Aim

What I would like to do in this discussion is to find out an expression for the freefall velocity v of a hamster at any time t. This discussion is open to all forum members as it will encompass a range of different Physics and Mathematical levels, from KS3 Physics/Maths (ages 11-14) up to degree level engineering. To assist those doing KS3/GCSE/A-Level Physics and Maths, I strongly suggest we limit answers to 3 sig fig where appropriate (it is recommended you use more in calculations then round the final answer, as this increases the accuracy of your answer).

Key Points

We will need to work out a few variables on the way to our final expression, ones that immediately spring to mind are:

- Mass and weight of the average hamster
- Volume and cross-sectional sirface area of the average hamster
- Freefall acceleration of the hamster with simple air resistance (up to terminal velocity)
- Freefall acceleration of the hamster through any fluid (with any density and viscosity, up to terminal velocity)
- Freefall acceleration of the hamster including drag coefficient of the hamster (optional)
- Velocity of the hamster as a function of time (derived from the above acceleration expressions)

More may be added as we progress, these were just the first few I thought of.

Data Required

Obviously, we're going to need some raw data in order to start this off.

- Hamster data (mass, area, volume)
- Gravitational acceleration constants
- Fluid resistance constants (including viscosities)
- Example drag coefficients (optional)

Physics Involved

To start people off, we will consider the basic Physics of a hamster in freefall. The hamster will fall due to its weight - the gravitational attraction it experiences due to the pull of the Earth's mass on its mass. Put simply, F=ma and W=mg (we shall simplify g to be -9.81m/s^2 for this discussion), so it falls with an acceleration of -9.81m/s^2 downwards. I shall define the vertical displacement to be positive when moving upwards, so anything moving downwards has a negative velocity and displacement. Therefore, g is negative, and is -9.81m/s^2.

Ignoring the effects of air resistance, its velocity will increase by -9.81m/s^s as long as it is in freefall. We can find the velocity as a function of time, and assuming the hamster started at rest the velocity will be:

v(t) = u + at (u = 0m/s; a = -9.81m/s^2)

v(t) = -9.81 * t

After 1s, v is -9.81m/s. After 2s, v is -19.62m/s (-19.6m/s to 3SF).

Feel free to continue this as you see fit, the topics we (as a group) can work on are listed above so I encourage all budding Physicists/Mathematicians/Engineers to have a go if they think they can. There are a few experienced Physicists and engineers amongst us forum regs (I myself teach Physics from ages 11-18), and I'm sure we will all be happy to occasionally cast an eye over this thread and sort out any major mistakes that crop up and answer questions that appear.

Finally, have fun! This is meant to be a light-hearted group problem solving exercise, that places important scientific concepts in a readily accessible way - who doesn't dream of pets in freefall? And remember, Physicists always like to prove theoretical results in an experiment, so I suggest Safire locks her hamster up rather sharpish!

Pad.