PH1004_Experiment_3 - PH1004 Exp 3: Collisions PH 1004...

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PH1004 Exp 3: Collisions 1 PH 1004 Laboratory Instructions Experiment 3 Collisions Backgr o und A collision is an isolated event in which each colliding particle exerts a force on one or more other particles for a relatively short period of time. Collisions can take place in many different forms and intensities. One example is a baseball bat coming into contact with a baseball. Another is a meteor striking a planet. In general, collisions can be categorized as elastic, inelastic, and perfectly inelastic. For an elastic collision, the momentum and the kinetic energy are both conserved. For an inelastic collision, only the momentum is conserved. A perfectly inelastic collision is one in which the colliding bodies or particles stick together after the collision. The example above of the meteor striking the planet is one such type of collision. In this experiment, we will use an air track to investigate the conservation of momentum and kinetic energy for elastic collisions, and the conservation of momentum for perfectly inelastic collisions. Collisions are characterized by momentum and impulse. To understand the concepts of momentum and impulse, we have to understand how these relate to physical concepts which we already know, such as forces and velocities. The momentum of an object is a vector quantity with the magnitude of mass times velocity: v m p r r = (3-1) The direction of the momentum vector coincides with that of the velocity vector. If we differentiate the momentum with respect to the time, we obtain: a m dt v d m v m dt d dt p d r r r r = = = ) ( . (3-2) Recalling Newton’s second law, a m F r r = , we can write
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PH1004 Exp 3: Collisions 2 dt p d F r r = . (3-3) Now consider a system of many objects, or particles, each with its own mass, velocity and momentum. The system of particles as a whole has a total linear momentum, P r , which is defined as the vector sum of the individual momenta: 3 2 1 ... p p p P r r r r + + + = (3-4) In terms of the velocity of the center of mass, com v r : com v M P r r = (3-5) where M = m 1 + m 2 +…+ m n is the total mass of the system. Taking the time derivative of Equation 3-5, we find com com a M dt v d M dt P d r r r = = . (3-6) Now, similarly to Equation (3-3), we may write Newton’s second Law for the system of colliding particles in the form dt P d F net r r = . (3-7) where net F r is the net external force acting on the system. Consider now a typical collision between two objects. Because the collision time is short and the forces between the particles in collision are large, it is generally a good approximation to assume that there are no significant external forces acting on the two object system during the collision. Setting 0 = net F r in Equation 3-7 then yields 0 = dt P d r and P r = constant. Thus, the momentum of the system is conserved. In other words, for both elastic and inelastic collisions, the vector sum of the momentum for each colliding object before the collision is equal to the vector sum of the momentum after the collision. Therefore,
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This note was uploaded on 07/27/2009 for the course PHYSICS 101 taught by Professor Wormer during the Spring '08 term at NYU Poly.

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PH1004_Experiment_3 - PH1004 Exp 3: Collisions PH 1004...

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