I think most of us are quite aware of Archimedes principle, but is there a reason to why it occurs? Is it just an observed property? Why is the upthrust equal to the weight of the liquid?
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Yesterday my friends and I were solving this easy-looking question:  A metal cube is placed in an empty vessel. When water is filled in the vessel  so that the cube is completely immersed in the water, the force on the bottom of the vessel in contact with the cube: (A) Will Increase (B) Will Decrease (C) Will remain the same (D) Will become zero  At first we thought the answer to be (B) considering the buoyant force acting opposite to the weight of the cube. But then, a question popped up in my mind: &quot;What causes this buoyant force even if no fluid was actually displaced?&quot; So I referred to the Archimedes' Statement:  Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. — Archimedes of Syracuse  But according to the question, no such fluid was displaced by the block ! So, here are my questions:  What is the basic reason behind buoyancy? Is it the pressure difference in fluids or the 'liquid-displaced' theory?  What must be the answer to the question (That I was solving) ?  Considering the case that you may say- &quot;The reason behind buoyancy is the pressure difference in the fluids&quot;; Will there be no buoyant force applied to the iron cube as there is no fluid layer present below the cube i.e. no pressure difference?   (Considering the iron cube is VERY dense and thus not allowing any fluid layer to push its way below it)  Or you might add another statement to the above question that-&quot;Yes, buoyant force is applied as there is always a fluid layer present below it...&quot; .Please do explain yourself.  If your answer is according to the Principle given by Archimedes of Syracuse , will there be no buoyant force on the cube as the cube didn't actually displace any fluid? Just like the case where you may consider it to be a part of the vessel itself.
29182
I have been wondering why a fluid in a rotating container has a parabola shape? Is it possible to prove this mathematically?
114778
Microscopically, the pressure exerted by a fluid on a surface in contact with it is caused by collisions of molecules of fluid with the surface. As a result of a collision, the component of a molecule's momentum perpendicular to the surface is reversed. The surface must exert an impulsive force on the molecule, and by Newton's Third Law the molecule exerts an equal force perpendicular to the surface. The net result of reaction force exerted by many molecules on the surface gives rise to the pressure on the surface.   The above is an extract from Physics by Resnick, Halliday &amp; Krane.  I've a few questions, conceptual in nature, which stemmed from the above paragraph -   All that is mentioned is that the component of molecule's momentum perpendicular to surface is reversed; nothing is mentioned about its magnitude. If, they wish to tell us that the collision is elastic (as in the case of kinetic theory of gases), why is this a valid assumption? Maybe, the right question to ask is, to what extent is it a valid assumption?  According to the aforementioned extract, pressure arises due to collisions between molecules and the surface. It is also a well known fact that pressure in a static fluid increases with depth. How can we explain that using this collision model? I'm confused because, the nature of collisions should be a property of the fluid, and should not vary with depth. Is this model - the one that talks about pressure arising due to collisions, sufficient to explain pressure related phenomena in all possible situations; or is it a mere approximation?
89168
We can show that pressure upward and downward in a fluid is caused by weight of fluid column or volume. A simple derivation of this:  $$\text{Pressure}=\frac{\text{Force}}{\text{Area}}=\frac{\text{Weight of the fluid column}}{\text{Area}}$$ $$~~~~~=\frac{\text{mg}}{\text{A}}=\frac{\rho Vg}{\text{A}}=\frac{\rho g\times Ah}{\text{A}}=\rho g h$$  I am able to show that pressure in a fluid at a height is $\rho gh$ upwards and downwards, but how can I show that it acts sideways too?  I found a pretty reasonable answer . So is this the correct reason?     Fluids are made of a large number of very small particles, much too   small to see. These particles are in constant, rapid motion. They bump   into one another. They bump into the walls of any container that holds   them. They bump into objects in the fluid.      As the particles of a fluid bump into an object in the fluid, they   apply forces to the object. The forces, acting over the object’s surface,   exert pressure on the object. When the pressure in a fluid increases, the   particles bump together more frequently. This increases the pressure   on objects in the fluid.      The pressure a fluid exerts on an object in the fluid is applied in   all directions. That is because the particles that make up the fluid can   move in any direction. These particles exert forces as they bump into   objects in the fluid.
6608
Let's say a 10N cube (in air, on Earth) rests flat on a scale at the bottom of a tank of water, and the scale reads 8N, so there is 2N of buoyant force on the cube.  How does the buoyant force manifest itself on the cube?  I assume the force is normal to the surface of the scale, but if there isn't any water under the cube, how does the water push up on the cube?
13956
I'm studying for my upcoming physics course and ran across this concept - I'd love an explanation.
99080
Can someone explain why a longitude wave can pass through the liquid, but a transverse wave can't. And can someone recommend some good animation of these processes.
56182
Can somebody explain to me graphically or intuitively why this is true? Because if we think in terms of the base of the triangle formed inside a unit circle it seems like it should not be negative.
104570
In most of the mechanics textbooks , the  is stated without any justification or an experiment to confirm this law. Also after introducing this law forces are also decomposed without any justification. Please suggest any links or books related to this. Any help will be appreciated. Thanks in advance.
45913
I am currently wondering about the famous .  Where does it come from mathematically that when you point with your thumb in the direction of the current, your curved fingers will point in the direction of the $B$-field? In other words, which mathematical operation does it come from? Probably it has to do with some vector product or Stokes theorem application, but I am not quite sure about it.
103442
What, specifically, causes newton's third law?  For instance, if I push on a wall, why is it that I experience a force in the opposite direction?    I seem to vaguely understand that is has something to do with electronic repulsion or molecular compression (maybe that's completely wrong, I don't know).  As a related question, what would happen if two objects that were /infinitely/ immovable (at the molecular level, it cannot be broken or compressed) collided with each-other?
79861
In accelerated fluids, fluid in a container can orient itself in a direction due to acceleration. In that case, pressure at different heights (at the surface) is same (atm). Then at the same height, pressure is different. How does this pressure increase along the horizontal?
17836
Special mention to the  that kicked this off:  Anyway, the host points out that a tunnel that connects a pair of points on the earth's surface can be thought of as a gravity train - where the force of gravity along the tunnel allows an object to fall through it and emerge on the other side. Any force perpendicular to the tunnel (in case the tunnel doesn't pass through the center of the earth) is ignored.   I worked it out and the equation is $a = -\frac{4}{3}\pi\rho G d$, where $d$ is the distance from the center of the tunnel and $\rho$ is the density of the earth.   Clearly, it is simple harmonic and therefore the period is constant and has no dependence on which two points were used to make the tunnel.   Does anyone have an intuition for why this should be the case? I imagine some Gauss' law type of argument should work here, but I cannot see it.  EDIT: More to the point, why even when the tunnel does not pass through the center, one obtains the same period. Is there any deeper explanation as to why this should be the case?
120278
Why is the d'Alembert's Principle  $$\sum_{i} (  {F}_{i} - m_i \bf{a}_i )\cdot \delta \bf r_i = 0$$  stated in terms of "virtual" displacements instead of actual displacements? Why is it so necessary to "freeze" time in displacements? Also, what would $\sum_{i} (  {F}_{i} - m_i \bf{a}_i )\cdot d \bf r_i$ correspond to if anything at all? In other words, what will be the value of the expression with real displacements instead of virtual ones?
62482
The hydrostatic paradox, states that the      height of the water in any container is independent of the shape of   the container.     This does make sense since it is only the height of the fluid relative to ground which determines the pressure, and it is the pressure equilibrium that decides the shape of the fluid. But then consider the (B) container in the figure below.     The pressure at a particular depth say, $h$ is same as in the case of the cylindrical container. But in the cylindrical case (A), any element of fluid is in equilibrium because the difference in pressure of the fluid element above it and that below it exactly balances the weight of the element. Extending this argument to (B), for any element at the edge, the pressure of the fluid above is the same as in the case of the cylindrical container, but below it is the surface of the container. This container, is in equilibrium with the atmospheric pressure outside, and therefore, would be exerting pressure equal to the atmospheric pressure onto the fluid within, which would not be enough to maintain the equilibrium of the fluid element. How then can the equilibrium of the fluid element at the edge be explained?
75408
Why is the  formulated in terms of virtual displacements rather than real displacements in time?  EDIT In other words, which step of the derivation of D'Alembert's principle (or Largrange's equation) will not work if one uses real displacements and why?
70325
When there is a film of water in between an object and the tabletop it rests on, it is difficult to pull the object directly upward. However, when you slide the object, it comes off easily. What is the physics behind this?