Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Monte Carlo methods for electron transport wikipedia , lookup
Angular momentum operator wikipedia , lookup
ALICE experiment wikipedia , lookup
Elementary particle wikipedia , lookup
ATLAS experiment wikipedia , lookup
Photon polarization wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Electron scattering wikipedia , lookup
Compact Muon Solenoid wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Momentum and impulse The momentum-impulse equation For a body of mass m, moving with velocity v, momentum mv Consider a constant force F acting for a time t on a body of mass m in the direction of its motion, causing the velocity to increase from u to v. Then F ma and v u at quickly yields Ft m(v u) mv mu. The product of the force and the time for which it acts is called the impulse of the force and is denoted by the vector J . impulse change in momentum J Ft mv mu Note : The impulse unit usually given is N s. Read Examples 13a, pp.263-266 & Example 13b, p.268 Do Exercise 13a, pp.266-268 & Exercise 13b, pp.268-269 Collision Two objects in contact exert equal and opposite forces on each other. Since objects are in contact with each other for the same time, they exert equal and opposite impulses on each other. As long as no external force acts on either object, the total momentum of the two objects remain constant. The Principle of Conservation of Linear Momentum : If in a specified direction, no external force affects the motion of a system, the total momentum in that direction remains constant. Note : Objects that collide and join together at impact are said to coalesce. It is advisable to draw separate "before" and "after" diagrams when solving problems involving collisions. Read Examples 13c, pp.270-272 Do Exercise 13c, pp.272-274 Loss of kinetic energy; finding the impulse When there is a sudden change in the motion of a system, there is usually a change in the total kinetic energy of the system. This is because some mechanical energy is converted into sound energy or heat energy (or both). When objects collide, equal and opposite impulses act on the two objects. When the system is treated as a whole, these impulses cancel and need not appear in calculations. The impulse which acts on one object causes the change in the momentum of that object only. So, if the magnitude of the impulses is required, it is sufficient to consider only one of the colliding objects. Read Examples, pp.274-276 Do Exercise 13d, pp.276-277 Impacts Many collisions so far have resulted in the objects coalescing at impact. Such impacts are called inelastic. However, if a bounce occurs at collision, we have an elastic impact and the colliding object(s) are said to be elastic. The simplest examples of inelastic impacts are direct impacts, i.e. an impact in which the direction of motion just before impact is parallel to the impulses that act at the instant of collision. Newton’s Law of Restitution Experimental evidence suggests that, for two colliding particles, the separation speed is always the same fraction of the approach speed. Newton's Law of Restitution : separation speed e approach speed e is called the coefficient of restitution and it is constant for any two particular objects; its value depends upon the materials of which the two objects are made. 0 e 1 If particles coalesce the separation speed is zero i.e. e 0. If the relative speeds are equal, e 1, the particles are said to be perfectly elastic (there will be no loss in kinetic energy). Read Examples 14a, pp.280-281; 14b, pp.284-286; 14c, pp.290-292 Collision with a fixed object Consider a particle of mass m, moving on a smooth horizontal surface with speed u, towards a fixed block whose face is perpendicular to the direction of motion of the particle. When the particle hits the block an impulse J is exerted on the particle by the block and, if the impact is elastic, the particle bounces off the block in the oppsite direction with speed v, say. If the direction of J is taken as positive, v eu J mv (mu ) Note : The conservation of linear momentum is not valid here since the impulse applied to the particle by the fixed surface is an external impulse. Do Exercises 14a, pp.281-283; 14b, pp.287-289; 14c, pp.293-295 Oblique impact with a fixed object Consider a sphere travelling on a horizontal surface colliding with a vertical wall, the direction of its velocity making an angle with the wall. The impulse exerted on the sphere is perpendicular to the wall and causes a change in the momentum of the sphere in that direction only; it does not affect the momentum parallel to the wall. The component of the velocity perpendicular to the wall may be changed whereas the component parallel to the wall must remain unchanged. Note : Newton's restitution law here applies to the component of velocity perpendicular to the surface before and after impact. Read Example 14d, p.297 Do Q1, Q2, Q7, pp.300-301