| MOMENTUM | ELASTIC COLLISION | COLLISION |
| CONSERVATION OF ENERGY | ISOLATED SYSTEM | IMPULSE |
| KINETIC ENERGY |
The momentum of a particle is defined as the product of its mass times its velocity. It is a vector quantity. The momentum of a system is the vector sum of the momenta of the objects which make up the system. If the system is an isolated system, then the momentum of the system is a constant of the motion and subject to the principle of conservation of momentum.
The basic definition of momentum applies even at relativistic velocities but then the mass is taken to be the relativistic mass. The most common symbol for momentum is p. The SI unit for momentum is kg m/s.
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A collision is an isloated event in which two or more bodies (colliding bodies) exert relatively strong forces on each other for a relatively strong orces on each other for a relatively short time.
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An elastic collision is defined as one in which both conservation of momentum and conservation of kinetic energy are observed. This implies that there is no dissipative force acting during the collision and that all of the kinetic energy of the objects before the collision is still in the form of kinetic energy afterward.
For macroscopic objects which come into contact in a collision, there is always some dissipation and they are never perfectly elastic. Collisions between hard steel balls as in the swinging balls apparatus are nearly elastic.
"Collisions" in which the objects do not touch each other, such as Rutherford scattering or the slingshot orbit of a satellite off a planet, are elastic collisions. In atomic or nuclear scattering, the collisions are typically elastic because the repulsive Coulomb force keeps the particles out of contact with each other.
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Energy can be defined as the capacity for doing work. It may exist in a variety of forms and may be transformed from one type of energy to another. However, these energy transformations are constrained by a fundamental principle, the Conservation of Energy principle. One way to state this principle is "Energy can neither be created nor destroyed". Another approach is to say that the total energy of an isolated system remains constant.
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An isolated system implies a collection of matter which does not interact with the rest of the universe at all - and as far as we know there are really no such systems. There is no shield against gravity, and the electromagnetic force is infinite in range. But in order to focus on basic principles, it is useful to postulate such a system to clarify the nature of physical laws. In particular, the conservation laws can be presumed to be exact when referring to an isolated system:
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Kinetic energy is energy of motion. The kinetic energy of an object is the energy it possesses because of its motion.Kinetic energy is an expression of the fact that a moving object can do work on anything it hits.
It quantifies the amount of work the object could do as a result of its motion. The total mechanical energy of an object is the sum of its kinetic energy and potential energy.
For an object of finite size, this kinetic energy is called the translational kinetic energy of the mass to distinguish it from any rotational kinetic energy it might possess - the total kinetic energy of a mass can be expressed as the sum of the translational kinetic energy of its center of mass plus the kinetic energy of rotation about its center of mass.
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The product of average force and the time it is exerted is called the impulse of force. From Newton's second law the impulse of force can be extracted and found to be equal to the change in momentum of an object provided the mass is constant.
The main utility of the concept is in the study of the average impact force during collisions. For collisions, the mass and change in velocity are often readily measured, but the force during the collision is not. If the time of collision can be measured, then the average force of impact can be calculated.
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