Tag Info

Hot answers tagged

36

The buoyant force on a body immersed in a fluid is equal to the weight of the fluid it displaces. In other words, $$ F_B = \rho_{\text{fluid}} V_{\text{body}} ~g $$ The force of gravity on the body is equal to $$ F_g = m_{\rm body} ~g $$ The apparent weight of this body will therefore be equal to the sum of these two forces. $$ W_{\rm app} = \rho_{\rm ...


28

Just my two cents to complement the other answers. The mistake in your reasoning is that: the state above (where the top touches the bottom) is equivalent to having a box like A (just a box holding a vacuum). is incorrect, it rather equivalent to a box full of air (there is air in between the walls, regardeless of the vertical position of the top). In ...


20

Stress is a tensor1 because it describes things happening in two directions simultaneously. You can have an $x$-directed force pushing along an interface of constant $y$; this would be $\sigma_{xy}$. If we assemble all such combinations $\sigma_{ij}$, the collection of them is the stress tensor. Pressure is part of the stress tensor. The diagonal elements ...


13

For each surface on a unit cube (see below), the stress on that surface can point in each of the three directions. (source) Since it is not necessarily the case that $\sigma_{11}=\sigma_{31}=\sigma_{21}$ (all pointing the in the same $\mathbf{e}_1$ direction)--or any of the other $\sigma_{ij}$ combinations, we need to have 9 components describing it, ...


13

1) Technically while you push it down it will cause an increase in pressure (so the weight will change) but assuming the box has a hole and the air can equalise then the weight of your initial and end state will be the same. This is because the air is equalised within the box at all stages and at the end state the air that was in the box is now above it. ...


8

You might get an order of magnitude estimate as follows. We make the rough assumption that everything ends up in its vessel as a monoatomic ideal gas - actually it will be a plasma, with a thermal energy per mole of $\frac{3}{2}\,R\,T_{final}$, where $T_{final}$ is the thermodynamic temperature of the plasma. Neglecting heats of vaporisation (we assume ...


7

Let me highlight lhree points: 1) The mass of a box is the sum of the mass of the box structure, and the mass of the box contents; 2) The force of gravity downward on the box depends only on the mass; (and the local acceleration of gravity) 3) The buoyant force upward depends only on the density of the surrounding medium and the volume of the box. So, ...


7

Just consider the same situation in water. A box filled with water, immersed in water will have more weight on a weighing machine than an empty box (with vacuum or air)--which might even float depending on the mass and volume of the box. The only difference in this case is the density of the medium.


6

Here's a way to think about it that avoids assuming the bouyant force equation is correct. All you need to know is that air pressure increases with depth / decreases with height. First off, before we put anything at all on our scale, there's already a large force pushing down on the scale's plate. $$F_0 = P_0 A_\mathrm{plate}$$ This force gets cancelled ...


6

A box filled with helium would weigh less than a box filled with air, because helium is less dense than air. A rigid box containing a vacuum would weigh even less than the same box filled with helium, because it is even less dense.


4

The internal pressure in the top of the box full of air is lower than the internal pressure at the bottom - because of the weight of the column of air. You experience this when you go up in a plane (or even an elevator) and your ears "pop". Air has mass. The box with air weighs more.


4

The weight is less with vacuum inside the box. The forces on the box are the gravity acting on the mass of the box and its contents, and the buoyant force which is equal to the weight of the inner volume of the box when filled with air. Let's say the box is one cubic meter, then the air content weighs some 1200 grams depending on temperature and local ...


4

You are correct that as you get very close to the center of the earth, the value of $g$ can become arbitrarily low. If you could somehow create a space there, you could potentially float in it because you would not be pulled in any particular direction with respect to the earth. But while gravity is not strong there, it is strong in other places (like your ...


4

The key thing you're forgetting is that the atmosphere also has a vertical pressure gradient, much like any body of water. This means that, if you take your box with the lid pressed down, (*) (*) z=h +------------+ | | | | | ...


3

It is a gate valve, as seen here: Source: http://www.roymech.co.uk/Useful_Tables/Drawing/Flow_sheets.html


3

The downstream side of the nozzle is much more important to maintaining the efficiency of the nozzle by controlling expansion wave. It also influences the uniformity of the flow exiting the nozzle. Symmetry would be perfectly fine, but you'd end up making the converging section bigger than it needs to be. Here's a bit more about the design of the nozzle ...


3

When you push the lid of the air-filled box down you are doing two things: Reducing the volume of the box; and Reducing the mass of the box and its contents (as the air is squeezed out). The weight measured on the scale is: "weight of the box and contents" - "buoyancy due to surrounding air" The "buoyancy due to surrounding air" is the weight of a ...


2

The effect is real. The heat in the bowl causes the production of steam in the cavity between it and the table. Depending on the temperature, this can be a far more powerful effect than mere thermal expansion of the air. The liquid between the bowl edge and the table acts like a liquid seal for a reasonably smooth and planar table/bowl interface - liquid ...


2

The "far away" phrase indicates that the airfoil does not disturb the velocity flow. In the image below (source), you can see how the airfoil affects the flow near the airfoil itself. But "far" above and below the airfoil, the flow isn't affected. This is your $v_\infty$ and, as WolphramJonny points out in the comments, this is equal to your $v_{in}=30$ m/s. ...


2

First you must find the speed when the ball comes out of water, the same way you calculate the speed of free fall of an item in the air. $$m\vec{a}=\Sigma{\vec{F_i}}$$ where the forces are : friction, weight, Archimedes force. Then again in the air where the Archimedes force may be neglected. If the air friction is neglected, it's easier using the potential ...


1

In order to understand how gravity affects objects at different points within or on a sphere, see the following link: http://en.wikipedia.org/wiki/Shell_theorem This basically states that inside a sphere, the gravitational force of shells further away from the centre than you cancel each other out. Considering your initial question about pressure at the ...


1

Surface tension is plausible : it implies that, at the level of the hole, the pressure in water will be less than 1 atm. Thus the pressure isolines will look like this: Quantitatively, curvature $c$ will be of the order $1/(1 $mm$)$ because the hole looks about 1 mm size in your video, which with pure water would lead to a pressure difference drop of the ...


1

The various answers above are, essentially, different ways of describing the same things.. Boyancy explains the difference... However you could also simply note that the box with the pushed-down lid still 'contains' the air -- it's just 'outside' the lid. The weight remains the same. If you managed to add a force-field at the top of the box, and then ...


1

The physical principle that applies here is called the Archimedes' principle. Emilio Pisanty's and other answers explains well what is going on. This answer is solely to provide the name of the underlying theory. The Archimedes' principle states basically that for a submerged object (in your case the box once with air in it, once without) the apparent ...


1

The weight is the same if its on your desk. It is dependent on the medium the box is in. Weight is determined by gravity and gravity itself is simply the effect of a pull on denser vs less dense molecules. If the box is sitting in air - the air has no effect on its weight because in relation to the air the box sits in there is zero weight, the same as a ...


1

Perhaps you could use the expansion of the pressurized container to measure the internal pressure? Even a metal container will expand by a few microns if it pressurized - this expansion could be measured using lasers. Does that meet your definition of 'not altering'? Although I suppose even lasers would heat the container by a miniscule amount, which ...


1

When opening the bottle in space, all the air that was initially in it will flow out due to the pressure difference. The inside of the bottle will then become approximatelly vacuum, so when you open it on Earth air will flow in it again. (Unless it's not sturdy enough (for example a plastic bottle), in which case it will be compressed/crumpelt before you ...


1

It seems your question asks simply is the effect on the box the same with 1 bar differential pressure of either air or water. Yes, the effect would be the same for air and water. Both are fluids exerting uniform differential pressure of 1 bar.


1

The shear and tension stress on the material would be the same, because only the difference matters for that. So for testing strength of the structure the cases are equivalent. The material would still be under the total pressure though, so if the material itself can't withstand that pressure, it would degrade (it may change crystalline structure, compounds ...


1

Water has its highest density at 4 degrees C. Ice always floats on water surface, because its density is less than water. An object dropped in water will sink, accelerating under the force of its weight (Mg), against the upthrust, as well as the viscous drag resulting from the downward motion; which increases as the speed of the object increase. There will ...



Only top voted, non community-wiki answers of a minimum length are eligible