Coefficient of restitution - Revision history

Vipul: /* Particular cases */

2010-05-29T20:28:46Z

Particular cases

← Older revision		Revision as of 20:28, 29 May 2010
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	\| [[Perfectly inelastic collision]] \|\| 0 \|\| the two bodies merge into one. Linear momentum is preserved in a manner that causes the maximum possible loss in kinetic energy.		\| [[Perfectly inelastic collision]] \|\| 0 \|\| the two bodies merge into one. Linear momentum is preserved in a manner that causes the maximum possible loss in kinetic energy.
			\|-
			\| Inelastic collision that is not perfectly inelastic \|\| between 0 and 1 \|\| the bodies do not merge. Linear momentum is preserved and some kinetic energy is lost.
			\|-
			\| [[Superelastic collision]] \|\| greater than 1 \|\| there is a gain in kinetic energy
	\|}		\|}

Vipul at 20:26, 29 May 2010

2010-05-29T20:26:12Z

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 <math>C_R = \frac{-v}{u}</math>.
 ===For a collision in three dimensions===
 For a collision in three dimensions, the velocities are vectors rather than scalars, so the above formula does not make sense. In this case, we interpret <math>u_1,u_2,v_1,v_2</math> as the components of velocities in the normal direction, i.e., the direction perpendicular to the plane of contact/tangent plane at the point of contact.
-==Constitutive factors and measurement==
+==Constitutive factors==
 The coefficient of restitution is dependent on the specific ''collision'' and cannot be inferred precisely from the geometry, velocity, and the kind of material in the colliding bodies. However, knowledge of the type of material and the geometry of the bodies usually allows for an approximate estimation of the coefficient of restitution.

Vipul: /* Definition */

2010-01-17T00:50:35Z

Definition

← Older revision		Revision as of 00:50, 17 January 2010
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	===For a collision in one dimension===		===For a collision in one dimension===

			We first consider the case of a [[head-on collision]], which can be considered a collision in one dimension.

	Suppose two objects are moving along a one-dimensional axis, collide, and then again move along the same one-dimensional axis. If their initial velocities are (as signed real numbers) <math>u_1</math> and <math>u_2</math> respectively and their final velocities are <math>v_1</math> and <math>v_2</math> respectively, then the '''coefficient of restitution''' (abbreviated '''COR''') or '''bounciness''' of the collision is defined as:		Suppose two objects are moving along a one-dimensional axis, collide, and then again move along the same one-dimensional axis. If their initial velocities are (as signed real numbers) <math>u_1</math> and <math>u_2</math> respectively and their final velocities are <math>v_1</math> and <math>v_2</math> respectively, then the '''coefficient of restitution''' (abbreviated '''COR''') or '''bounciness''' of the collision is defined as:

Vipul at 00:42, 17 January 2010

2010-01-17T00:42:38Z

← Older revision		Revision as of 00:42, 17 January 2010
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	===For a collision in one dimension===		===For a collision in one dimension===

	Suppose two objects are moving along a one-dimensional axis, collide, and then again move along the same one-dimensional axis. If their initial velocities are (as signed real numbers) <math>u_1</math> and <math>u_2</math> respectively and their final velocities are <math>v_1</math> and <math>v_2</math> respectively, then the '''coefficient of restitution''' or '''bounciness''' of the collision is defined as:		Suppose two objects are moving along a one-dimensional axis, collide, and then again move along the same one-dimensional axis. If their initial velocities are (as signed real numbers) <math>u_1</math> and <math>u_2</math> respectively and their final velocities are <math>v_1</math> and <math>v_2</math> respectively, then the '''coefficient of restitution''' (abbreviated '''COR''') or '''bounciness''' of the collision is defined as:

	<math>C_R := \frac{v_2 - v_1}{u_1 - u_2}</math>.		<math>C_R := \frac{v_2 - v_1}{u_1 - u_2}</math>.
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	The coefficient of restitution is also sometimes denoted as <math>e</math>.		The coefficient of restitution is also sometimes denoted as <math>e</math>.

			Note that the ordering of speeds in the numerator is opposite the ordering in the denominator. This reflects the fact that after the collisions, the direction of relative speed changes, because of a ''bouncing back'' effect.

			===For a collision with a stationary object===

			If the collision is between a moving object and a heavy stationary object (which remains stationary even after the collision), then the coefficient of restitution is the ratio, with a negative sign, of the final velocity of the moving object to its initial speed. If the initial speed is <math>u</math> and the final speed is <math>v</math>, the coefficient of restitution is given by:

			<math>C_R = \frac{-v}{u}</math>.
	===For a collision in three dimensions===		===For a collision in three dimensions===

Vipul: Created page with '==Definition== {{quick phrase|quick phrase::bounciness of a collision, quick phrase::final velocity difference divided by initial velocity difference}} ===For a collisi…'

2010-01-17T00:39:36Z

Created page with '==Definition== {{quick phrase|quick phrase::bounciness of a collision, quick phrase::final velocity difference divided by initial velocity difference}} ===For a collisi…'

New page

==Definition==

{{quick phrase|[[quick phrase::bounciness of a collision]], [[quick phrase::final velocity difference divided by initial velocity difference]]}}

===For a collision in one dimension===

Suppose two objects are moving along a one-dimensional axis, collide, and then again move along the same one-dimensional axis. If their initial velocities are (as signed real numbers) <math>u_1</math> and <math>u_2</math> respectively and their final velocities are <math>v_1</math> and <math>v_2</math> respectively, then the '''coefficient of restitution''' or '''bounciness''' of the collision is defined as:

<math>C_R := \frac{v_2 - v_1}{u_1 - u_2}</math>.

The coefficient of restitution is also sometimes denoted as <math>e</math>.

===For a collision in three dimensions===

For a collision in three dimensions, the velocities are vectors rather than scalars, so the above formula does not make sense. In this case, we interpret <math>u_1,u_2,v_1,v_2</math> as the components of velocities in the normal direction, i.e., the direction perpendicular to the plane of contact/tangent plane at the point of contact.

==Constitutive factors and measurement==

The coefficient of restitution is dependent on the specific ''collision'' and cannot be inferred precisely from the geometry, velocity, and the kind of material in the colliding bodies. However, knowledge of the type of material and the geometry of the bodies usually allows for an approximate estimation of the coefficient of restitution.