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{{short description|Instance of two or more bodies physically contacting each other within a short period of time}}
{{other uses}}
{{About|physics models|accidents|}}
{{redirect|Jostle|the racehorse|Jostle (horse)}}
]
{{short description|Instance of two or more bodies physically contacting each other within short period of time}}
In ], a '''collision''' is any event in which two or more bodies exert ]s on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the force. In ], a '''collision''' is any event in which two or more bodies exert ]s on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the force.<ref>{{Cite journal|last=Schmidt|first=Paul W.|date=2019|title=Collision (physics)|url=https://www.accessscience.com/content/collision-physics/149000|journal=Access Science|language=en|doi=10.1036/1097-8542.149000}}</ref>


== Types of collisions ==
Some examples of physical interactions that scientists would consider collisions are the following:
* When an insect lands on a plant's leaf, its legs are said to collide with the leaf.
* When a cat strides across a lawn, each contact that its paws make with the ground is considered a collision, as well as each brush of its fur against a blade of grass.
* When a boxer throws a punch, their fist is said to collide with the opponent's body.
* When an ] merges with a ], they are considered to collide.

Some colloquial uses of the word collision are the following:
* A ] involves at least one automobile.
* A ] occurs between airplanes.
* A ] accurately involves at least two moving maritime vessels hitting each other; the related term, '']'', describes when a moving ship strikes a stationary object (often, but not always, another ship).

In physics, collisions can be classified by the change in the total ] of the system before and after the collision:

* If most or all of the total kinetic energy is lost (] as heat, sound, etc. or absorbed by the objects themselves), the collision is said to be ]; such collisions involve objects coming to a full stop. An example of such a collision is a car crash, as cars crumple inward when crashing, rather than bouncing off of each other. This ], for the ] and bystanders should a crash occur - the frame of the car absorbs the energy of the crash instead.
* If most of the kinetic energy is conserved (i.e. the objects continue moving afterwards), the collision is said to be ]. An example of this is a baseball bat hitting a baseball - the kinetic energy of the bat is transferred to the ball, greatly increasing the ball's velocity. The sound of the bat hitting the ball represents the loss of energy.
* And if all of the total kinetic energy is conserved (i.e. no energy is released as sound, heat, etc.), the collision is said to be ''perfectly elastic''. Such a system is an ] and cannot occur in reality, due to the ].

== Physics ==
] happens when an object hits a plane surface. If the kinetic energy after impact is the same as before impact, it is an elastic collision. If kinetic energy is lost, it is an inelastic collision. The diagram does not show whether the illustrated collision was elastic or inelastic, because no velocities are provided. The most one can say is that the collision was not perfectly inelastic, because in that case the ball would have stuck to the wall.]] ] happens when an object hits a plane surface. If the kinetic energy after impact is the same as before impact, it is an elastic collision. If kinetic energy is lost, it is an inelastic collision. The diagram does not show whether the illustrated collision was elastic or inelastic, because no velocities are provided. The most one can say is that the collision was not perfectly inelastic, because in that case the ball would have stuck to the wall.]]
Collision is short-duration interaction between two bodies or more than two bodies simultaneously causing change in motion of bodies involved due to internal forces acted between them during this. Collisions involve forces (there is a change in ]). The magnitude of the velocity difference just before impact is called the '''closing speed'''. All collisions conserve ]. What distinguishes different types of collisions is whether they also conserve ]. The line of impact is the line that is collinear to the common normal of the surfaces that are closest or in contact during impact. This is the line along which internal force of collision acts during impact, and Newton's ] is defined only along this line. Collisions are of three types: Collision is short-duration interaction between two bodies or more than two bodies simultaneously causing change in motion of bodies involved due to internal forces acted between them during this. Collisions involve forces (there is a change in ]). The magnitude of the velocity difference just before impact is called the '''closing speed'''. All collisions conserve ]. What distinguishes different types of collisions is whether they also conserve ] of the system before and after the collision. Collisions are of two types:
#''']''' If all of the total kinetic energy is conserved (i.e. no energy is released as sound, heat, etc.), the collision is said to be ''perfectly elastic''. Such a system is an ] and cannot occur in reality, due to the ].
#perfectly elastic collision
#''']'''. If most or all of the total kinetic energy is lost (] as heat, sound, etc. or absorbed by the objects themselves), the collision is said to be ]; such collisions involve objects coming to a full stop. An example of this is a baseball bat hitting a baseball - the kinetic energy of the bat is transferred to the ball, greatly increasing the ball's velocity. The sound of the bat hitting the ball represents the loss of energy. A "perfectly inelastic" collision (also called a "perfectly plastic" collision) is a ] of inelastic collision in which the two bodies ] after impact. An example of such a collision is a car crash, as cars crumple inward when crashing, rather than bouncing off of each other. This ], for the ] and bystanders should a crash occur - the frame of the car absorbs the energy of the crash instead.
#inelastic collision
#perfectly inelastic collision.


The degree to which a collision is elastic or inelastic is quantified by the ], a value that generally ranges between zero and one. A perfectly elastic collision has a coefficient of restitution of one; a perfectly inelastic collision has a coefficient of restitution of zero. The line of impact is the line that is collinear to the common normal of the surfaces that are closest or in contact during impact. This is the line along which internal force of collision acts during impact, and Newton's ] is defined only along this line.
Specifically, collisions can either be ''],'' meaning they conserve both momentum and kinetic energy, or ''],'' meaning they conserve momentum but not kinetic energy.

An inelastic collision is sometimes also called a ''plastic collision.'' A “perfectly inelastic” collision (also called a "perfectly plastic" collision) is a ] of inelastic collision in which the two bodies ] after impact.

The degree to which a collision is elastic or inelastic is quantified by the ], a value that generally ranges between zero and one. A perfectly elastic collision has a coefficient of restitution of one; a perfectly inelastic collision has a coefficient of restitution of zero.

==Types of collisions==
There are two types of collisions between two bodies - 1) Head-on collisions or one-dimensional collisions - where the velocity of each body just before impact is along the line of impact, and 2) Non-head-on collisions, oblique collisions or two-dimensional collisions - where the velocity of each body just before impact is not along the line of impact.

According to the coefficient of restitution, there are two special cases of any collision as written below:

# A perfectly ] is defined as one in which there is no loss of ] in the collision. In reality, any macroscopic collision between objects will convert some kinetic energy to ] and other forms of energy, so no large-scale impacts are perfectly elastic. However, some problems are sufficiently close to perfectly elastic that they can be approximated as such. In this case, the coefficient of restitution equals one.
# An ] is one in which part of the kinetic energy is changed to some other form of energy in the collision. ] is conserved in inelastic collisions (as it is for elastic collisions), but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy. In this case, coefficient of restitution is not equal to one.

In any type of collision there is a phase when for a moment colliding bodies have the same velocity along the line of impact.Then the kinetic energy of bodies reduces to its minimum during this phase and may be called a maximum deformation phase for which momentarily the coefficient of restitution becomes one.


Collisions in ] approach perfectly elastic collisions, as do scattering interactions of ] which are deflected by the ]. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are almost perfectly elastic. Collisions in ] approach perfectly elastic collisions, as do scattering interactions of ] which are deflected by the ]. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are almost perfectly elastic.


==Examples==
Collisions between hard spheres may be nearly elastic, so it is useful to calculate the limiting case of an elastic collision. The assumption of conservation of momentum as well as the conservation of kinetic energy makes possible the calculation of the final velocities in two-body collisions.

==Allision==
In ], it is occasionally desirable to distinguish between the situation of a vessel striking a moving object, and that of it striking a stationary object. The word "allision" is then used to mean the striking of a stationary object, while "collision" is used to mean the striking of a moving object.<ref>merriam-webster.com, "". Accessed November 7, 2014.</ref><ref>{{cite journal |title=Admiralty Court Rejects Equal Division Rule and Apportions Damages Unequally in Multiple Fault Collision Case |journal=Columbia Law Review |volume=63 |issue=3 |date=March 1963 |page=554 footnote 1 |doi=10.2307/1120603 |jstor=1120603 |quote=The striking by a vessel of a fixed object such as a bridge, technically termed 'allision' rather than 'collision'}}.</ref><ref>{{cite journal |first=Wayne K. |last=Talley |title=Safety Investments and Operating Conditions: Determinants of Accident Passenger-Vessel Damage Cost |journal=Southern Economic Journal |volume=61 |issue=3 |date=January 1995 |jstor=1061000 |page=823, note 11 |doi=10.2307/1061000 |quote=collision&mdash;vessel struck or was struck by another vessel on the water surface, or struck a stationary object, not another ship (an allision)}}.</ref> Thus, when two vessels run against each other, courts typically use the term collision whereas when one vessel runs against another, they typically use the term allision.<ref>{{cite journal |last1=Healy |first1=Nicholas J. |last2=Sweeney |first2=Joseph C. |title=Basic Principles of the Law of Collision |journal=Journal of Maritme Law and Commerce |date=July-October 1991 |volume=22 |issue=3 |page=359}}</ref> The fixed object could also be a ] or ]. While there is no great difference between the two terms and often they are even used interchangeably, determining the difference helps clarify the circumstances of emergencies and adapt accordingly.<ref>{{Cite web|url=https://response.restoration.noaa.gov/about/media/you-say-collision-i-say-allision-lets-sort-whole-thing-out.html|title=You Say Collision, I Say Allision; Let's Sort the Whole Thing Out {{!}} response.restoration.noaa.gov|website=response.restoration.noaa.gov|language=en|access-date=2018-08-28}}</ref> In the case of ''Vane Line Bunkering, Inc. v. Natalie D M/V,'' it was established that there was the presumption that the moving vessel is at fault, stating that "''presumption derives from the common-sense observation that moving vessels do not usually collide with stationary objects unless the vessel is mishandled in some way.''”<ref>{{Cite news|url=https://www.leagle.com/decision/infdco20180222d82|title=Vane Line Bunkering, Inc. {{!}} Civil Action No. 17-1882. {{!}} 20180222d82 {{!}} Leagle.com|last=Judge|first=ELDON E. FALLON, District|work=Leagle|access-date=2018-08-28|language=en}}</ref> This is also referred to{{by whom|date=December 2019}} as ''The Oregon Rule.''<ref>See , especially paragraph 10.</ref>

==Analytical vs. numerical approaches towards resolving collisions==
Relatively few problems involving collisions can be solved analytically; the remainder require ]. An important problem in simulating collisions is determining whether two objects have in fact collided. This problem is called ].

{{cleanup|section|date=February 2011}}

==Examples of collisions that can be solved analytically==


===Billiards=== ===Billiards===
{{Anchor|Cue sports}}Collisions play an important role in ]. Because the collisions between ] are nearly elastic, and the balls roll on a surface that produces low ], their behavior is often used to illustrate ]. After a zero-friction collision of a moving ball with a stationary one of equal mass, the angle between the directions of the two balls is 90 degrees. This is an important fact that professional billiards players take into account,<ref>{{cite web|last=Alciatore |first=David G. |date=January 2006 |url=http://billiards.colostate.edu/technical_proofs/TP_3-1.pdf |title=TP 3.1 90° rule |access-date=2008-03-08 }}</ref> although it assumes the ball is moving without any impact of friction across the table rather than rolling with friction. {{Anchor|Cue sports}}Collisions play an important role in ]. Because the collisions between ] are nearly ], and the balls roll on a surface that produces low ], their behavior is often used to illustrate ]. After a zero-friction collision of a moving ball with a stationary one of equal mass, the angle between the directions of the two balls is 90 degrees. This is an important fact that professional billiards players take into account,<ref>{{cite web|last=Alciatore |first=David G. |date=January 2006 |url=http://billiards.colostate.edu/technical_proofs/TP_3-1.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://billiards.colostate.edu/technical_proofs/TP_3-1.pdf |archive-date=2022-10-09 |url-status=live |title=TP 3.1 90° rule |access-date=2008-03-08 }}</ref> although it assumes the ball is moving without any impact of friction across the table rather than rolling with friction.
Consider an elastic collision in two dimensions of any two masses ''m''<sub>1</sub> and ''m''<sub>2</sub>, with respective initial velocities '''u'''<sub>1</sub> and '''u'''<sub>2</sub> where '''u'''<sub>2</sub> = '''0''', and final velocities '''V'''<sub>1</sub> and '''V'''<sub>2</sub>. Consider an elastic collision in two dimensions of any two masses ''m''<sub>1</sub> and ''m''<sub>2</sub>, with respective initial velocities '''u'''<sub>1</sub> and '''u'''<sub>2</sub> where '''u'''<sub>2</sub> = '''0''', and final velocities '''V'''<sub>1</sub> and '''V'''<sub>2</sub>.
Conservation of momentum gives ''m''<sub>1</sub>'''u'''<sub>1</sub> = ''m''<sub>1</sub>'''V'''<sub>1</sub> + ''m''<sub>2</sub>'''V'''<sub>2</sub>. Conservation of momentum gives ''m''<sub>1</sub>'''u'''<sub>1</sub> = ''m''<sub>1</sub>'''V'''<sub>1</sub> + ''m''<sub>2</sub>'''V'''<sub>2</sub>.
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Taking the ] of each side of the former equation with itself, |'''u'''<sub>1</sub>|<sup>2</sup> = '''u'''<sub>1</sub>•'''u'''<sub>1</sub> = |'''V'''<sub>1</sub>|<sup>2</sup> + |'''V'''<sub>2</sub>|<sup>2</sup> + 2'''V'''<sub>1</sub>•'''V'''<sub>2</sub>. Comparing this with the latter equation gives '''V'''<sub>1</sub>•'''V'''<sub>2</sub> = 0, so they are perpendicular unless '''V'''<sub>1</sub> is the zero vector (which occurs ] the collision is head-on). Taking the ] of each side of the former equation with itself, |'''u'''<sub>1</sub>|<sup>2</sup> = '''u'''<sub>1</sub>•'''u'''<sub>1</sub> = |'''V'''<sub>1</sub>|<sup>2</sup> + |'''V'''<sub>2</sub>|<sup>2</sup> + 2'''V'''<sub>1</sub>•'''V'''<sub>2</sub>. Comparing this with the latter equation gives '''V'''<sub>1</sub>•'''V'''<sub>2</sub> = 0, so they are perpendicular unless '''V'''<sub>1</sub> is the zero vector (which occurs ] the collision is head-on).


===Perfectly inelastic collision=== ===Perfect inelastic collision===
] ]


In a perfectly inelastic collision, i.e., a zero ], the colliding particles ]. It is necessary to consider conservation of momentum: In a perfect ], i.e., a zero ], the colliding particles ]. It is necessary to consider conservation of momentum:
::<math>m_a \mathbf u_a + m_b \mathbf u_b = \left( m_a + m_b \right) \mathbf v \,</math> ::<math>m_a \mathbf u_a + m_b \mathbf u_b = \left( m_a + m_b \right) \mathbf v \,</math>
where '''v''' is the final velocity, which is hence given by where '''v''' is the final velocity, which is hence given by
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The reduction of total kinetic energy is equal to the total kinetic energy before the collision in a ] with respect to the system of two particles, because in such a frame the kinetic energy after the collision is zero. In this frame most of the kinetic energy before the collision is that of the particle with the smaller mass. In another frame, in addition to the reduction of kinetic energy there may be a transfer of kinetic energy from one particle to the other; the fact that this depends on the frame shows how relative this is. The reduction of total kinetic energy is equal to the total kinetic energy before the collision in a ] with respect to the system of two particles, because in such a frame the kinetic energy after the collision is zero. In this frame most of the kinetic energy before the collision is that of the particle with the smaller mass. In another frame, in addition to the reduction of kinetic energy there may be a transfer of kinetic energy from one particle to the other; the fact that this depends on the frame shows how relative this is.
With time reversed we have the situation of two objects pushed away from each other, e.g. shooting a ], or a ] applying ] (compare the ]). With time reversed we have the situation of two objects pushed away from each other, e.g. shooting a ], or a ] applying ] (compare the ]).

==Examples of collisions analyzed numerically==


===Animal locomotion=== ===Animal locomotion===
Collisions of an animal's foot or paw with the underlying substrate are generally termed ground reaction forces. These collisions are inelastic, as kinetic energy is not conserved. An important research topic in ] is quantifying the forces generated during the foot-ground collisions associated with both disabled and non-disabled gait. This quantification typically requires subjects to walk across a ] (sometimes called a "force plate") as well as detailed ] and ] (sometimes termed kinetic) analysis. Collisions of an animal's foot or paw with the underlying substrate are generally termed ground reaction forces. These collisions are inelastic, as kinetic energy is not conserved. An important research topic in ] is quantifying the forces generated during the foot-ground collisions associated with both disabled and non-disabled gait. This quantification typically requires subjects to walk across a ] (sometimes called a "force plate") as well as detailed ] and ] (sometimes termed kinetic) analysis.


===Hypervelocity impacts===
==Collisions used as an experimental tool==
] on comet ].]]
Collisions can be used as an experimental technique to study material properties of objects and other physical phenomena.
Hypervelocity is very high ], approximately over 3,000 ] (11,000&nbsp;km/h, 6,700&nbsp;mph, 10,000&nbsp;ft/s, or ] 8.8). In particular, hypervelocity is velocity so high that the strength of materials upon impact is very small compared to ]l stresses.<ref Name="AIAA">{{cite book

|title= Critical technologies for national defense
===Space exploration===
|author= Air Force Institute of Technology
An object may deliberately be made to crash-land on another celestial body, to do measurements and send them to Earth before being destroyed, or to allow instruments elsewhere to observe the effect. See e.g.:
|year= 1991
*During ], ], ], ] and ], the ] (the rocket's third stage) was crashed into the ] in order to perform seismic measurement used for characterizing the lunar core.
|publisher= AIAA
* ]
|location=
* ] - ] satellite
|isbn= 1-56347-009-8
* ] - ] probe
|page= 287

|url= https://books.google.com/books?id=HsEorBWNGWwC&dq=Hypervelocity+3%2C000&pg=PA287}}</ref> Thus, ]s and ]s behave alike under hypervelocity impact. An impact under extreme hypervelocity results in ] of the ] and target. For structural metals, hypervelocity is generally considered to be over 2,500&nbsp;m/s (5,600&nbsp;mph, 9,000&nbsp;km/h, 8,200&nbsp;ft/s, or Mach 7.3). ] ] are also examples of hypervelocity impacts.
===Mathematical description of molecular collisions===
Let the linear, angular and internal momenta of a ] be given by the set of ''r'' variables { ''p''<sub>''i''</sub> }. The state of a molecule may then be described by the range ''δw''<sub>''i''</sub> = δ''p''<sub>1</sub>δ''p''<sub>2</sub>δ''p''<sub>3</sub> ... δ''p''<sub>''r''</sub>&hairsp;. There are many such ranges corresponding to different states; a specific state may be denoted by the index ''i''. Two molecules undergoing a collision can thus be denoted by (''i'', ''j'') (Such an ordered pair is sometimes known as a ''constellation''.)
It is convenient to suppose that two molecules exert a negligible effect on each other unless their center of gravity approach within a critical distance ''b''. A collision therefore begins when the respective centers of gravity arrive at this critical distance, and is completed when they again reach this critical distance on their way apart. Under this model, a collision is completely described by the matrix <math>\begin{pmatrix}i&j\\k&l\end{pmatrix} </math>, which refers to the constellation (''i'', ''j'') before the collision, and the (in general different) constellation (''k'', ''l'') after the collision.
This notation is convenient in proving Boltzmann's ] of ].

==Attack by means of a deliberate collision==
Types of attack by means of a deliberate collision include:
* striking with the body: unarmed ], ], ]ing
* striking with a weapon, such as a ], ] or ]
* ] with an object or vehicle, e.g.:
**], the practice of driving a car into a building in order to break in
** a ], medieval weapon used for breaking down large doors, also a modern version is used by police forces during raids
An attacking collision with a distant object can be achieved by throwing or launching a ].


==See also== ==See also==
{{colbegin}} {{colbegin}}
*] *]
*]
*] *]
*]
*] *]
*]
*] *]
*] *]
*]
*] *]
*] *]
*] *]
*]<br /> - collisions between ]s *] - collisions between ]s
*]
*] *]
*]
*]
*]
{{colend}} {{colend}}


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==External links== ==External links==
* - Oblique inelastic collision between two homogeneous spheres. * - Oblique inelastic collision between two homogeneous spheres.
* - One Dimensional Collision Flash Applet. * - One Dimensional Collision Flash Applet.
* - Two Dimensional Collision Flash Applet. * - Two Dimensional Collision Flash Applet.

Latest revision as of 09:34, 29 November 2024

Instance of two or more bodies physically contacting each other within a short period of time This article is about physics models. For accidents, see Collision (disambiguation).
A 3D simulation demonstrating collision with a ball knocking over some blocks.
A 3D simulation demonstrating a collision with a ball knocking over a bunch of blocks

In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word collision refers to incidents in which two or more objects collide with great force, the scientific use of the term implies nothing about the magnitude of the force.

Types of collisions

Deflection happens when an object hits a plane surface. If the kinetic energy after impact is the same as before impact, it is an elastic collision. If kinetic energy is lost, it is an inelastic collision. The diagram does not show whether the illustrated collision was elastic or inelastic, because no velocities are provided. The most one can say is that the collision was not perfectly inelastic, because in that case the ball would have stuck to the wall.

Collision is short-duration interaction between two bodies or more than two bodies simultaneously causing change in motion of bodies involved due to internal forces acted between them during this. Collisions involve forces (there is a change in velocity). The magnitude of the velocity difference just before impact is called the closing speed. All collisions conserve momentum. What distinguishes different types of collisions is whether they also conserve kinetic energy of the system before and after the collision. Collisions are of two types:

  1. Elastic collision If all of the total kinetic energy is conserved (i.e. no energy is released as sound, heat, etc.), the collision is said to be perfectly elastic. Such a system is an idealization and cannot occur in reality, due to the second law of thermodynamics.
  2. Inelastic collision. If most or all of the total kinetic energy is lost (dissipated as heat, sound, etc. or absorbed by the objects themselves), the collision is said to be inelastic; such collisions involve objects coming to a full stop. An example of this is a baseball bat hitting a baseball - the kinetic energy of the bat is transferred to the ball, greatly increasing the ball's velocity. The sound of the bat hitting the ball represents the loss of energy. A "perfectly inelastic" collision (also called a "perfectly plastic" collision) is a limiting case of inelastic collision in which the two bodies coalesce after impact. An example of such a collision is a car crash, as cars crumple inward when crashing, rather than bouncing off of each other. This is by design, for the safety of the occupants and bystanders should a crash occur - the frame of the car absorbs the energy of the crash instead.

The degree to which a collision is elastic or inelastic is quantified by the coefficient of restitution, a value that generally ranges between zero and one. A perfectly elastic collision has a coefficient of restitution of one; a perfectly inelastic collision has a coefficient of restitution of zero. The line of impact is the line that is collinear to the common normal of the surfaces that are closest or in contact during impact. This is the line along which internal force of collision acts during impact, and Newton's coefficient of restitution is defined only along this line.

Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are almost perfectly elastic.

Examples

Billiards

Collisions play an important role in cue sports. Because the collisions between billiard balls are nearly elastic, and the balls roll on a surface that produces low rolling friction, their behavior is often used to illustrate Newton's laws of motion. After a zero-friction collision of a moving ball with a stationary one of equal mass, the angle between the directions of the two balls is 90 degrees. This is an important fact that professional billiards players take into account, although it assumes the ball is moving without any impact of friction across the table rather than rolling with friction. Consider an elastic collision in two dimensions of any two masses m1 and m2, with respective initial velocities u1 and u2 where u2 = 0, and final velocities V1 and V2. Conservation of momentum gives m1u1 = m1V1 + m2V2. Conservation of energy for an elastic collision gives (1/2)m1|u1| = (1/2)m1|V1| + (1/2)m2|V2|. Now consider the case m1 = m2: we obtain u1 = V1 + V2 and |u1| = |V1| + |V2|. Taking the dot product of each side of the former equation with itself, |u1| = u1•u1 = |V1| + |V2| + 2V1•V2. Comparing this with the latter equation gives V1•V2 = 0, so they are perpendicular unless V1 is the zero vector (which occurs if and only if the collision is head-on).

Perfect inelastic collision

a completely inelastic collision between equal masses

In a perfect inelastic collision, i.e., a zero coefficient of restitution, the colliding particles coalesce. It is necessary to consider conservation of momentum:

m a u a + m b u b = ( m a + m b ) v {\displaystyle m_{a}\mathbf {u} _{a}+m_{b}\mathbf {u} _{b}=\left(m_{a}+m_{b}\right)\mathbf {v} \,}

where v is the final velocity, which is hence given by

v = m a u a + m b u b m a + m b {\displaystyle \mathbf {v} ={\frac {m_{a}\mathbf {u} _{a}+m_{b}\mathbf {u} _{b}}{m_{a}+m_{b}}}}

The reduction of total kinetic energy is equal to the total kinetic energy before the collision in a center of momentum frame with respect to the system of two particles, because in such a frame the kinetic energy after the collision is zero. In this frame most of the kinetic energy before the collision is that of the particle with the smaller mass. In another frame, in addition to the reduction of kinetic energy there may be a transfer of kinetic energy from one particle to the other; the fact that this depends on the frame shows how relative this is. With time reversed we have the situation of two objects pushed away from each other, e.g. shooting a projectile, or a rocket applying thrust (compare the derivation of the Tsiolkovsky rocket equation).

Animal locomotion

Collisions of an animal's foot or paw with the underlying substrate are generally termed ground reaction forces. These collisions are inelastic, as kinetic energy is not conserved. An important research topic in prosthetics is quantifying the forces generated during the foot-ground collisions associated with both disabled and non-disabled gait. This quantification typically requires subjects to walk across a force platform (sometimes called a "force plate") as well as detailed kinematic and dynamic (sometimes termed kinetic) analysis.

Hypervelocity impacts

Video of the hypervelocity impact of NASA’s Deep Impact probe on comet Tempel 1.

Hypervelocity is very high velocity, approximately over 3,000 meters per second (11,000 km/h, 6,700 mph, 10,000 ft/s, or Mach 8.8). In particular, hypervelocity is velocity so high that the strength of materials upon impact is very small compared to inertial stresses. Thus, metals and fluids behave alike under hypervelocity impact. An impact under extreme hypervelocity results in vaporization of the impactor and target. For structural metals, hypervelocity is generally considered to be over 2,500 m/s (5,600 mph, 9,000 km/h, 8,200 ft/s, or Mach 7.3). Meteorite craters are also examples of hypervelocity impacts.

See also

Notes

  1. Schmidt, Paul W. (2019). "Collision (physics)". Access Science. doi:10.1036/1097-8542.149000.
  2. Alciatore, David G. (January 2006). "TP 3.1 90° rule" (PDF). Archived (PDF) from the original on 2022-10-09. Retrieved 2008-03-08.
  3. Air Force Institute of Technology (1991). Critical technologies for national defense. AIAA. p. 287. ISBN 1-56347-009-8.

References

External links

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