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When you move your cursor across the screen, it can only be located at discrete (set fixed) locations because it is made up of individual pixels. The pixels are fixed regions that display the colors. Many discrete things are man-made, such as computer screens.

People usually experience space and time as being continuous (non-discrete). Pretend you are in a very large room, and there are large tiles on the floor. As you walk across the room, you could stop at any time. Your right foot may land such that the tip of your big toe just touches a line between tiles. (Really though, you could have stopped such that the middle of your right foot was on the line. Or you could have stopped such that the heel of your foot was on the line.) We experience a continuous world, but man often makes discrete devices to make our lives easier.

I should mention though that on really, really, really small scales, such as those smaller than the size of an atom, particles can behave in a more discrete way. For example, electrons have a high probability of only being at certain fixed distances from the center of an atom. The center of an atom is where the protons (positive charge) and neutrons (no charge) are. The small mass, negatively charged electrons orbit around the center. The electrons are highly likely to be at some fixed distance, which is often referred to as a level. They might be found at a position that is not one of these levels, but the probability (likelihood) of finding an electron in-between fixed levels is very low.

Dr. Heather Elliott
(January 2003)

For related questions, please visit the Basics questions.

I think that you're right that the colder ball will contract, but if it goes furthur, it is because of the reduced air resistance. It's got a smaller cross section and so has to push less air out of the way. A denser ball of the same size will travel further because it has more kinetic energy (more mass and the same velocity). But I believe the size difference is what is important for your experiment.

Dr. Eric Christian

For related questions, please visit the Properties of Matter questions.

The weight of the car is actually not important. If there was no air drag and no friction, the two cars would actually travel at exactly the same speed. And even the air drag (assuming the two cars are roughly the same size) is probably not very important. I suspect that friction in the turning of the wheels is the major cause of a difference in speed.

The speed difference is more for the higher track because the drag and friction cause a difference in acceleration, which is how fast the speed changes, and that difference lasts longer (happens for longer time) on the higher track.

Dr. Eric Christian
(January 2004)

For related questions, please visit the Forces and Motion questions.

This is not our area of expertise, but I can tell you about accelerometers in a general sense.

There are a number of different kinds of accelerometers, which are useful in different contexts. The ordinary bathroom scale is a device that, in effect, measures the acceleration of gravity, and there are clearly many different kinds of scales -- spring, balance beam and piezo-electric.

The spring and piezo-electric accelerometers work on the principle of using a material that deforms elastically in response to the acceleration and then measuring the deformation. Piezo-electric devices are often favored, because the output can be readily be digitized and stored automatically. Calibration of the device allows the acceleration to be determined.

I found an article that appears to discuss the principles in a reasonably clear manner. This might be of some use.

Dr. Randy Jokipii
(January 2004)

For related questions, please visit the Forces and Motion questions.

The problem with this is that you can't jump anywhere near fast enough to make a difference (unless you can leap tall buildings in a single bound). You could slow yourself down relative to the elevator if your timing was perfect (the elevator would also actually speed up due to your jump), but you'd still hit pretty hard, just a split second later. Even if you could jump fast enough to cancel all of the velocity the elevator has from falling, the top of the elevator would still take you out. Kids, don't try this at home :)

Dr. Eric Christian
(April 2001)

For related questions, please visit the Forces and Motion and Gravity questions.

The harness that attaches the skydiver to the parachute is somewhat springy, to help absorb the shock. So what happens after the parachute opens is that the skydiver continues downward faster than the parachute, which stretches the harness. At some point, the harness is stretched to its maximum and the skydiver is moving downward at the same speed as the parachute. The stretching of the harness then pulls the skydiver upward relative to the parachute (think bungee jumping), and he or she reaches the maximum upward velocity relative to the parachute at the point where the harness is at its natural length, when there is no more upward force. If there weren't any friction or gravity, that upward velocity, again relative to the parachute, would be equal to the difference between the downward velocities of the parachute and the skydiver.

So, neglecting complications, if the parachute is moving at half the speed of the skydiver, the skydiver would be jerked to an absolute stop relative to the ground.

In real life, the speed (terminal velocity) of a skydiver is about 120 mph, and the parachute is more like 15 mph. In the absence of friction and gravity, the skydiver would, at maximum, be moving upward at 105 mph relative to the parachute or upwards at 90 mph relative to the ground. Real life friction will greatly reduce that, but I think it's still likely that, for a second or so, the skydiver is actually moving upward relative to the ground.

Dr. Eric Christian
(October 2008)

There are two different ways that we can "feel like we're spinning".

One is that we can feel the force that the spinning puts on our body. An object traveling in a circle (or part of a circle, as a turn would be) experiences an outward force, away from the center of the circle or turn. One way you might feel it is as a push toward the side of a car when it makes a quick turn: a turn to the right pushes you to the left, and vice versa. This force is called centrifugal force, and the amount of force depends on the mass, velocity, and distance of the object from the center of the turn.

F_c = mv²/r, where F_c = centrifugal force, m = mass, v = velocity, and r = radius

So standing on the side of a rotating Earth, we might expect to feel centrifugal force as a push away from the Earth's axis, directly up at the equator, up and off to the side in the US, and directly to the side near the poles. But we don't feel it, because even though we're moving at nearly 1000 mph through space, when you divide by the large radius of the Earth, you get a very small number for the centrifugal force -- too small to feel. Plus, it's a constant (unchanging) force, and we've felt it our entire lives. So even if it was larger, it would probably feel "normal", and we would not feel like we were spinning.

The other way we notice spinning is for our eyes to see the background moving behind an object. This is what you see if you ride on an inside horse on a merry-go-round and look at an outside horse, for example. The people standing nearby (background) appear to move sideways.

But everything on the Earth is spinning around it with us, so nothing on Earth counts as background to help see the rotation. The Sun, moon, and stars appear to be moving as the Earth rotates, but they're moving very slowly (one revolution per day). It take them minutes to move the width of a finger held at arm's length -- just too slow for our brains to register the spinning.

Eric Christian and Beth Barbier
(November 2004)

For related questions, please visit the Forces and Motion and Gravity questions.

Yes, the speed of the train would be added to the speed of the baseball, when viewed from the ground. A person on the train would see the baseball moving at the same speed as a person on the ground would see a baseball thrown from the ground. You can prove it this way: if you throw the ball at 10 mph forward, it still moves forward on the train. If it were only moving 10 mph relative to the ground, it would be flying backwards at 50 mph on the train, even though you threw it forward.

Dr. Eric Christian
(February 2002)

For related questions, please visit the Forces and Motion questions.

I don't think it's really possible for the ball to have picked up any appreciable speed. I think it's a matter of perception. Between the pitcher and the batter, your mind has much more time to analyze the path of the ball. Plus the downward curvature due to gravity adds to the perception of "slowness". The sudden redirection and the short distance between the batter and the catcher forces the mind to react quickly, which it translates into a "faster" ball. But I don't see any way in which the forward moving bat could add velocity backwards to the ball (conservation of momentum).

Dr. Eric Christian
(April 2000)

For related questions, please visit the Forces and Motion questions.

This is outside of our area of expertise, but there are a couple of good websites that should help you:

• Amusement Park Physics - this one lets you design your own roller coaster
• Roller Coaster Physics - this one has a nice animation - click on "potential energy" or any of the other labels for more information

Beth Barbier
(November 2005)

Here's an amusement park ride question that Dr. Moebius took on:
The skycoaster (or ripcord) is a thrill ride where riders are pulled by a cable up to the top of one of two launch towers. Riders pull a cord that releases them from the winch cable and allows them to swing between the towers. How can I calculate the speed of the rider at the bottom of the arc without knowing the tension in the swing cable?

I prepared a sketch that is supposed to capture the situation. In the case you describe, the cord, which allows the rider to swing from tower A to tower B (of equal height), is attached to another attachment point above the two towers and midway between them. Now the rider can swing on an arc with a radius equal to the length of the cord l.

Starting at tower A at rest, the rider will pick up speed until he/she reaches the lowest point exactly underneath the hinge point before slowing down again to rest when arriving at tower B.

What is at play here is "energy conservation", or nature's equivalent to "There is no such thing as a free lunch." After having been hoisted up the tower, the rider has gained "potential energy" in Earth's gravitation. Taking the circular path to the lowerst point, the rider "falls" the height h . While falling, the rider must pick up speed and thus kinetic energy (or motion energy). For the speed v, or the kinetic energy that he/she reaches, it doesn't matter whether the fall is straight down by h or on an arc path as forced here by the cord. In both cases the kinetic energy attained is equal to the difference in potential energy given by the height difference h.

To capture this in simple equations, let us say that the potential energy is 0 at the lowest point of the ride. At the top of the tower, the rider has the potential energy:

E_Pot = h * g * M

where g is the Earth's gravitational acceleration and M the mass of the rider. While falling, the rider is losing this potential energy, and in exchange for the lost potential energy, the rider gains kinetic energy:

E_kin = M * v²/2

Since no energy is magically appearing or disappearing, the sum of both types of energy remains the same:

E_Total = E_kin + E_Pot

At the top of the tower, E_kin = 0 at the bottom of the ride the potential energy is 0. Maintaining that the sum of both is the same at the top and bottom, we get:

h * g * M = E_Pot = E_kin = M * v²/2

Yes, the rider is accelerating and decelerating along the arc, but there is no need to compute the changing acceleration in order to find the maximum speed. Also, we don't need to know the tension in the cord. It just keeps the rider on the arc. That's all!

By the way, the height difference h can be computed from the cord length l and the distance between the towers d, using Pythagoras' Theorem:

Dr. Eberhard Moebius
(December 2007)

This is a good and interesting question that is rooted in everyday experience. Indeed, it appears that sound and light arrive simultaneously when we attend a play in a theater or watch a movie. The reason is that we are very close to the stage or screen and loudspeaker. This may already be different during a concert in a stadium: For somebody in the distant rows the sound of the band and its movement is out of synch. The speed of sounds is approx. 300 m/s (1000 ft/s), while the speed of light is 300,000 km/s (approx.190,000 miles/s). Therefore, the sound arrives about 1/3 of a second after the corresponding movement, i.e. starts to be recognizable. In a theater the time difference is too short to be recognized.

The most striking experience of the different speed of light and sound is during a thunderstorm. Unless the thunderstorm is exactly upon us, a silent lightning is followed by a substantially delayed thunder. Yet both originate the same place and time. In fact, one can estimate the distance of the thunderstorm from the difference by counting .twenty-one, twenty-two, etc.. starting with the lightning. Saying each number takes about one second. The distance of the thunderstorm in miles is the number of seconds counted dived by five. Thus a thunderstorm is a great time to find out without instrumentation that sound is indeed much slower than light.

Dr. Eberhard Moebius
(November 2003)

For related questions, please visit the Light and Sound and Speed of Light questions.

Rainbows are formed by the refraction (bending) of light inside water droplets. Check out this web site at the University of Wisconsin for a nice picture.

Dr. Louis Barbier

For related questions, please visit the Light and Sound questions.

It all has to do with energy. Snow and rain land in what is called an inelastic collision. In this type of inelastic collision, almost all of the kinetic energy (the energy of motion) is converted into something else: sound energy, heat, etc. A raindrop both weighs more and is moving faster than a snowflake. Although the mass and velocity of both rain and snow has wide variations, a "typical" snowflake weighs about 3 mg and is moving at about 2 m/sec. A "typical" raindrop weighs 30 mg and is moving at 6 m/sec and so has (KE=1/2 m v²) -- nearly a hundred times the energy of a typical snowflake. More energy to convert to sound means a louder sound. In detail, the impact causes the surface (roof, car, Earth) to vibrate more, which causes the surrounding air to vibrate more, which means a louder sound.

Eric Christian
(January 2010)

The effect you describe sounds consistent with a temperature inversion layer. What we see through a layer of air depends on its index of refraction, relative to layers above and below. The index of refraction depends upon temperature, pressure, and most importantly composition. It is not unusual for the atmosphere to become stratified, which you know as a pilot. When the index of refraction decreases inside a layer compared to layers above and/or below, it is said to be super-refracting. This is often caused by a temperature inversion. When the index of refraction changes, the light coming to you (the observer) is bent and you see these kinds of optical illusions. The index of refraction is most affected by the humidity level, and temperature inversions are usually a sign of transitions from humid to dry air.

Dr. Louis Barbier
(April 2001)

For related questions, please visit the Light and Sound and Energy and Temperature questions.

This is easy to see with a picture. Draw a box a certain distance away from your eye. Light reaches your eye from the two extreme corners of the box, and those light rays make an angle with respect to one another. Now redraw the box 5 times further away, and draw the same two light rays from the corners. You'll see that the angle between the two lines has changed. Now think about what would happen if you keep moving the box further away... that angle between the two light rays will keep getting smaller and smaller. Try it for yourself. I hope that helps.

Dr. Louis Barbier

For related questions, please visit the Basics and Light and Sound questions.

When you put a secondary mirror in the path, you block some of the light that can get to the primary mirror. But you block a fraction of the light from all parts of the image, not all the light from a fraction of the image. So the contrast may be reduced because you're not collecting as much light, but you still see the whole image.

Dr. Eric Christian

For related questions, please visit the Light and Sound questions.

First, let me say that scientific evidence does not support the claim that magnetic fields from things like power lines harm humans. There is also no scientific evidence that strap-on magnets or any type of magnetic therapy can help your health in any way. Weak magnetic fields just don't do much. Extremely strong magnetic fields (that are created in laboratories) may cause currents in your blood and brain, but I've never heard of anyone being harmed by this. The medical procedure "Magnetic Resonance Imaging" (MRI) uses magnetic fields much stronger than those generated by electrical wires or microwave ovens or whatever, and thousands of people a day safely undergo MRI. So I don't really think that there's much of a problem.

Dr. Eric Christian
(February 2001)

For related questions, please visit the Electricity and Magnetism questions.