http://www.htta.net/table-tennis-vocabulary/
Coefficient of restitution
Sports equipment
The coefficient of restitution entered the common vocabulary, among golfers at least, when golf club manufacturers began making thin-faced drivers with a so-called “trampoline effect” that creates drives of a greater distance as a result of an extra bounce off the clubface. The USGA (America’s governing golfing body) has started testing drivers for COR and has placed the upper limit at 0.83, golf balls typically have a COR of about 0.78. According to one article (addressing COR in tennis racquets), “[f]or the Benchmark Conditions, the coefficient of restitution used is 0.85 for all racquets, eliminating the variables of string tension and frame stiffness which could add or subtract from the coefficient of restitution.”
The International Table Tennis Federation specifies that the ball must have a coefficient of restitution of 0.94.
Equation
Picture a one-dimensional collision. Velocity in an arbitrary direction is labeled “positive” and the opposite direction “negative”.
The coefficient of restitution is given by
for two colliding objects, where
v1 is the scalar final velocity of the first object after impact
v2 is the scalar final velocity of the second object after impact
u1 is the scalar initial velocity of the first object before impact
u2 is the scalar initial velocity of the second object before impact
Even though the equation does not reference mass, it is important to note that it still relates to momentum since the final velocities are dependent on mass.
For an object bouncing off a stationary object, such as a floor:
, where
v is the scalar velocity of the object after impact
u is the scalar velocity of the object before impact
The coefficient can also be found with:
for an object bouncing off a stationary object, such as a floor, where
h is the bounce height
H is the drop height
For two- and three-dimensional collisions the velocities used are the components perpendicular to the tangent line/plane at the point of contact.
Further details*
The COR is generally a number in the range [0,1]. Qualitatively, 1 represents a perfectly elastic collision, while 0 represents a perfectly inelastic collision. A COR greater than one is theoretically possible, representing a collision that generates kinetic energy, such as land mines being thrown together and exploding. For other examples, some recent studies have clarified that COR can take a value greater than one in a special case of oblique collisions. These phenomena are due to the change of rebound trajectory of a ball caused by a soft target wall. A COR less than zero would represent a collision that pulls two objects closer together instead of bouncing them apart.
An important point: the COR is a property of a collision, not necessarily an object. For example, if you had five different types of objects colliding, you would have different CORs (ignoring the possible ways and orientations in which the objects collide), one for each possible collision between any two object types.
Generally, the COR is thought to be independent of collision speed. However, in a series of experiments performed at Florida State University in 1955, it was shown that the COR varies as the collision speed approaches zero, first rising significantly as the speed drops, then dropping significantly as the speed drops to about 1 cm/s and finally rising again as the collision speed approaches zero. This effect was observed in slow speed collisions involving a number of different metals.
Speeds after impact
The equations for collisions between elastic particles can be modified to use the COR, thus becoming applicable to inelastic collisions as well, and every possibility in between.
and
where
v’a is the final velocity of the first object after impact
v’b is the final velocity of the second object after impact
va is the initial velocity of the first object before impact
vb is the initial velocity of the second object before impact
ma is the mass of the first object
mb is the mass of the second object
Derivation
The above equation can be derived from the analytical solution to the system of equations generated by the definition of the COR and the law of the conservation of momentum (which holds for all collisions):
See also
Collision
Elastic collision
Inelastic collision
References
^ http://books.google.com/books?id=PrOKEcZXJ58C&pg=PA85&lpg=PA85&dq=coefficient+of+restitution+bounciness&source=bl&ots=djGGbJndgr&sig=w1UnRQPEnRPZu4qAfwgYWkjDbAk&hl=en&ei=xCyMSoTKAsmltgfinpXlBg&sa=X&oi=book_result&ct=result&resnum=3
^ “Everything You Need to Know About COR”. http://findarticles.com/p/articles/mi_m0HFI/is_5_53/ai_84454550.
^ “Coefficient of Restitution”. http://www.racquetresearch.com/coeffici.htm.
^ Table Tennis / Essentials During Action Proper at SportsTM. Accessed January 2008.
^ “IMPACT STUDIES ON PURE METALS”. http://www.burgy.50megs.com/thesis.htm.
Cross, Rod (2006). The bounce of a ball. Physics Department, University of Sydney, Australia. http://www.physics.usyd.edu.au/~cross/PUBLICATIONS/BallBounce.pdf. Retrieved 2008-01-16. “In this paper, the dynamics of a bouncing ball is described for several common ball types having different bounce characteristics. Results are presented for a tennis ball, a baseball, a golf ball, a superball, a steel ball bearing, a plasticene ball, and a silly putty ball.”.
External links
Wolfram Article on COR
Bennett & Meepagala (2006). “Coefficients of Restitution”. The Physics Factbook. http://hypertextbook.com/facts/2006/restitution.shtml.
Chris Hecker’s physics introduction
“Getting an extra bounce” by Chelsea Wald
FIFA Quality Concepts for Footballs – Uniform Rebound
Categories: Mechanics | Classical mechanics
About the Author
I am a professional writer from China Crafts Suppliers, which contains a great deal of information about electric steam kettle , electric kettle plastic, welcome to visit!
VOCABULARY IN 20 LANGUAGES = Table tennis balls