Stump Me Questions Answered in October 2002

Almost from the beginning, the colors red and white have been used in visual advertising for Coca-Cola to dramatize the trademark.  The earliest use of red in our advertising was by Atlanta drug stores selling Coca-Cola.  They would hang a white oil cloth sign on the store front or awning with slogans printed in red that stated "Drink Coca-Cola, Delicious and Refreshing 5 cents" or "Coca-Cola Sold Here 5 cents."

In 1890, the trademark "Coca-Cola" began to appear in red in newspapers.  During the late 1920s, the trademark "Coca-Cola" was used in white on a "Standard Red" background.  The color arrangement of red on white and white on red has been used alternately over the years.  In 1970, the Dynamic Ribbon Device was introduced, and the "Standard Red" became brighter.

"Although we do not have information on the actor who performs the spoken portion of these commercials, we can tell you that the singer is David Bickler.  He was the lead singer of the 80's rock band, Survivor."

"Duh!!! Because it was a TV show. Was anything on that show realistic? Fun yes, Documentary no."

Potash was the designation of a crude form of potassium carbonate derived as residue from the repeated boiling of wood ashes in a cauldron (or in 18th century parlance, a pot - hence, the name “potash”).  Potash or the more refined pearlash may rightly be thought America's first industrial chemical because this substance was an essential ingredient in the making of soap, glass and gun-powder.  Thanks to Anton S. for the help.

2)  There are many factors that can contribute to this question.  First, it depends on the molecular structures of the glass ball and the rubber ball.  Now if the rubber ball is a basic elastic ball it undergoes an inelastic collision.  An inelastic collision is one in which total kinetic energy is not the same before and after the collision.  When the ball collides with the surface it deforms and some energy is lost to the deformation.  Also energy is converted to rotational energy and elastic potential energy causing the ball to bounce depending on its molecular properties (what type of rubber and how bouncy).  Also note that some collisions are elastic collision such that kinetic energy before the collision is the same after the collision, billiard balls undergo this type of collision.

A glass ball of sufficient density and hardness will also exhibit similar properties.  Suppose the glass ball is made of bulletproof glass.  If you were to drop it on a sufficiently hard surface it would also undergo an inelastic collision in with some energy is lost due to impact.  Since energy is conserved the remaining energy is converted to potential energy and then to kinetic energy as the ball bounces upward.  Glass balls will bounce under certain conditions.

It is possible that under the right combination of glass hardness, rubber density and surface structure the glass ball may bounce higher than the rubber ball.  For instance, if the glass was very hard and dropped on a hard surface it would bounce to nearly the height that it was dropped.  Some energy is lost during impact but that majority of the initial kinetic energy is returned as final kinetic energy causing the glass ball to bounce.  If a rubber ball that was fairly soft was dropped on that same surface much of the kinetic energy would be transformed in to deformation energy and the rubber ball would not bounce very high. So it really depends on the properties of the rubber, glass and the surface that the objects are being dropped upon.  Thanks to Nathan C. of the American Physical Society for the help.

((8*8)/3)+3. For those of you who can't follow that, multiply 8 and 8, divided by 3, and add 3.

"According to Einstein’s Special Theory of Relativity the laws of physics remain the same for all frames of reference (Postulate 1) and the speed of light in a vacuum (299,792,458 m/s) is measured as a constant for all frames of reference (Postulate 2).  Frames of reference are locations of observers that are in motion with respect to other reference frames.  Also note that there are no absolute reference frames within the universe.

With all that said the question can be analyzed. The driver of the car is at rest within his frame of reference that is to say that if his velocity is constant he does not feel the effects of motion.  For instance if you are driving down the highway and not accelerating, having a constant velocity, you do not feel as though you are moving, since you are at rest within the system.  The same holds for the driver in the car traveling at the speed of light. Now according Einstein’s Postulate 2 of Special Relativity the speed of light is constant in all reference frames and according to postulate 1 the laws of physics are the same in all reference frames.  Therefore when the driver of the car turns his headlights on he will see a beam of light leaving his car at a constant velocity of 299,792,458 m/s.

The laws of physics are upheld and the speed of light stays constant. However common sense tells you that the speed of the light leaving the headlights should be the speed of light plus the speed of the car. The speed of light must be constant for all reference frames, for someone within the car and someone outside of the car. Recall from basic physics that velocity (speed) is distance divided by time. Well in order for the velocity of light to be constant in every reference frame distance and time must be altered. This is where Special Relativity comes in. Distance and time become relative values for moving observers as they approach the speed of light. That is to say that objects in motion undergo relative spatial and temporal changes as they approach the speed of light.

For purposes of understanding the outcome of the question we will stick to spatial changes. For an object in motion its length contracts in the direction of motion relative to and outside observer. But for an observer traveling at the same velocity the length is upheld since everything traveling at that velocity contracts by the same ratio. So for someone at rest within the car all length is contracted by the same factor and measurements made by the observer at rest moving at the speed of light will not coincide with another observer outside the car. Since everything that is at rest within the car undergoes the same factor of contraction the light is observed to leave the car at its constant speed as measured by someone within the car."

"Of course you could.  Remember the first and second postulates of Einstein’s Special Theory of Relativity. According to Special Relativity objects moving near the speed of light undergo length contraction in the direction of motion and time dilation, which can be calculated by the Lorentz transformation equations and the gamma factor equation.  Everything that is at rest within the system contracts and dilates by the same factor, therefore someone who is at rest within the system does not observe effects such as length contraction, and time dilation.

For example suppose a sleepy space traveler went to sleep for 12 hours in his spaceship which was traveling at 99.999% the speed of light.  As measured by his clock he would go to sleep and wake up 12 hours later.  Remember everything in his reference frame, i.e. his entire ship, is subject to the same factor of dilation, therefore he does not notice the effects of the dilation as measured by his watch.

However, an outside observer would measure something much different.  Let’s say our sleepy space traveler comes back to earth after his near light speed nap.  He left Earth just as we went to sleep and woke up just as he returned to Earth.  He yawns and steps out of his spacecraft saying, “I’ve been asleep for 12 hours.”  A person at rest with respect to planet Earth would say, “No you haven’t you’ve been asleep for 111.5 days!”

This is because of time dilation.  According to Special Relativity time dilation occurs at a factor of 223.6 while traveling at 99.999% the speed of light.  That is to say for every one-hour experienced by the sleepy space traveler a person at rest with respect to earth experiences 223.6 hours!  So the space traveler gets his twelve hours of sleep as measured by his clock, but his friends back on Earth have watched the sun rise and set one hundred and eleven times!"