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65

It travels forwards instead of backwards in an accelerating car for the same reason that a helium balloon travels upwards instead of downwards under the influence of gravity. Why is that? In an accelerating car, for all intents and purposes the acceleration can be considered a change in the amount and direction of gravity, from pointing straight down to ...


52

The balls are entering the water well below the surface. The pressure there is much higher than at the surface. The work needed to push the balls into the water at this depth cancels the work gained when they float back up. We can ignore the gravitational force on the balls since gravity pulls down as much as up as you traverse the loop. Mathematically, ...


44

When your car accelerates forward, the air inside moves back relative to the car. This creates a slightly high pressure in the rear of the vehicle and a low pressure up front. Since helium is lighter than air, it moves away from the region of high pressure. A similar balloon filled with $CO_2$ would move back, since it is heavier than the surrounding air


39

The balloon has a very small mass and friction is large (large surface area), so the oscillation is very damped.


38

Here is a free body diagram of the balls: … and one of the water volume: The four balance equations are $$ \begin{align} B_1 - T_1 - m_1 g & =0 \\ B_2 + T_2 - m_2 g & = 0 \\ F_1 + T_1 - B_1 - M g & = 0 \\ F_2 - B_2 - M g & = 0 \end{align} $$ where $\color{magenta}{B_1}$,$\color{magenta}{B_2}$ are the buoyancy forces, ...


35

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 ...


34

Good question. Assume we have one cube of ice in a glass of water. The ice displaces some of that water, raising the height of the water by an amount we will call $h$. Archimedes' principle states that the weight of water displaced will equal the upward buoyancy force provided by that water. In this case, $$\text{Weight of water displaced} = ...


33

Here is an explanation that needs no explicit equations. Consider the following diagram, in which part1 and part2 represent the ice. The displaced water volume equals part2 volume and has as much mass as (part1+part2) Now look at what happens when both part1 and part2 melt: their mass does not change, it is (part1+part2) it becomes water. And we just ...


22

The weight on the left bowl would be the weight of the water plus vase plus ping-pong ball (plus thread, ignored). The weight on the right bowl would be the weight of the water plus vase plus the buoyancy of the steel ball (plus the buoyancy of the submerged thread, ignored). That buoyancy is the weight of an equivalent volume of water. Since the ping-pong ...


22

Tied balloons do behave like a pendulum, you only need really massive ones: You can see it live in a video. Hot air balloons have such a big amount of..erm...hot air that during the start you can expect oscillations because while the surface area is big, the mass inside is so big that the dampening is low enough. They are not exactly like a pendulum ...


21

Fun question. Here's my "me-too" answer. Suppose the car has just emerged from a river, so there's a lot of water in it, and the balloon is tied to the floor. Then you drive away. The air in the car is just like a bunch of water :)


19

A Thought Experiment We can arrive at an intuitive explanation without any special knowledge of physics. The strategy is to re-create the setup as closely as possible while keeping the two sides in balance. Imagine that you start with two identical beakers, filled with the same amount of water, no balls. Placed on the scale, they balance. On the left, ...


18

Average human body volume = 0.0664 $m^3$ (seems low to me, but that's according to Wolfram Alpha: http://www.wolframalpha.com/input/?i=volume+human+body). Density of air depends on temperature and pressure, but is about 1.2 or 1.3 $kg/m^3$. That means we displace, on average, about 80 g of air, giving us a buoyancy of about 0.8 N (about 1/6 lb). The ...


13

It acts precisely like water in a cup. Or, more specifically, like the air in the cup. Since the helium is a much lower density than the nitrogen and other gasses in your car, it can be visualized like an air bubble in a bottle. The container for the helium(the balloon) has negligible mass. When you accelerate forward, the water in a bottle will move ...


13

The energy needed to submerge a ball is equal to the energy gain from other ball to emerge from the water on the other side, so any waste on friction drives the process impossible.


12

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. ...


11

Buoyancy is dependent on the density difference between the object and the surrounding fluid. Though the pressure goes up in the ocean with increasing depth, the density remains more or less constant because water is almost incompressible. The pressure in water increases by about $100\,{\rm kPa}$ for every $10\,{\rm m}$ of depth, and the Marianas trench is ...


11

As the comments above indicate, factors like density, pressure and temperature are important for a Jupiter submariner. Of course nobody yet has the exact details of Jupiter's interior structure, but there's a diagram in this LASP page[WebCite archived version] that indicates the following: ...


10

This diagram is my attempt to show the situation first when the rock is in the boat and secondly when you've chucked the rock over the side. The mass of the boat of $M$ and the mass of the rock is $m$. The density of water is $\rho_w$ and the density of the rock is $\rho_r$. In the first case Archimedes' principle tells us that the volume of water ...


10

What is probably being referred to here indirectly is the fact that air with moisture in it is less dense that dry air. The question becomes, is the buoyancy force of an empty egg with the optimal moisture content of air sufficient to overcome it's weight? Searching around I see that water vapor has a density of 0.804g/Land dry air has a density of 1.27 ...


8

The problem is in the seal. The amount of work to move the seal against the water pressure is the same amount of energy that is gained by the balls when they are pushed up by the water. Even if we remove the seal and we imagine a magic "one-way pass-through" wall, the ball would still need to displace the same volume of water as itself in order to get into ...


8

The reason behind buoyancy is the pressure difference in fluids. More specifically, the difference in hydrostatic pressure on different levels, since the hydrostatic pressure of water increases with depth ($p=\rho gh$ wher $h$ is the distance below the surface). The part of the body which is subject to higher hydrostatic pressure will be pushed more upwards ...


7

You will displace air equal to your volume. If your volume is $v$,you will displace air of volume $v$, If the density of air is $d$, then the mass of the air displaced will be equal to the product of volume and density. and thus force on you according to Archimedes ' principle =$vdg$, 'g' is the acceleration due to gravity. Archimedes' principle indicates ...


7

The chest region provides the least dense region in the body since it traps a large airspace. And for either scenario (back floating or vertical) the chest is submerged. So the only difference you need to consider is that in the vertical position, the head (at least above the nostrils) needs to be above the water line so that the person can breathe. But in ...


7

Expanding on @SebastianRiese's comment, the buoyant force already takes care of the downward force caused by the upper liquids. Lets consider the problem from a physical perspective. There is the downward force from gravitation, the downward force from the liquid above, and the upward force from the liquid above. In the diagram, the gravitational ...


7

Balloons are buoyant because the air pushes on them. The air doesn't know what's in the balloon, though. It pushes on everything the same, so the buoyant force is the same on all balloons of the same size. If the "balloon" is just a lump of air with an imaginary boundary, then the lump won't go anywhere because the air isn't moving on average. So the ...


7

The Costa Concordia wasn't sunken, it was aground. Which meant that part of it was still above the water. The ping pong solution can only be used if the ship is completely underwater. Otherwise, it will have an opposite effect. The buoyant force (force by which a fluid pushes up on a body, thus keeping it afloat), is proportional to the mass of the fluid ...


7

Trivially the density of the water increases identically to the object and so bouyancy is maintained...


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, ...



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