A large portion of the kinetic energy is converted to other forms of energy such as sound energy and thermal energy. A collision in which total system kinetic energy is not conserved is known as an inelastic collision.
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Return to List of Animations. An elastic collision is one that also conserves internal kinetic energy. Internal kinetic energy is the sum of the kinetic energies of the objects in the system. Figure 1 illustrates an elastic collision in which internal kinetic energy and momentum are conserved. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic—some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound.
One macroscopic collision that is nearly elastic is that of two steel blocks on ice. Another nearly elastic collision is that between two carts with spring bumpers on an air track. Icy surfaces and air tracks are nearly frictionless, more readily allowing nearly elastic collisions on them. Figure 1. An elastic one-dimensional two-object collision. Momentum and internal kinetic energy are conserved.
Now, to solve problems involving one-dimensional elastic collisions between two objects we can use the equations for conservation of momentum and conservation of internal kinetic energy.
First, the equation for conservation of momentum for two objects in a one-dimensional collision is. By definition, an elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals the sum after the collision. First, visualize what the initial conditions mean—a small object strikes a larger object that is initially at rest.
This situation is slightly simpler than the situation shown in Figure 1 where both objects are initially moving. To find two unknowns, we must use two independent equations. Because this collision is elastic, we can use the above two equations.
Once we simplify these equations, we combine them algebraically to solve for the unknowns. There are two solutions to any quadratic equation; in this example, they are. As noted when quadratic equations were encountered in earlier chapters, both solutions may or may not be meaningful. In this case, the first solution is the same as the initial condition. The first solution thus represents the situation before the collision and is discarded. The result of this example is intuitively reasonable.
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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