Collision

Japanese: 衝突 - しょうとつ

A phenomenon in which two objects gradually approach each other from a distance much greater than their size, and interact with each other for a short time. In most cases, the objects move away from each other again, but there are also cases where the two objects merge. Since the change in potential energy of external forces such as gravity is usually small immediately before and after a collision, excluding interactions, the mechanical energy is often considered to be the energy (1/2) mv ² of the motion of the center of gravity of each object (where m is the total mass of the object and v is the speed of the center of gravity) and the relative motion (rotation, vibration, etc.) with respect to the center of gravity. If the momentum of the two objects just before the collision is p ₁ = m ₁ v ₁ , p ₂ = m ₂ v ₂ , and those just after the collision are p ₁ ' = m ₁ v ₁ ', p ₂ ' = m ₂ v ₂ ', then the law of conservation of momentum as a vector quantity is p ₁ + p ₂ = p ₁ ' + p ₂ ' (1)
is always true. The sum of the angular momentum of two objects is also conserved. However, the kinetic energy of the center of gravity is conserved.

does not necessarily hold true. The total momentum of an object is equal to the momentum of the center of gravity, but the energy is not. We must also consider the kinetic energy of relative motion (internal motion such as rotation and vibration) with respect to the center of gravity, and changes in elastic energy due to deformation, and consider their mutual conversion. Internal motion includes not only vibration and rotation that appear as macroscopic motion, but also the thermal motion of microscopic atoms and molecules. If there is no change in energy other than the center of gravity motion, equation (2) holds true, and the collision in this case is called an elastic collision. If this is not the case, it is called an inelastic collision. In the case of a macroscopic collision between two spheres, the ratio of the magnitude of the normal components at the contact point of the relative velocities v ₂ '- v ₁ ' and v ₂ - v ₁ is called the restitution coefficient or bounce coefficient. It is empirically known that this takes a value between 0 and 1, depending on the material of the spheres. If the restitution coefficient is 0, the two spheres will stick together, and in an elastic collision, the restitution coefficient is 1. Microscopic particles must be treated using quantum mechanics, so wave mechanics is applied, and collision phenomena are treated in the form of wave scattering. For this reason, collisions are often called scattering. Since it is not possible to track the behavior of individual particles, and a flow of many particles is dealt with, the way in which they collide with target particles varies, and the particles that emerge after the collision scatter. In this case, the quantity that is the subject of research is the collision cross section (scattering cross section), which indicates the proportion of particles that emerge in a particular direction. Note that if the type or number of particles changes before and after a collision, it is called a reaction.

[Koide Shoichiro]

[Reference] | Momentum | Scattering | Scattering cross section | Elastic collision

Macroscopic collision of two spheres
©Shogakukan ">

Macroscopic collision of two spheres

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

Japanese:

二つの物体が、その大きさよりずっと大きい距離からしだいに近づき、短い時間だけ相互作用を及ぼし合う現象。ふたたび離れていくことが多いが、2物体が合体してしまう場合もある。衝突の直前と直後で、重力のような外力の位置エネルギーの変化は小さいのが普通なので、相互作用を別にすると、力学的エネルギーとしては、各物体の重心運動のエネルギー(1/2)mv²（mは物体の全質量、vは重心の速さ）と、重心に対する相対運動（回転や振動など）を考えることが多い。2物体が衝突直前にもっていた運動量をp₁＝m₁v₁, p₂＝m₂v₂、衝突直後のそれらをp₁'＝m₁v₁', p₂'＝m₂v₂'とすると、ベクトル量としての運動量保存則
　　p₁＋p₂＝p₁'＋p₂'　(1)
はかならず成り立つ。また2物体の角運動量の和も保存される。しかし、重心運動の運動エネルギーの保存

は成り立つとは限らない。物体の全運動量は重心の運動量に等しいが、エネルギーはそうではなく、重心に対する相対的な運動（回転や振動などの内部運動）の運動エネルギーや変形などによる弾性エネルギーの変化なども考えて、それらの相互転換を考慮しなければいけないからである。内部運動には、巨視的に運動とみえる振動や回転のほかに、微視的な原子・分子の熱運動も含まれる。重心運動以外のエネルギーに変化がなければ(2)式が成り立ち、この場合の衝突は弾性衝突とよばれる。そうでない衝突を非弾性衝突という。巨視的な2球の衝突の場合には、相対速度v₂'－v₁'とv₂－v₁の、接触点における法線成分の大きさの比をとって、反発係数またははねかえり係数とよぶ。これは、球の材質で決まる0と1の間の値をとることが経験的に知られている。衝突で両球がくっついてしまうのは反発係数が0の場合であり、弾性衝突では反発係数は1である。微視的な粒子は量子力学で扱わねばならないので、波動力学が適用され、衝突現象は波の散乱という形式で処理される。このために衝突のことを散乱ということが多い。個々の微粒子の行動の追跡はできず、多数の粒子の流れを扱うので、それと標的粒子との衝突の仕方はさまざまで、衝突して出てくる粒子は散らばる。この場合、どの方向へ出てくる粒子はどのくらいの割合かを示す衝突断面積（散乱断面積）という量が研究の対象となる。なお、衝突前後で粒子の種類や数が変わる場合には反応とよぶ。