How Does Mathematics Explain the Mechanism of a Cartesian Diver?

  • Thread starter Thread starter crazykartman69
  • Start date Start date
  • Tags Tags
    Cartesian Works
AI Thread Summary
The Cartesian diver operates based on the principles of pressure and volume as described by the equation P1*V1=P2*V2, reflecting the behavior of gases in a closed system. When pressure is applied to the bottle, it compresses the air inside the diver, causing the volume of air to decrease and the density of the diver to increase. As the density surpasses that of water, the diver sinks. The discussion also raises questions about the relative air pressure inside the container compared to the external environment before pressure is applied. Understanding these mathematical relationships is key to explaining the mechanism of a Cartesian diver.
crazykartman69
Messages
1
Reaction score
0
i would like to know how a cartesian diver works using mathematics. I have found how the diver works using words and explanation but not using equations and math. Please HELP!
 
Physics news on Phys.org
P1*V1=P2*V2 Since you basically have a closed system (the diver plus the water bottle) by applying pressure on the bottle, you are effectively transferring this pressure to the cartesian diver. This is because water is pretty much uncompressible. So, because the pressure is increased, the volume of air must decrease. Because we have a closed system, the water goes into the void created by the compressed air, the density increases until it is greater than that of water and it sinks.
 
Hey I am new here and i also need help on the Cartesian Diver. I was just wondering if The air pressure is the same, less than, much less than, greater or much greater than the air pressure outside of the bottle or container before pressure is applied to the container.
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
View full post »

Similar threads

Why do some heats of matches go down first in a Cartesian diver experiment?
Replies
1
Views
2K
B Cartesian Space vs. Euclidean Space
Replies
10
Views
2K
Physics of a diver used in trolling?
Replies
1
Views
3K
Why does the Cartesian diver sink when the bottle is turned upside down?
Replies
1
Views
4K
The definition of generalised momentum
Replies
43
Views
4K
I Electric guitar sustain calculation
Replies
6
Views
1K
MHB How do I understand notational mathematics?
Replies
3
Views
848
Freefall problem of a diver jumping horizontally upward
Replies
7
Views
3K
How does the rotation of a diver in the air conserve angular momentum?
Replies
7
Views
2K
The pendulum using Lagrange in cartisian
Replies
2
Views
854

Hot Threads

Recent Insights

Back
Top