Simple Nature - Light and Matter

A moving object’s momentum equals the sum of the momenta of all its atoms. To avoidhaving to carry out this sum, we can use the concept of the center of mass. The center of masscan be defined as a kind of weighted average of the positions of all the atoms in the object,x cm =∑mj x j∑mj,and although the definition does involve a sum, we can often locate the center of mass bysymmetry or by physically determining an object’s balance point. The total momentum of theobject is then given byp total = m total v cm .The rate of transfer of momentum is called force, F = dp/ dt, and is measured in units ofnewtons, 1 N = 1 kg·m/s 2 . As a direct consequence of conservation of momentum, we have thefollowing statements, known as Newton’s laws of motion:If the total force on an object is zero, it remains in the same state of motion.F = dp/ dtForces always come in pairs: if object A exerts a force on object B, then object B exertsa force on object A which is the same strength, but in the opposite direction.Although the fundamental forces at the atomic level are gravity, electromagnetism, andnuclear forces, we use a different and more practical classification scheme in everyday situations.In this scheme, the forces between solid objects are described as follows:A normal force, F n , is perpendicular to the surface of contact, and preventsobjects from passing through each other by becomingas strong as necessary (up to the point where the objectsbreak). “Normal” means perpendicular.Static friction, F s , is parallel to the surface of contact, and prevents thesurfaces from starting to slip by becoming as strong asnecessary, up to a maximum value of F s,max . “Static”means not moving, i.e. not slipping.Kinetic friction, F k , is parallel to the surface of contact, and tends to slowdown any slippage once it starts. “Kinetic” meansmoving, i.e. slipping.Work is defined as the transfer of energy by a force. (“By a force” is meant to exclude energytransfer by heat conduction.) The work theorem states that when a force occurs at a single pointof contact, the amount of energy transferred by that force is given by dW = F · dx, where dx isthe distance traveled by the point of contact. The kinetic energy theorem is dK cm = F total·dx cm ,where dK cm is the change in the energy, (1/2)mv 2 cm, an object possesses due to the motion ofits center of mass, F total is the total force acting on the object, and dx cm is the distance traveledby the center of mass.The relationship between force and interaction energy is U = − dF/ dx. Any interaction canbe described either by giving the force as a function of distance or the interaction energy as afunction of distance; the other quantity can then be found by integration or differentiation.An oscillator subject to friction will, if left to itself, suffer a gradual decrease in the amplitudeof its motion as mechanical energy is transformed into heat. The quality factor, Q, is defined as949