Centridipity problem

Question

Two objects are fixed inside a moving car by strings so that they can both move freely.
The car's windows are closed.

• A wind chime is suspended from the roof.
• A helium balloon is tethered to the floor.

When the car goes round a left hand bend:

1. Which way does the wind chime move?

2. Which way does the helium balloon move?

3. Does the wind chime make any sound?

4. Does the helium balloon pop?

Please say why they will be so? Feel free to conduct the experiment.

_{An old chestnut inspired by Initiation Puzzle.}

Answer 1

In the frame of the car, there are two forces: gravity pointing down, and centrifugal pointing to the right. In effect, we can analyze physics in the frame of the car by pretending like there is an effective gravitational field pointing down and to the right. Hence:

The wind chime hangs in the direction of the effective field, so it moves to the right. The helium balloon floats opposite the direction of the effective field (since it's lighter than the surrounding air molecules), so it moves to the left.

If the car goes into the bend quasistatically, and once in the bend, it keeps a constant speed and radius of curvature, then:

The wind chime and balloon will be in their respective equilibrium positions. Assuming a quasistatic transition to the new equilibrium position, the wind chime will not make noise (if the transition is rough, then the wind chime will make noise until its oscillation damps to the new equilibrium). The helium balloon will not pop either.