Elastic collisions and Newton's law of restitution
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Elastic collisions. Impulse
Equations are omitted for technical reasons - download the original pdf
When two objects collide each exerts a force on the other, the result of which is that one or both cease to move in the same direction as before. Assuming the mass has been unaltered during the collision, and noting that: momentum = mass ´ velocity We conclude that the principle effect of collision is to change the momentum of one or both of the colliding objects. The following diagram shows a ball colliding with a wall. We may consider the wall's momentum to remain unaltered but the ball's momentum does change. The effect of the collision is to change the momentum of the ball. [Diagram goes here - download the original to see it.] In the next diagram we see a ball, A, that collides with a stationary ball, B. The result is that A and B move in the directions shown. The collision has caused a change in the momentum of both A and B. [Diagram goes here - download the original to see it.] Because of the importance of this concept of change of momentum, we give it a special name of impulse. Impulse = change in momentum. The effect of a collision is for one object to cause a change of momentum in another. We say that an impulse has been communicated. Because momentum is a vector, impulse is also a vector. Its units are the same as the units of momentum - that is Newton seconds (N s). Because of the law of conservation of momentum, when two objects, A and B collide, the impulse communicated by A to B must equal the impulse given by B to A. Since impulse is a vector quantity, impulse can be resolved into components. That is impulse can be resolved into, for example, horizontal and vertical components. Then the law of conservation of momentum applies to both the horizontal and vertical components. That is, in a collision between two objects, A and B, the vertical component given by A to B must equal the vertical component given by B to A. A similar rule applies to the horizontal component.
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Contents of
Elastic collisions and Newton's law of restitution
1 Elastic collisions. Impulse
2 Impulse and Newton's law of Restitution
3 The coefficient of restitution
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