An elastic collision is when two objects collide and bounce back with little or no deformation. For example, two rubber balls bouncing together would be elastic. Two cars hitting each other would be inelastic, as the cars crumple, and do not bounce back. In a perfectly elastic collision (the simplest case), no kinetic energy is lost, and so the kinetic energy of the two objects after the collision is equal to their total kinetic energy before the collision. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms (heat, sound). The other rule to remember when working with elastic collisions is that momentum is conserved.
Consider two particles, indicated by subscripts 1 and 2. Let "m" and "m" be the masses, "u" and "u" be the velocities before the collision and "v" and "v" be the velocities after collision.
Since it is an elastic collision, the total momentum before the collision is the same as the total momentum after the collision.
Given that momentum (p) is calculated as
We can calculate the momentum before the collision to be:
and the momentum after the collision to be:
Setting the two equal gives us our first equation:
The second rule we use is that the total kinetic energy remains the same, meaning that the initial kinetic energy is equal to the final kinetic energy.
The formula for kinetic energy is:
So, using the same variables as before:
The initial kinetic energy is:
The final kinetic energy is:
Setting the two to be equal ( since the total kinetic energy remains the same):
These equations may be solved directly to find "v" when "u" are known or vice versa.
Here is a sample problem, which can be solved using either conservation of momentum, or conservation of energy:
For example:
After collision:
Using Conservation of Momentum:
After doing multiplication, and then subtracting formula_11 from both sides, we get:
Summing the left side, then dividing by formula_13 gives us:
We could have also solved this problem using Conservation of Energy:
Multiplying both sides by formula_18, and then do all the required multiplications gives us:
Adding the numbers on the left, subtracting formula_20 from both sides, and dividing by formula_13 gives us:
Taking the square root of both sides gives us an answer of formula_23.
Unfortunately, we'd still need to use conservation of momentum to figure out whether formula_24 is positive or negative.
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Michael Adams (born 17 November 1971 in Truro, Cornwall) is a British chess grandmaster (1989). His highest ranking was world #4, achieved several times from October 2000 to October 2002. He achieved a peak FIDE rating of 2755.
He has achieved good results in World Chess Championship tournaments. At the FIDE World Chess Championship 2004, he reached the final, narrowly losing out to Rustam Kasimdzhanov in the tie-break games.
Adams won the British Chess Championship in 1989 at the age of seventeen. Making only rare appearances, he won (jointly) in 1997, and won again in 2010 and 2011. A fine score of 6½/7 in the 2011 European Club Championship marked a return to form, but his results are no longer so consistent as they used to be.
Sodium carbonate
Sodium carbonate is a chemical compound. It is composed of sodium and carbonate ions. Its chemical formula is NaCO. It is a base. It reacts with acids to produce carbon dioxide. It is made by reacting sodium hydroxide with carbon dioxide or by heating sodium bicarbonate. It is produced industrially by the Solvay process. It is used to make glass. It is also used in pools and cooking. It is used as an electrolyte.
Solvay process
The Solvay process is a way to make sodium carbonate and sodium dicarbonate invented by Ernest Solvay. It is essentially the reaction of carbon dioxide with ammonia and sodium chloride to produce ammonium chloride and sodium bicarbonate. The sodium bicarbonate may be heated to produce sodium carbonate.The process consists of saturation of cold, concentrated solution of sodium chloride with ammonia.
Potassium carbonate
Potassium carbonate, also known as potash or pearl ash, is a chemical compound. It is made of potassium and carbonate ions. Its chemical formula is KCO.
Potassium carbonate is a white solid. It dissolves in water. It is similar to sodium carbonate. It reacts with acids to make carbon dioxide and a potassium salt. It does not dissolve in alcohol. It is basic. It is a mild drying agent.
It is made by the reaction of carbon dioxide with potassium hydroxide.
It is used to soften water (remove some of the ions from water) and make soap. It is used to put out fires. It can be used as an electrolyte to electrolyze water.
Bicarbonate
Bicarbonate is an anion (a negatively-charged ion). Its chemical formula is HCO. It reacts with acids to produce carbon dioxide. A sample compound is sodium bicarbonate. It forms carbonate when heated.
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Harrison wrote the song while sick in bed at a hotel room in Bournemouth, England, where the Beatles were playing some shows during the summer of 1963. Harrison never regarded it highly, saying, "It was a fairly crappy song. I forgot all about it completely once it was on the album." He considered it an exercise in whether he could write a song, later saying, "at least it showed me that all I needed to do was keep on writing, and then maybe eventually I would write something good." Harrison received a writing credit for two earlier songs, "In Spite of All the Danger" (McCartney/Harrison) and "Cry for a Shadow" (Harrison/Lennon). Both were recorded by the Beatles but neither was released officially by the band until 1995's "Anthology 1" compilation. "Don't Bother Me" is considered Harrison's first song by most (including the composer himself).