Everything about Collisions totally explained
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.
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.
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 m
1 and m
2, with respective initial and final velocities v
1, V
1 and v
2, V
2
Collision in the x Direction: m
1v
1 = m
1V
1cosΦ+m
2V
2cosθ
Collision in the y Direction: 0 = m
1V
1sinΦ-m
2V
2sinθ
Conservation of Energy for Elastic Collision: 1/2m
1v
12 = 1/2m
1V
12+1/2m
2V
22
Now consider the case m
1 = m
2, we then obtain 3 equations:
1. v
12 = V
12+V
22.
2. v
1 = V
1cosΦ+V
2cosθ.
3. 0 = V
1sinΦ-V
2sinθ.
So the vector
v1=
V1+
V2.
The dot product of the vector
v1 yields
v1•v1 = V
12+V
22+2
V1V2 = v
12
Equation 1 tells us however that v
12 = V
12+V
22 and so 2
V1V2 = 0
Now, 2
V1V2 = V
1V
2cos(θ+Φ) = 0 so cos(θ+Φ)=0 and θ+Φ=90°.
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.
Further Information
Get more info on 'Collisions'.
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