G-FORCE PROJECT

When different forces are applied to an object, "G-force" is a term used to describe the resulting acceleration, and is in relation to acceleration due to gravity (g). Thus a G-force equivalent to twice the force of gravity is \(2 \mathrm{~g}\) (" 2 gees").

Astronauts have developed their own terminology, based on sensations. Forward acceleration is often referred to as "eyeballs-in", where the G-force pushes the body backwards, while backward acceleration is referred to as "eyeballs-out". Similarly, vertical acceleration upwards is referred to as "blood towards feet".

In general, humans have a greater tolerance to forward acceleration than backward acceleration, since blood vessels in the retina appear more sensitive in the latter direction. Early experiments showed that untrained humans were able to tolerate \(17 \mathrm{~g}\) eyeballs-in (compared to \(12 \mathrm{~g}\) eyeballs-out) for several minutes without loss of consciousness or apparent long-term harm. The human body is also considerably better at surviving G-forces that are horizontal, that is, perpendicular to the spine.

Amusement park rides such as roller coasters subject humans to a variety of forces in different directions. These rides typically do not expose humans to much more than about \(3 \mathrm{~g}\) of horizontal force for approximately three seconds. There are exceptions which reach a maximum of \(4.5 \mathrm{~g}\) for up to 1.3 seconds.

The task

The following table illustrates the tolerance of human beings to horizontal G-force. The notation "+Gx" represents a positive acceleration in the horizontal direction i.e. eyeballs-in, so that a force of \(+\mathrm{Gx}\) of 20 means a forward acceleration of 20 (which humans can tolerate for $0.1$ minutes).

Define appropriate variables and parameters, and identify any constraints for the data.

Using technology plot the data points on a graph. Comment on any apparent trends shown in the graph.

What type of function models the behaviour of the graph? Explain why you chose this function. Create an equation (a model) that fits the graph.

On a new set of axes, draw your model function and the original data points. Comment on any differences. Revise your model if necessary. Discuss the implications of your model in terms of G-forces acting on a human being.

Use technology to find another function that models the data. On a new set of axes, draw your model function and the function you found using technology. Comment on any differences.

The table below illustrates the tolerance of human beings to vertical G-forces. The notation " \(+\mathrm{Gz}\) " represents a positive acceleration in the vertical direction i.e. blood towards feet.

How well does your first model fit this new data?

What changes, if any, need to be made to your model to fit this new data?

Discuss any limitations to your model and the implications of your model in terms of G-forces acting on a human being.

Price: $16.56

Solution: The downloadable solution consists of 9 pages, 756 words and 6 charts.
Deliverable: Word Document