This app is used to demonstrate how a spherical object with a finite volume immersed in a fluid experiences an upthrust due to the differences in pressure around it.
Given that the centre of mass remains in the same position within the fluid, as the radius increases, the pressure due to the fluid above the object decreases while the pressure below increases. This is because hydrostatic pressure at a point is proportional to the height of the fluid above it.
It can also be used to show that when the volume becomes infinitesimal, the pressure acting in all directions is equal.
The following codes can be used to embed this into SLS.
This Geogebra app allows students to explore how the position of the centre of gravity as well as the width of its base affect the stability of an object.
A siphon operates through the combined effects of gravity and air pressure, which work together to move liquid from a higher elevation to a lower one. Gravity is the primary force driving the flow, as it pulls the liquid from the higher container down through the siphon tube to the lower container. The liquid’s potential energy, due to its elevated position, is converted into kinetic energy as it flows downward.
Air pressure plays a crucial supporting role by maintaining the continuous flow of liquid. Atmospheric pressure on the liquid’s surface in the higher container pushes the liquid into the siphon tube. This pressure counteracts gravity’s pull that might otherwise cause the liquid to fall back into the higher container. As the liquid moves downwards, it creates a partial vacuum in the upper part of the tube, allowing atmospheric pressure to push more liquid into the tube, sustaining the flow.
Thus, a siphon can continue to operate as long as the outlet is lower than the liquid surface in the source container, the tube remains filled with liquid, and atmospheric pressure supports the flow.
This demonstration can be modified for use as a magic trick.
Materials:
Glass of water
Piece of cardboard that is larger than the mouth of the glass.
Procedure:
Fill the glass up with water.
Place the piece of cardboard over the mouth of the glass.
Holding the cardboard against the mouth of the glass, invert the glass.
Release the hand slowly.
Explanation
Water can remain in an inverted glass with the piece of cardboard underneath because atmospheric pressure is acting upward on the cardboard, holding it up together with the water. There is little air pressure within the g;ass, so the downward force acting on the cardboard is mainly the weight of the water, which is to the order of several newtons whereas atmospheric pressure exert an upward force of several thousand newtons.
Modification:
Drill a small hole in a plastic cup, near the base.
Seal the hole with your thumb and fill the cup with water.
Place the cardboard over the mouth of the cup.
Invert the cup together with the cardboard, while keeping your thumb over the hole.
Using a magic word as the cue, shift your thumb slightly to allow a little air into the cup. This will cause the cardboard and water to fall. As the air pressure within the cup is equal to that of the atmosphere.
This simple demonstration can be done anywhere at home using the following items:
an empty glass
a toothpick
two forks
The video below demonstrates how to do it. When the forks are balanced on the mouth of the glass with the toothpick, the centre of gravity of the forks-and-toothpick system will adjust itself so that it lies vertically below the pivoting point. This is possible because the forks form a V-shape within which the centre of gravity can exist.
Ever wondered how a submarine sinks and floats? The demonstration here can be used to explain the changes in forces involved and is going to impress most people who see it for the first time. It consists of a floating object inside a sealed plastic bottle that sinks when the bottle is given a tight squeeze and floats again when the squeeze is released.
I have seen the Cartesian diver being made with something else, such as a packet of ketchup or a dropper. The method given below works better than those and uses things that are easily available around the house.
Materials
A plastic water-bottle
A pen cap
Some modelling clay
Water
Procedure
The first step is to attach some modelling clay on the tail of the pen cap to serve as weight so that when placed into water, the pen cap floats upright. There has to be just enough weight added so that the pen cap will “just float”. That is, if any more is added, the cap will sink. It takes some time to find the balance and the best way to do so is to test it in a basin of water.
Once the correct weight is attached to the pen cap, place it upright into the filled water bottle and close the cap.
Test it out by giving the bottle a tight squeeze. (If it remains afloat even when you have given it the tightest squeeze, take the pen cap out and add more weight.
If it sinks straightaway, remove some weight. This should not be necessary if we have already carried ou the t test in the basin.)
Physics Principles Explained
There are two ways to explain this demonstration, one for those who cannot be bothered with equations, and the other for those who are keen on delving deeper.
Using the simple idea of density, we can explain that when the bottle is squeezed, some of the water enters the pen cap and compresses the air trapped within. Hence, the collective density of the submerged pen cap, together with its air and water content, increases. (Note that we are not referring to the density of the pen cap alone, which is a constant.) When this density exceeds that of the water around it, the pen cap sinks. The action is reversed when the squeeze is released.
Some would prefer an alternative explanation. This invokes the idea of forces acting on the pen cap, namely, upthrust and weight. Archimedes’ principle, otherwise known as the law of buoyancy, states that the any object that is partially or fully submerged in a fluid (liquid or gas) experiences an upward force known as the upthrust that is equal in magnitude to the weight of the fluid which is displaced. In mathematical terms,
$$U=\rho Vg$$
where $\rho$ is the density of the fluid, V is the volume of the fluid that is displaced and g is the acceleration of free-fall.
This force opposes the weight of the object and the result determines the direction that the object will move.
For the case of the Carteesian diver, upthrust is varied by changing the volume of fluid, V, that is displaced by the air within the pen cap. When the bottle is squeezed, part of the original volume of air is now occupied by the water which enters due to a higher pressure. This means that the volume of fluid displaced decreases, and as a result, upthrust decreases.
