27:
219:. 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
167:, 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
802:
59:
751:
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
65:
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
136:. 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. An inelastic collision is sometimes also called a
497:
70:
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
623:
740:
752:
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
776:
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
781:
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
522:
849:
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).
642:
66:
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.
50:
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.
186:. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are almost perfectly elastic.
114:
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
106:; such collisions involve objects coming to a full stop. A "perfectly inelastic" collision (also called a "perfectly plastic" collision) is a
1069:
1063:
496:
976:
147:
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
829:
8.8). In particular, hypervelocity is velocity so high that the strength of materials upon impact is very small compared to
1001:
130:. If most of the kinetic energy is conserved (i.e. the objects continue moving afterwards), the collision is said to be
1044:
1011:
152:
765:
1057:
92:
156:
107:
871:
507:
216:
168:
164:
20:
747:
The reduction of total kinetic energy is equal to the total kinetic energy before the collision in a
806:
748:
122:
and bystanders should a crash occur - the frame of the car absorbs the energy of the crash instead.
618:{\displaystyle m_{a}\mathbf {u} _{a}+m_{b}\mathbf {u} _{b}=\left(m_{a}+m_{b}\right)\mathbf {v} \,}
942:
911:
735:{\displaystyle \mathbf {v} ={\frac {m_{a}\mathbf {u} _{a}+m_{b}\mathbf {u} _{b}}{m_{a}+m_{b}}}}
969:
511:
183:
111:
16:
Instance of two or more bodies physically contacting each other within a short period of time
790:
179:
62:
841:
behave alike under hypervelocity impact. An impact under extreme hypervelocity results in
8:
906:
876:
503:
126:
101:
100:
as heat, sound, etc. or absorbed by the objects themselves), the collision is said to be
1090:
1085:
866:
1032:
1040:
1007:
886:
881:
208:
143:
131:
119:
30:
A 3D simulation demonstrating a collision with a ball knocking over a bunch of blocks
950:
822:
212:
46:
on each other in a relatively short time. Although the most common use of the word
83:. What distinguishes different types of collisions is whether they also conserve
115:
782:
484:
204:
84:
1079:
954:
896:
853:
163:
The degree to which a collision is elastic or inelastic is quantified by the
87:
of the system before and after the collision. Collisions are of three types:
75:). The magnitude of the velocity difference just before impact is called the
901:
846:
826:
778:
410:
175:
97:
178:
approach perfectly elastic collisions, as do scattering interactions of
920:
753:
200:
850:
786:
26:
915:
891:
842:
818:
810:
80:
72:
999:
830:
35:
761:
757:
1060:- Oblique inelastic collision between two homogeneous spheres.
801:
838:
834:
311:. Conservation of energy for an elastic collision gives (1/2)
58:
43:
19:
This article is about physics models. For accidents, see
825:(11,000 km/h, 6,700 mph, 10,000 ft/s, or
514:. It is necessary to consider conservation of momentum:
785:(sometimes called a "force plate") as well as detailed
96:. If most or all of the total kinetic energy is lost (
645:
525:
211:, and the balls roll on a surface that produces low
734:
617:
413:of each side of the former equation with itself, |
1077:
462:. Comparing this with the latter equation gives
634:is the final velocity, which is hence given by
110:of inelastic collision in which the two bodies
42:is any event in which two or more bodies exert
490:
1030:
766:derivation of the Tsiolkovsky rocket equation
215:, their behavior is often used to illustrate
856:are also examples of hypervelocity impacts.
805:Video of the hypervelocity impact of NASA’s
1003:Critical technologies for national defense
1000:Air Force Institute of Technology (1991).
1072:- Two Dimensional Collision Flash Applet.
1066:- One Dimensional Collision Flash Applet.
967:
614:
800:
796:
155:and cannot occur in reality, due to the
57:
25:
1034:The Principles of Statistical Mechanics
940:
1078:
476:= 0, so they are perpendicular unless
53:
793:(sometimes termed kinetic) analysis.
233:, with respective initial velocities
199:Collisions play an important role in
968:Alciatore, David G. (January 2006).
771:
993:
171:is defined only along this line.
13:
14:
1102:
1051:
483:is the zero vector (which occurs
272:. Conservation of momentum gives
203:. Because the collisions between
1039:Reissued (1979) New York: Dover
694:
669:
647:
610:
563:
538:
495:
982:from the original on 2022-10-09
961:
934:
1:
1024:
93:Perfectly inelastic collision
194:
157:second law of thermodynamics
7:
1058:Three Dimensional Collision
859:
821:, approximately over 3,000
817:Hypervelocity is very high
491:Perfect inelastic collision
487:the collision is head-on).
189:
182:which are deflected by the
10:
1107:
1037:. Oxford: Clarendon Press.
872:Coefficient of restitution
510:, the colliding particles
508:coefficient of restitution
169:coefficient of restitution
165:coefficient of restitution
79:. All collisions conserve
21:Collision (disambiguation)
18:
1070:Two Dimensional Collision
1064:One Dimensional Collision
941:Schmidt, Paul W. (2019).
353:|. Now consider the case
955:10.1036/1097-8542.149000
927:
749:center of momentum frame
912:Kinetic theory of gases
258:, and final velocities
217:Newton's laws of motion
120:safety of the occupants
1031:Tolman, R. C. (1938).
814:
736:
619:
151:. Such a system is an
67:
31:
1006:. AIAA. p. 287.
943:"Collision (physics)"
914:- collisions between
804:
797:Hypervelocity impacts
737:
620:
184:electromagnetic force
61:
29:
643:
523:
180:sub-atomic particles
907:Inelastic collision
877:Collision detection
504:inelastic collision
127:Inelastic collision
54:Types of collisions
867:Ballistic pendulum
815:
732:
615:
138:plastic collision.
68:
32:
970:"TP 3.1 90° rule"
887:Elastic collision
882:Contact mechanics
823:meters per second
807:Deep Impact probe
772:Animal locomotion
730:
149:perfectly elastic
144:Elastic collision
1098:
1038:
1018:
1017:
997:
991:
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833:stresses. Thus,
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213:rolling friction
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506:, i.e., a zero
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1052:External links
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947:Access Science
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783:force platform
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485:if and only if
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409:|. Taking the
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205:billiard balls
196:
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174:Collisions in
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85:kinetic energy
55:
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15:
9:
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3:
2:
1103:
1092:
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1084:
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1045:0-486-63896-0
1042:
1036:
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1015:
1013:1-56347-009-8
1009:
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978:
971:
964:
956:
952:
948:
944:
937:
933:
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897:Impact crater
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764:(compare the
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502:In a perfect
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108:limiting case
105:
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78:
77:closing speed
74:
64:
60:
51:
49:
45:
41:
37:
28:
22:
1033:
1002:
995:
984:. Retrieved
963:
946:
936:
902:Impact event
843:vaporization
816:
775:
746:
631:
629:
501:
494:
477:
470:
463:
456:
449:
442:
435:
428:
421:
414:
403:
396:
389:
382:
375:
368:
367:: we obtain
361:
354:
347:
340:
333:
326:
319:
312:
305:
299:
292:
286:
279:
273:
266:
259:
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234:
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220:
198:
173:
162:
153:idealization
148:
142:
137:
132:
125:
116:is by design
102:
91:
76:
69:
47:
39:
33:
779:prosthetics
411:dot product
207:are nearly
176:ideal gases
1080:Categories
1025:References
986:2008-03-08
921:Projectile
754:projectile
201:cue sports
118:, for the
98:dissipated
63:Deflection
1091:Mechanics
1086:Collision
916:molecules
851:Meteorite
809:on comet
787:kinematic
760:applying
339:| + (1/2)
325:| = (1/2)
195:Billiards
103:inelastic
48:collision
40:collision
977:Archived
892:Friction
860:See also
847:impactor
831:inertial
819:velocity
811:Tempel 1
512:coalesce
190:Examples
112:coalesce
81:momentum
73:velocity
854:craters
845:of the
791:dynamic
756:, or a
209:elastic
133:elastic
36:physics
1043:
1010:
839:fluids
835:metals
762:thrust
758:rocket
630:where
247:where
44:forces
980:(PDF)
973:(PDF)
928:Notes
448:| + 2
441:| + |
402:| + |
395:| = |
388:and |
1041:ISBN
1008:ISBN
837:and
827:Mach
789:and
420:| =
265:and
240:and
226:and
38:, a
951:doi
768:).
434:= |
34:In
1082::
975:.
949:.
945:.
381:+
374:=
360:=
298:+
285:=
254:=
1047:.
1016:.
989:.
957:.
953::
813:.
725:b
721:m
717:+
712:a
708:m
700:b
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688:b
684:m
680:+
675:a
670:u
663:a
659:m
652:=
648:v
632:v
611:v
606:)
600:b
596:m
592:+
587:a
583:m
578:(
574:=
569:b
564:u
557:b
553:m
549:+
544:a
539:u
532:a
528:m
481:1
478:V
474:2
471:V
469:•
467:1
464:V
460:2
457:V
455:•
453:1
450:V
446:2
443:V
439:1
436:V
432:1
429:u
427:•
425:1
422:u
418:1
415:u
407:2
404:V
400:1
397:V
393:1
390:u
386:2
383:V
379:1
376:V
372:1
369:u
365:2
362:m
358:1
355:m
351:2
348:V
346:|
344:2
341:m
337:1
334:V
332:|
330:1
327:m
323:1
320:u
318:|
316:1
313:m
309:2
306:V
303:2
300:m
296:1
293:V
290:1
287:m
283:1
280:u
277:1
274:m
270:2
267:V
263:1
260:V
256:0
252:2
249:u
245:2
242:u
238:1
235:u
231:2
228:m
224:1
221:m
159:.
23:.
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