Topple Bottle; inquiry based learning.
A simple investigative exercise using easily available resources, plastic water bottles, water, sand, piece of wood, protractor, ruler.
If a bottle is tilted it will topple when the centre of gravity (C of G) is displaced beyond the point where the bottle remains in contact with the ground.
Why is the C of G of a performance vehicle kept as low as possible?
How are tall vehicles tested for stability?
Research the possible reasons for the sinking of the Mary Rose.
The Cof G of an empty bottle is in the middle. If the container is filled with water, the Cof G of the water will be in the middle of the water and will have the effect of lowering the Cof G of the now partly filled container downwards from the middle of the container.
Assume initially that the container is empty, ask students to predict how the topple angle will change with h as a full bottle is gradually emptied.
This is far from trivial as the C of G will start in the middle, descend towards the bottom of the bottle as it is emptied, but then rise back towards the middle as the bottle approaches being completely empty.
The observant will notice that the C of G must also move away from the axis of the bottle as it is tilted because the surface remains horizontal.
Will this make things worse or better for a cornering tanker?
How is the situation changed for a grain tanker?
Real life situations arise for tankers, particularly when half full and the fuel sloshes in the tanks. For this reason tankers are equipped with baffles in the tanks to prevent sloshing.
BLOODHOUND SSC gets through a tonne of liquid hydrogen peroxide in about 20 seconds (not to mention nearly half a ton of jet fuel)! The C of G shifts during this process.
Why is this important? You will need to remember that BLOODHOUND SSC is a thrust driven vehicle. As the rocket is ignited, turning effects around the C of G will result in greater downward force on the front wheels and lifting of the rear wheels, quite the reverse of an ordinary friction driven vehicle (whose front wheels lift when the vehicle starts). These forces will change as the fuel tank is emptied.
How can the engineers control these changing vertical forces on the front and rear wheels? You may want to draw some diagrams, don't forget to use arrows to represent forces, and don't forget that length of arrow and direction are important.