Collision

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In physics, collision means the action of a system of bodies exchanging momentum during a period of time in which all external forces can be neglected.

Contents 1 Dynamics 2 Billiards 3 Traffic 4 See also 5 External links

[edit] Dynamics

Collisions involve forces (there is a change in velocity). Collisions can be elastic, meaning they conserve energy and momentum, inelastic, meaning they conserve momentum but not energy, or totally inelastic (or plastic), meaning they conserve momentum and the two objects stick together.

The magnitude of the velocity difference at impact is called the closing speed.

The field of dynamics is concerned with moving and colliding objects.

[edit] Billiards

In billiards, collisions play an important role. 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 low-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 appears to be an important fact that many professional billiard players take into account.

Consider an elastic collision in 2 dimensions of any 2 masses m₁ and m₂, with respective initial and final velocities v₁, V₁ and v₂, V₂

Collision in the x Direction: m₁v₁ = m₁V₁cosΦ+m₂V₂cosθ

Collision in the y Direction: 0 = m₁V₁sinΦ-m₂V₂sinθ

Conservation of Energy for Elastic Collision: 1/2m₁v₁² = 1/2m₁V₁²+1/2m₂V₂²

Now consider the case m₁ = m₂, we then obtain 3 equations: 1. v₁² = V₁²+V₂². 2. v₁ = V₁cosΦ+V₂cosθ. 3. 0 = V₁sinΦ-V₂sinθ.

So the vector v₁=V₁+V₂.

The dot product of the vector v₁ yields v₁•v₁ = V₁²+V₂²+2V₁V₂ = v₁²

Equation 1 tells us however that v₁² = V₁²+V₂² and so 2V₁V₂ = 0

Now, 2V₁V₂ = V₁V₂cos(θ+Φ) = 0 so cos(θ+Φ)=0 and θ+Φ=90°.

[edit] Traffic

In traffic such a collision can be between two vehicles, a vehicle and a person, a vehicle and an object, two persons or a person and an object (and more if an animal is involved). It is an accident or even a disaster. At level crossings sometimes a train collides with a vehicle or person. Due to the velocity and mass of a train it needs a long distance to stop, typically longer than the train driver can see ahead. When a train collides with a car this is more likely to be deadly for the people in the car than for those in the train, because the train has more mass and momentum.

[edit] See also

• Collision detection
• Car accident
• Elastic collision
• Inelastic collision
• Mid-air collision
• Friction
• Collision (physical attack)
• Projectile
• Space debris
• Impact event
• Impact crater
• Kinetic theory - collisions between molecules

[edit] External links

• Three Dimensional Collision - Oblique inelastic collision between two homogeneous spheres.
• Two Dimensional Collision - Java applet that simulates elastic collisions.
• One Dimensional Collision - One Dimensional Collision Flash Applet as well as theory behind it.