# The Accelerating Balloon

## Table of contents

**Skills used in this module.** Able to extract information from a representation. Able to evaluate the consistency of different representations. Able to identify the assumptions a model relies upon.

This Modules explores a classic demonstration.

A He balloon on a string is in a plexiglass box which is accelerated to the right from rest. Contrary to expectations, the balloon moves towards the front of the box, in the direction of the acceleration.

Here is a YouTube video showing the same effect:

https://www.youtube.com/watch?v=0WqEXRGBZNc

## Some Background

As is discussed in many textbooks, the concepts of *mass*, *weight*, and *apparent weight *are related but different. The mass, in kg, is an intrinsic property of an object; its value is unique and always the same. The weight, in N, is the force exerted on an object by gravity; the weight of an object on the surface of the Earth is different than the weight of the same object on the surface of the Moon. In our everyday life we treat the words mass and weight as being the same thing, but in physics they are not the same.

But what about astronauts in the International Space Station in orbit around the Earth? They appear to be weightless, but there is a force of gravity due to the Earth that is acting on them and the whole Space Station causing it and the astronauts to move in a circular orbit around the Earth. So we say that the *apparent weight* of the astronauts is zero, although their weight is not zero.

## Activity 1

Explain why the balloon moved as it did.

As is typical in physics, there is more than one correct explanation for the behaviour of the balloon.

In considering your answer, you may wish to think about a centrifuge, which separates materials according to their density. A hand-driven centrifuge is shown to the right. Crucial is that the containers holding the samples can pivot, so when the centrifuge turns their bottoms swing outward away from the axis of rotation.

You may also wish to remember Archimedes’ principle: the magnitude of the buoyant force on an object in a fluid is equal to the weight of the displaced liquid. Here are some issues that you may wish to consider:

- Is Archimedes’ principle about the weight, which is the force exerted on the displaced fluid by gravity, or the apparent weight? The following questions explore this further.
- Would the buoyant force stay the same in an elevator that is accelerating upwards?
- What about the same object in the same fluid on a planet where the acceleration due to gravity was greater than 9.8 m/s
^{2}? What about if the object and fluid were in free fall? - If you were sitting on the plexiglass box while it was accelerating, in what direction would your apparent weight point?

Some of these issues and more are explored in Activity 4 of Mechanics Module 3.

## Activity 2

If the balloon and box are moving at constant velocity, so the string holding the balloon is vertical, and then the box starts slowing down, what will be the motion of the balloon relative to the box?

What about if the box is moving at constant speed, but is going around a curve to the right? What about if the curve is to the left?

This Guide was written by David M. Harrison, Dept of Physics, Univ. of Toronto, in May 2016.