2014/01/02 What is a system in Physics? CONSERVATION of MOMENTUM in ONE DIMENSION A system in Physics is a small part of the universe that we are considering, when solving a particular problem. Can we make scientific sense of Everything outside the system is called what is happening here? the environment or surroundings. Earth as a closed system Open & closed systems. Momentum – revise concepts: In closed system, temperature, volume, pressure etc. are kept constant and are not affected by • p = m.v Momentum & impulse external forces from outside the system. Open, closed & isolated systems In an open system these values can change and • Momentum is a vector quantity (direction probably do not remain constant for long. must be taken into account) Momentum of a rocket • Δp = m(vf – vi) • Impulse = F Δt • F Δt = m(vf – vi) The principle of conservation of The law of conservation of Newton's cradle momentum. momentum. There are no external forces acting N.B. The law of conservation of momentum states: on the system. The only forces are those due to the interaction of the The total linear momentum of an isolated system colliding bodies. remains constant (is conserved). Large Newton cradle In an isolated system, the total momentum before a collision or explosion equals the total momentum after the collision or explosion Air track - conservation of momentum click here 1 2014/01/02 • The law of conservation of momentum can be verified experimentally. According to Newton’s third law, during a BUT …… collision the force that A exerts on B (F1) equals the force B exerts on A (F2), but in opposite directions. • Consider 2 objects, A and B, of masses m and m , traveling at initial velocities v A B 1 2 i1 and vi2. F1 = - F2 • They collide and travel at velocities v and f1 Newton's third law vf2 after the collision. Conservation of momentum According to Newton’s Second Law: m2 m2 m1 m1 m v – m v m2vf2 – m2vi2 1 f1 1 i1 Before collision = After collision t t2 Velocity = v 1 Velocity = vf i The times of contact are equal, and so: m v – m v = - (m v – m v ) 1 f1 1 i1 2 f2 2 i2 Time of collision p before the collision = m v Or: 1 i p after the collision = (m1 + m2) vf Momentum is conserved during a collision. p before the collision = p after the collision m v = (m + m ) v Conservation of Newton's second law 1 i 1 2 f momentum Conservation of momentum during an The conservation of momentum during explosion a collision. During a collision in an isolated system, the total linear momentum is conserved. Mass of p before the explosion = 0 each = 1 kg p after the explosion = 0 Scenario 1 above: m.v = -m.v (Take left P after = p before Scenario 2 above: m.2u = -2m.u as +) 2 2014/01/02 A cannon ball of mass 900g is fired from a Can you solve these problems? cannon of mass 40kg. The ball leaves the muzzle of the cannon at 250 m.s-1. Calculate the magnitude and direction of the velocity of the cannon (recoil velocity). Momentum & canon What is the velocity of granny and boy after the collision? ELASTIC COLLISIONS Elastic and Inelastic collisions • The linear momentum of a system is Elastic collisions occur when ALWAYS conserved during a collision or objects come apart after colliding. an explosion. Inelastic collisions occur when colliding objects move • N.B. Kinetic energy is as a single unit after colliding. only conserved during an elastic collision. Elastic collisions Elastic and Inelastic Collision • In an elastic collision no energy is lost due Newton's Cradle to deformation or friction. No sound or light is emitted. INELASTIC COLLISIONS Elastic collisions •Work is required to change the shape of an object (deformation). Inelastic collisions •Heat energy is generated during the deformation of a colliding object. Some energy is converted into sound. •This causes the total kinetic energy of the system to be less after the collision than before the collision. Inelastic •Such a collision is known collisions as an inelastic collision. 3 2014/01/02 * Represents a collision. Elastic collision: P before = P after Equations Elastic for * calculations. *Elastic collision m1v1 + m2v2 = m1v3 + m2v4 In elastic collisions, objects come apart after the collision Elastic collision: P before = P after Inelastic * * m1v1 +(- m2v2) = (-m1v3) + m2v4 In inelastic collisions, the objects remain locked together after the collision and move as 1 unit. Remember the sign convention: select a direction as +. Inelastic collision Conservation of momentum in collisions What must you be able to do? Inelastic collision: P before = P after • Define the laws that govern the way * objects collide. m1v1 + m2v2 = (m1 + m2)v3 • State the law of conservation of N.B. momentum. Inelastic collision: • Apply this knowledge in calculations. P before = P after • Compare momentum and kinetic energy * changes during collisions. m1v1 + (-m2v2) = (m1 + m2)v3 Conservation of energy Two-dimensional collisions click here Summary 4 .