspective.

OK. Gravity and the random movement of air molecules produces an
atmosphere on the earth that is dense in the direction of “falling.”
Meanwhile, in the car rounding a curve, the air will be densest in the
direction of “fall” in a good analogy.

A balloon, even within its own dimensions, in either case will
experience a greater density of air on the side of falling, and a lesser
density on the opposite side. You see the effect as buoyancy when the
pressure difference produces a force greater than the balloon’s weight.
Since the pressure difference for its size is small, only a very
lightweight balloon will be buoyant.

So, the answer to the puzzle is valid from either a layman’s vision of
“effective” gravity, OR from an external view of the aspect of inertia.

Incidentally, you experience the same effect if you put two birthday
candles opposite and at the rim of a rotating record turntable. The
flames will point towards the center. Here, the flame “rises” as its
gases become hotter and less dense by expansion. The ball of warm gas
behaves just like a helium balloon without its rubber envelope.

How about that!�

Well, how about that…, I don�t think anyone can beat you, Ian, giving such a detailed and argumented explanation !

Okay, Maty Yeminy had a remark on this. In the end, I also like a simple explanation for an seemingly difficult problem. That’s what the Mind Breakers is all about: Only the best puzzles and riddles ! If you want quantity, please go to the “Rec.Puzzles Archives” on the main page or other puzzle sites.

‘The previous answer you got from “nobody” had it all. The last answer
from Ian did not add anything. Just a very long explanation of nothing
more than what was already given. All the rest is completely
superfluous.

What I say here is also no addition to what was already given by
“nobody” but it surely encompasses all that Ian has given.

It is this simple.

The reason a bowling ball will move to the outside of the curve is that
it has inertia. Air has inertia too. However the bowling ball’s inertia
is greater and therefore it will tell the air that wants to move to the
outside of the curve: No way, you are going to the inside. I have more
inertia, I will displace you and send you to the inside because I want
to go outside.

Now, this is exactly what the air says to the helium baloon because it
has more inertia.

That’s it. Whoever has more inertia wins, and the other is displaced to
the inside of the curve.

The credit should go to “nobody.”‘

Tania Ake has some more creative thoughts on the motion of the balloon !

‘For the balloon question: I’m not sure if the physics professor covered
this, but your other respondents failed to take into effect that, as the car
is turning, it is also decelerating. Therefore, the balloon would not only
tilt to the outside of the car, but, more correctly, toward the driver
(assuming we are in America).’