Topic: earth's rotation
Topic: battery tester
Topic: density of water vs. ice
Topic: tapping a cup
Topic: stability of the atom
Topic: field mill
Topic: Rotate And Flip
Topic: energy conservation
Topic: parabolas and trajectories
Do you get better gas mileage if you drive east?
No. You use gas to accelerate your car and to move it relative
to the surface of the earth while working against friction. You are not using gas to
keep it rotating with the surface of the earth about the earth axis. It is doing that even
if it sits parked in your driveway.
An airplane uses fuel to generate lift and to move against friction relative to the air if flies in. If this air is moving eastward with the jet stream, then an airplane uses less fuel covering the same distance when moving east than when moving west.
I have noted the wind vectors on weather maps are parallel, and not orthogonal , to the isobars. Why?
Whenever a pressure gradient develops over an area, the pressure
gradient force begins moving the air directly across the isobars. If the earth did not
rotate, this force and friction would be the only forces acting on the wind. However the
earth does rotate.
A moving mass travels in a straight line unless it is acted on by some outside force. However, if one views the moving mass from a rotating platform, it appears to be deflected. To illustrate this start rotating the turntable of an old record player. Take a ruler and a piece of chalk and draw a straight line from the center to the outer edge of the turntable. Now stop the turntable. On it you see the line spiraling outward from the center. To a viewer on the turntable, some "apparent force" deflected the chalk.
A similar "apparent" force deflects moving particles on the earth. It is called the Coriolis force. It is always at right angle to the wind direction and directly proportional to the wind speed. As the wind speed increases, the Coriolis force increases. The Coriolis force varies with latitude, from zero at the equator to a maximum at the poles.
When a pressure gradient is first established, wind begins to flow from lower to higher pressure directly across the isobars. However, as soon as the air is moving, the Coriolis force deflects it. In the northern hemisphere it is deflected to the right. When the wind is deflected a full 90 degrees, it is parallel to the isobars. At this time the pressure gradient force and the Coriolis force exactly balance and the wind remains parallel to the isobars. Surface friction can disrupt this balance. The angle of surface wind to isobars is about 10 degrees over water and increases with roughness of terrain.
How do airbags hurt people?
Airbags are designed to be leaky cushions. When a car comes to a
stop in a very short time interval in a crash, the driver or passenger will keep on going
forward with approximately the same speed that the car had before the crash. If the
occupants of the front seats are not wearing seat belts, they will collide with the
steering wheel, dashboard or windshield after a very short time interval. Airbags are
supposed to soften the impact by slowing the person down. The person is supposed to make
contact with the airbag after it is fully inflated. As the person pushes against the
airbag, the bag pushes back slowing the person down. But the force with which the bag
pushes back decreases rapidly, because the bag is leaking air and is rapidly deflating. It
is supposed to deflate in 1/3 of a second.
Because the person is supposed to hit the airbag when it is fully inflated, the airbag must inflate very rapidly. The initial explosion in the airbag triggered by the crash must therefore produce a high pressure gas, which then expands rapidly. When the sensor activates the airbag in a collision, a mixture of chemicals is ignited through an electrical impulse. This causes a relatively slow kind of detonation which liberates a pre- calculated volume of nitrogen gas. This gas fills the airbag in approximately 1/20 second. If the pressure is not high enough, the airbag will not grow big enough in 1/20 of a second.
Nearly all airbag accidents happen when a person comes in contact with the airbag while it is inflating. The airbag will then not provide a cushion, but hit the person with appreciable force. Smaller people, who have their car seat pushed forward, are likely to come into contact with the airbag while it is still inflating, because then there is only a short distance between the person and the compartment where the bag is stored. Rear facing child seats are also close to the airbag compartment. When the bag explodes, it then hits the occupants with full force. The airbags are designed to contact the chest area of an average size man. If an exploding airbag hits a person in the chest, the likelihood of injury is not very high. But people that have the seat pulled forward are often shorter that average, and the exploding bag is likely to hit them in the neck or head. Now the likelihood of injury increases dramatically.
Explain how an astronaut in an orbiting satellite can use a spring with a known spring constant to measure his mass.
The astronaut and the spacecraft are both falling freely. A spring scale is useless, since the scale and the astronaut are accelerating at the same rate. The scale does not push against the astronaut and therefore reads zero.
Assume that the mass of the spaceship is much greater than the mass of the astronaut. The astronaut can attach one end of the spring to the wall of the spaceship and the other end to himself. When he then pushes off the wall, he will start oscillating back and forth with respect to the wall. The spring first stretches, then compresses, and so on. The astronaut can use a watch to time the oscillation. He thus can determine the period T of the oscillation. The period T is the time it takes to complete on full cycle of the motion, i.e. from maximum stretch to maximum stretch. He can then calculate his mass m ( in kilogram ) by multiplying the spring constant k (in Newton per meter) by the period (in seconds) squared ad dividing by 4 pi ( 3.1416 ) squared.
Many batteries now come with a battery tester. How does a battery tester work?
A battery tester is a dark, brown strip. If each end is pressed against the poles of a battery, a part of the strip turns yellow. The length of the yellow portion of the strip depends on the condition of the battery. If you look on the back side of the strip, you will see a wedge-shaped piece of conducting material. The strip itself is a liquid crystal. This liquid crystal changes color at approximately 115 degrees Fahrenheit. You can show this by putting it in a glass of hot water.
If you press the ends of the conducting wedge against the poles of a battery a current will flow through the wedge. The current is given by Ohms law, I=V/R, where R is the total resistance of the wedge. The resistance per unit length, however, is not constant. It is higher in the narrower portion of the wedge and lower in the wider portion. The power dissipated per unit length, which is equal to the square of the current times the resistance per unit length, is therefore largest in the narrowest portion of the wedge. The wedge heats up more here. Heat causes the liquid crystal strip to turn yellow.
A new battery produces a large enough current to even heat up the wide portion of the wedge and turn the liquid crystal above it yellow. As the battery gets used up, the current decreases and the length of the yellow portion decreases as only the narrow parts of the wedge get hot enough to turn the crystal above yellow.
What is the mechanism of sparks? Are sparks caused easier in humid air or dry air?
A spark in air is a form of an electrical discharge. The normally insulating air is transformed into a conductor, a process called electrical breakdown. Normally air consists of neutral molecules of nitrogen, oxygen, and other gases, in which electrons are tightly bound to atomic nuclei. However, some loose charges are always present. In an electric field these charges accelerate. If the field is strong enough, the charges can pick up enough speed before hitting an air molecule to be able to knock an electron off that molecule. As a result more and more loose charges are produced. Their motion constitutes a discharge or spark. Air breaks down if the electric field strength is approximately 1000 Volts per millimeter. Typically very high electric fields are present near sharp points and new electron - ion pairs are produced in their vicinity. The higher the humidity, the lower is the electric field strength needed to cause a breakdown.
Once ionized, air becomes quite conductive. When nitrogen and oxygen atoms recombine with electrons, they emit light of a purple color. If a large amount of current flows the air is heated and expands, creating the telltale `POP' . The hotter the air becomes, the closer to white, and then on to blue it will glow.
Why should water be most dense at 4°C? If the crystals take up more space than the liquid, the water should continue to increase density down to 0°!
Water, like most things in nature, expands when heated and
contracts when cooled except in the temperature range between 4 degrees Celsius and 0
degrees Celsius. The hydrogen bond gives water this unique properties. To
understand the hydrogen bond, we first have to take a close look at the water molecule.
A water molecule is made of two hydrogen atoms and one oxygen atom. The hydrogen-oxygen bond which is responsible for the existence of the water molecule, is a normal covalent bond. Hydrogen bonding forms a weak bond between hydrogen atoms and oxygen atoms of adjacent water molecules. This bond is a lot weaker than a normal covalent bond.
In ice, a water molecule has four nearest neighbors to which it is bonded via hydrogen bonds. The geometry leads to a rigid, rather open hexagonal structure. When the temperature is raised above the melting point, jostling begins to destroy this open hexagonal structure. Liquid water has a partially ordered structure in which hydrogen bonds are constantly being formed and broken. In liquid water each molecule is hydrogen bonded on the average to 3.4 other water molecules. Molecules are now allowed into the open spaces of the hexagonal structure. This allows the molecules to move closer to each other and lowers the density. As the temperature increases towards 4 degrees Celsius, molecules move through the liquid so fast that fewer bonds are formed at any one time, shortening the average time each bond exists and increasing the density even further. At atmospheric pressure the temperature of greatest density is at 4 degrees Celsius.
For more information and nice images see
Water and Ice: ( http://cwis.nyu.edu/pages/mathmol/modules/water/info_water.html) and
Expansion of Water as it Freezes: ( http://tqd.advanced.org/2690/exper/exp6.htm ).
After adding most types of powder mix to a cup and stirring, when you tap the bottom of the cup the pitch of the cup changes gradually as the tapping continues. Does this have something to do with the mix coming out of solution and thus changing the density of the liquid?
I have not observed this phenomenon. A number of apparently contradictory solutions to the problem were suggested at Last Word Archive: Tuneful tea. Please check it out.
WHY doesn't a bound electron (e.g. an electron in a atom of hydrogen) produce bremsstrahlung radiation?
Why do you expect the bound electron to produce bremsstrahlung? Because Maxwells equations predict that accelerating charges, charges that change their speed or direction of motion, emit radiation. A classical picture of the atom as a miniature solar system, with the electron in a well defined orbit around the nucleus, leads to the prediction of bremsstrahlung. Radiating its energy away, the electron spirals into the nucleus, the atom is unstable. The stability of the atom is now explained in terms of quantum mechanics. Whenever we are dealing with particles confined to volumes of atomic dimensions, the postulates of quantum mechanics must be used to describe their behavior. (The laws of classical mechanics are approximations to the laws of quantum mechanics, which work when we are dealing with macroscopic phenomena.) In quantum mechanics the electron does not "orbit " the proton. It is found in the region around the proton. The space occupied by the atom is the space where we are likely to find the electron. This space is as small as allowed by the uncertainty principle. The electron is not allowed to radiate any more of its energy away and fall into the nucleus.
What is a field mill? How does it work?
A fiel mill is a device to measure electric fields. When a grounded conducting plate is exposed to an electric field, it acquires by induction a net surface charge. This surface charge q is proportional to the strength of the electric field E. Changes in the electric field lead to changes in the surface charge. When the surface charge changes, a current flows between the plate and the ground.
A field mill consists of a sensing plate, which is connected to the ground via an impedance Z, a segmented ground-connected rotor which turns in front of the sensing plate, and an electronics module. When the ground connected rotor covers the sensing plate, it shields it from the electric field, ad the surface charge on the plate is zero. When the plate becomes uncovered, a current flows between the ground and the plate to establish a surface charge q. Since the rotor covers and uncovers the plate several times per revolution, charge must be continuously moved to and away from the plate. An alternating current flows between the ground and the plate. This current results in a voltage across the impedance Z. The field strength can be measured by measuring this voltage, amplified by the electronics module. The meter can be a voltmeter or an oscilloscope.
What causes the colors on a water/detergent bubble?
Ordinary white light (daylight) is a superposition of electromagnetic waves with different wavelengths. Different colors correspond to different wavelengths and ordinary white light contains many colors. When a wave moves from one material into another, part of the wave is reflected and part it is refracted or bend as it moves into the second material. The different colors of light are bend by different amounts, and therefore move in different directions inside the second material. (See "White Light")
Waves have a another property. Two waves with the same wavelength moving in the same direction can reinforce each other if their crest coincide or cancel each other out if crest and trough coincide. This is called interference. The soap film making up a soap bubble has two surfaces. When light hits a soap bubble, some part of the light is reflected from the outer surface and some part from the inner surface of the film. These two reflected waves can interfere. Because the different colors are bend by different amounts inside the material of the soap film, the directions along which the wave reflected from the second surface reinforces the wave reflected from the first surface depends on the color of the light. Different colors are reinforced when the light makes a different angle with the surface. The soap bubble has a curved surface, so light reaching our eyes from different parts of the surface makes a different angle with the surface, and thus appears at a different color.
I take a hammer and hold it so that the striker is on the left and the nail puller is on the right. Then I flip the hammer in the air one complete revolution so that the handle is again in my hand. This time the striker is on the right and the puller is on the left. Other objects behave the same way. Shoes, blocks of wood, etc. Why do these things reverse themselves instead of just flipping around and landing the way they were in my hand originally?
For every three dimensional object we can find three perpendicular principal axes of inertia. These are axes passing through the center of mass of the object about which the object can spin without wobbling. For a symmetric object, such as a sphere, any three perpendicular axes passing through the center are principal axes. But for an object without rotational symmetry only one set of principal axes may exist.
Take for example an simple box-shaped object, with different dimensions for width, length, and height, such as an eraser or a book The principal axes pass through the center and are perpendicular to the faces of the box.
The box shaped object has a different moment of inertia about each of the axis. The moment of inertia about an axis is the product of the mass times the average of the square of the perpendicular distance from the axis. The moment of inertia is largest about axis 3 and smallest about axis 1. The farther the average distance of the mass from the axis of rotation, the greater is the moment of inertia.
Newton's laws predict that for any object with three different principal moments of inertia the motion about the axes with the largest and smallest moment of inertia is stable. By stable motion we mean that the object will wobble but will not flip if you set it rotating about an axis close to but not exactly aligned with the principal axis. For the box, motion about axis 3 and axis 1 is stable. If the object is rotating about an axis close to axis 3 or axis 1 it will not flip. Motion about the axis with the intermediate moment of inertia, however, is unstable. If you set it rotating about an axis just slightly off axis 2, it will flip.
For a hammer, the approximate location of the center of mass and the principal axes of inertia are shown in the figure.
The arrows indicate the approximate average distance of the mass from the principal axis of the same color. The smallest moment of inertia is associated with axis 1 and the largest moment is associated with axis 3. The motion about these axes is stable. The intermediate moment of inertia is associated with axis 2 and the motion about this axis is unstable. When you spin the hammer about an axis just slightly off axis 2, it will flip.
Suppose I take a book from a table and set it on the floor. The book's potential energy is decreased. What has become of this energy? (i.e. there should be a corresponding increase in some other form of energy or matter -- but what is it?) (My guess -- increased thermal energy in the person's body)
You are right. Energy is not created or destroyed, just transferred. If the book simply drops to the floor, potential energy is first converted into ordered kinetic energy of the book, and then into disordered kinetic energy (thermal energy) of the particles in the floor. If you carefully set the book on the floor, you are exerting a force on the book, to cancel out the force of gravity. You are pulling up on the book. Newton's third law says that the book is exerting a force on you of the same magnitude, but opposite in direction. The book is pulling down on your hand. The force on your hand is in the direction in which your hand travels as it sets the book to the floor, so it is doing positive work on you. This energy is stored somewhere in your body, most likely as thermal energy.
What is the relationship between parabolas and trajectories?
The trajectory of an object is the path taken by the object as it moves through space. If the trajectory lies in a plane, then we can set up a x-y coordinate system in that plane and describe the trajectory by giving y as a function of x.
The trajectory of a fast cannonball, fired at an angle, looks similar to the trajectory
in figure a). The trajectory of a light children's ball is strongly affected by the drag
from the air and looks similar to the trajectory in figure b). The trajectory in figure a)
is a parabola. The equation that gives y as a function of x, y(x)=A-B(x-C)(x-C), is the
equation of a parabola. A parabola is any function y(x) that can be written as
y(x)=a+bx+cxx, with a, b, and c arbitrary constants. The trajectory in figure b) is not a
In our solar system planes have elliptical trajectories, and the trajectories of some comets are nearly parabolic.