How do you determine the volume of water passing through a weir? – R

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How do you determine the volume of water passing through a weir? – R

If the speed of the water were uniform as it passes through the opening, you could measure that speed and multiply it by the cross-section of the weir to obtain the volume of water passing through the weir each second. However, since the flow is faster near the center of the flow, it’s difficult to calculate the volume flowing each second. Your best bet is probably to divide the opening into a number of regions and then to measure the water’s velocity at the center of each region. Multiply each velocity by the cross-sectional area of that region and then sum up all the products to obtain the overall volume flow per second.

If air in a rigid 80 cubic foot scuba tank is pressurized to 3000 psi, giving th…

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If air in a rigid 80 cubic foot scuba tank is pressurized to 3000 psi, giving the diver a certain amount of breathing time, then why does bottom time decrease with depth? I know about external pressure, but how does the pressure affect air inside the tank? – RJ

The deeper a scuba diver goes, the greater the water pressure and the more the water presses in on the diver’s chest. To be able to breathe, the air in the diver’s mouth must have roughly the same pressure as the water around the diver’s chest. That way, the diver will be able to use chest muscles to breathe the air into the diver’s lungs. But the pressure of the air in the diver’s mouth is proportional to its density and thus to the number of air molecules contained in each liter of air. At great depths, the diver must breathe dense, high-pressure air and this air contains a great many air molecules per liter. Since the scuba tank contains only so many air molecules, these molecules are consumed more rapidly at great depths than they are at shallow depths. The scuba regulator automatically controls the density of air entering the diver’s mouth so that the air pressure is equal to the surrounding water pressure. That way, the air is easy to breathe. The deeper the diver goes, the more air molecules the regulator releases into each of the diver’s breaths and the faster the air in the scuba tank is consumed.

In Exercise #9 on pg. 33: If you are riding on an escalator, with a suitcase, do…

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In Exercise #9 on pg. 33: If you are riding on an escalator, with a suitcase, doesn’t the escalator supply the upward force? Doesn’t this also mean that the forces of the suitcase and escalator cancel one another to produce a net force of zero?

First, let’s suppose that the suitcase is resting directly on the escalator and you are not touching it (I had intend that you hold the suitcase in your hand). Because the suitcase is traveling at constant velocity, the net force on it must be zero. Since the suitcase has a downward weight, the escalator must be pushing upward on the suitcase with a force exactly equal in magnitude to the suitcase’s weight. As you suggest, the force of the suitcase’s weight and the support force of the escalator cancel one another to produce a net force of zero on the suitcase. Now, if you are holding the suitcase, it’s your job to exert this upward force on the suitcase. Once again, that upward force is equal in magnitude to the weight of the suitcase.

With Newton’s first law, the word “tends” seems a bit ambivalent. Does this wo…

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With Newton’s first law, the word “tends” seems a bit ambivalent. Does this word suggest there are exceptions to the rule?

The statement of inertia contains the word “tends” (an object in motion tends to continue in motion and object at rest tends to remain at rest) because it doesn’t deal with the presence or absence of forces. If forces were outlawed, then the word “tends” could be dropped from the statement.

However, Newton’s first law is not ambivalent and does not contain the word “tends.” It states directly that an object that’s free of outside forces moves at constant velocity. No ifs, ands, or buts. If I have inserted the word “tends” into this law in class, it was a mistake on my part.

Why is the element mercury a liquid at room temperature when none of its neighbo…

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Why is the element mercury a liquid at room temperature when none of its neighbors on the periodic table are? — BZ, Trenton, NJ

The answer to that question lies at least partly in the electronic structure of the mercury atom. The mercury atom is the largest member of the third row of transition metals, meaning that it is the atom at which the 5d shell of electrons is finally filled completely. Whenever a shell of electrons is filled, that shell can no longer assist in forming chemical bonds. While the d shell electrons normally help hold transition metal atoms together, making these metals strong and hard to melt, the filling of the 5d shell makes it hard for mercury atoms to stick to one another. In contrast to metals like tungsten and tantalum, which melt only at very high temperatures, mercury is a liquid at room temperature. Actually, the zinc atom is the atom at which the 3d shell is filled and the cadmium atom is the atom at which the 4d shell is filled. While those two metals are solid at room temperature, they have very low melting points.

What happens to gas in a gas mask?

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What happens to gas in a gas mask? — TF, Auburn, WA

Most gas masks remove toxic molecules from the air by allowing those molecules to react with or stick to a surface inside the mask. Molecules are generally too small to remove from the air with simple filters, so they must be removed by chemical processes. Highly reactive molecules, such as chlorine, fluorine, and ozone, naturally attack and bind with many chemicals and are easily removed by a mask containing those chemicals. Other molecules aren’t so reactive and must be collected in a more complicated manner. Sometimes the gas mask will contain a reactive chemical that seeks out specific toxic molecules in the air and binds chemically to those molecules. But some mask simply use activated carbon, which just sticks molecules to its surface. The molecules don’t stick very tightly to the carbon surface, so they can be driven off by baking the carbon. But the carbon is finely divided so that it has an enormous amount of surface area and can accumulate a great many molecules before it becomes “full.” Finally, some gas masks contain catalysts that decompose certain toxic molecules, chopping them up before they enter your lungs.

Could you see a laser beam in outer space since it can’t reflect off of anything…

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Could you see a laser beam in outer space since it can’t reflect off of anything? — RM, Rochester, NY

No. The reason that you can see a very intense laser beam as it passes through the air is that light can scatter off of dust particles and air molecules. When it does, some of the laser light is sent toward your eyes and you see the light coming toward you from the laser beam’s path. But if there is no air in the path of the laser beam, the light will travel without scattering and you won’t see the path at all.

How do neon lamps work?

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How do neon lamps work? — TF, Auburn, WA

A neon lamp consists of a neon-filled tube with an electrode (a metal wire) at each end. When you put enough electrons on one of the electrodes and remove enough electrons from the other, electrons will begin to leap off the first electrode and accelerate toward the other electrode. Because the density of neon atoms in the tube is relatively low, only about 1/1000th that of air molecules in normal air, the electrons can travel long distances without colliding with a neon atom. As the electrons accelerate, their kinetic energies increase. However, these electrons occasionally collide with neon atoms and, when they do, they can give up some of their kinetic energies to those atoms. The neon atoms then end up with excess energy and they often emit this energy as light. The color of this light is determined by the structure of a neon atom and tends to be the familiar red of a neon sign.

Why do we see colors when light strikes atoms?

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Why do we see colors when light strikes atoms? — GN, Marine City, MI

When white light strikes a molecule, that molecule may absorb some of the light. Light interacts with molecules as particles called “photons” and whether a particular photon is absorbed depends on the structure of the molecule and the color of the photon. Each molecule has the ability to absorb only certain colors of light. For example, a particular molecule may absorb only red photons. As a result, your eye will see only green and blue light photons coming from that molecule when it’s exposed to white light and you will perceive that molecule as having a blue-green color known as cyan. In general, the colors that you see coming from molecules that are illuminated by white light are the colors of light that the molecules don’t absorb.

On really cold winter days at temperatures well below zero, I’ve noticed that su…

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On really cold winter days at temperatures well below zero, I’ve noticed that sunlight is brighter and whiter than on days that are a little below freezing. Why does this happen? — CP, Madison, WI

The colder the air is, the less humidity it can hold. That’s because at low temperature, water molecules in the air are much more likely to land on a surface and stick than they are to break free from a surface and enter the air. Thus cold air is relatively free of water molecules. Water molecules in the air tend to bind together briefly and form tiny particles that scatter light. The sky is blue because of such scattering from tiny particles. With less water in the air, there is less scattering of sunlight. As a result, the sky is a darker blue, almost black, and the sunlight that reaches you directly from the sun retains a larger fraction of its blue light. The sun appears less red and more blue-white than on a warmer, more humid day.