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Transcript
Linear momentum and the impulse-momentum theorem Definition of linear momentum of a particle Consider a system of N particles, each with a position vector, ri . The ith particle has mass mi and velocity, vi . We define the linear momentum of the particle by pi mivi . The linear momentum of the system of particles is then written P i pi . Next, we contemplate how to change the value of p for a particle. Obviously, the mass can not change and therefore to change p we must do it by changing v, i.e we must accelerate the particle. Newton’s second law gives Fnet = m dv/dt = d [mv]/dt = dp/dt. This becomes for a system of particles, Fextnet = dP/dt, Where, Fextnet is the sum of only the external forces acting on the particles of the system. Rearranging gives the impulse-momentum theorem, Fnet dt = p, where the impulse of a force is defined, I F dt. this is the area under F vs t graph For example, Fnet t = Fnet t = p where the average force is used. A consequence of the impulse-momentum theorem is the law of conservation of momentum: If the net external force acting on a system is zero, then the momentum of the system is constant. An important application is to collisions. In the simplest case we consider the collision of two particles in one-dimension, of which there are two extreme regimes. completely inelastic Only momentum of the two-body system is conserved. Elastic Both momentum and kinetic energy of the two-body system is conserved. EXAMPLES [in class]
