# Elastic And Inelastic Collision Problem Solving Pdf

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When starting to investigate collision problems, we usually consider situations that either start or end with a single body. The reason for this self-imposed limitation is that such problems can be solved by applying momentum conservation alone, namely the result that the total linear momentum of an isolated system is constant. The analysis of more general collisions requires the use of other principles in addition to momentum conservation. To illustrate this, we now consider a one-dimensional problem in which two colliding bodies with known masses m sub 1 and m sub 2 , and with known initial velocities u subscript 1 x end and u subscript 2 x end collide and then separate with final velocities v subscript 1 x end and v subscript 2 x end.

The problem is that of finding the two unknowns v subscript 1 x end and v subscript 2 x end. Conservation of momentum in the x -direction provides only one equation linking these two unknowns:.

In the absence of any detailed knowledge about the forces involved in the collision, the usual source of an additional relationship between v subscript 1 x end and v subscript 2 x end comes from some consideration of the translational kinetic energy involved. The precise form of this additional relationship depends on the nature of the collision. Collisions may be classified by comparing the total translational kinetic energy of the colliding bodies before and after the collision.

If there is no change in the total kinetic energy, then the collision is an elastic collision. If the kinetic energy after the collision is less than that before the collision then the collision is an inelastic collision. In some situations e. In the simplest case, when the collision is elastic, the consequent conservation of kinetic energy means that. This equation, together with Equation 1 will allow v subscript 1 x end and v subscript 2 x end to be determined provided the masses and initial velocities have been specified.

We consider this situation in more detail in the next section. Real collisions between macroscopic objects are usually inelastic but some collisions, such as those between steel ball bearings or between billiard balls, are very nearly elastic.

The kinetic energy which is lost in an inelastic collision appears as energy of a different form e. Collisions in which the bodies stick together on collision and move off together afterwards, are examples of completely inelastic collisions. In these cases the maximum amount of kinetic energy, consistent with momentum conservation, is lost.

Momentum conservation usually implies that the final body or bodies must be moving and this inevitably implies that there must be some final kinetic energy; it is the remainder of the initial kinetic energy, after this final kinetic energy has been subtracted, that is lost in a completely inelastic collision.

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## Collisions and conservation laws

Impedance of rigid bodies in one-dimensional elastic collisions. Janilo Santos I, 1 ; Bruna P. In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance matching as a way to understand efficiency of energy transmission in elastic collisions, we find a solution which frames the problem in terms of this conception. We show that the mass of the ball can be seen as a measure of its impedance and verify that the problem of maximum energy transfer in elastic collisions can be thought of as a problem of impedance matching between different media.

## Solving elastic collision problems the hard way

Let us consider various types of two-object collisions. These collisions are the easiest to analyze, and they illustrate many of the physical principles involved in collisions. The conservation of momentum principle is very useful here, and it can be used whenever the net external force on a system is zero. We start with the elastic collision of two objects moving along the same line—a one-dimensional problem. An elastic collision is one that also conserves internal kinetic energy.

The learning objectives in this section will help your students master the following standards:. When objects collide, they can either stick together or bounce off one another, remaining separate. Kinetic energy is the energy of motion and is covered in detail elsewhere. The law of conservation of momentum is very useful here, and it can be used whenever the net external force on a system is zero.

Principles of Mechanics pp Cite as. When two billiard balls collide, in which direction would they travel after the collision? If a meteorite hits the earth, why does the earth remain in its orbit?