Physics 121 for Majors Class 9 Newton s Laws Standard Model Last Class Matrices Classical boosts Lorentz boosts Space-time four-vectors Space and time problems in relativity Today s Class Newton s Laws Examples Fundamental Forces Virtual Particles Geometric Theories Families of Particles Hadrons Mesons Leptons Gauge Particles Section 1 Newton s Laws Isaac Newton 1646-1727 Laws of Motion Law of Universal Gravitation Calculations of Planetary Motion Invented Calculus Opticks 1
Newton s Associates Principia -- 1687 Halley s Comet St. Paul s Cathedral Edmund Halley Thomas Hooke Christopher Wren Mass Quantity of Matter The quantity of matter is the measure of the same, arising from its density and bulk conjointly. mass = density volume Motion Quantity of Motion The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjointly. Natural Motion momentum = mass velocity 2
The First Law Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it. around natural motion is rectilinear at constant velocity This is Descartes postulate How Force Works We can conceptualize force as a push or pull. Use your intuition: How Force Works The larger mass accelerates less. Their momenta are the same. If we push on two objects with different masses the same amount from rest, how do their accelerations compare? How do their momenta compare? Defining Force The Second Law The change of motion is proportional to the motive force impressed, and is made in the direction of the right line in which that force acts. The change in momentum is proportional to the force and is in the direction of the force. 3
Equations The best way to represent the 2nd Law is the way Newton stated it: If the mass does not change, we can write: So we usually write: Force Force is anything that can change momentum - or changes straight line motion at constant speed. We can conceptualize it as a push or pull. Balanced forces cancel and produce no change of momentum. So any change of momentum is the result of an imbalance of forces. Conservation of Momentum Forces are Binary Forces always act between pairs of objects. Forces are vectors. If one object is affected by multiple forces, the net force is vector the sum of forces. It is the net force that changes momentum. The Third Law To every action there is always an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. Forces come from interactions between pairs of objects, the force on one being equal and opposite the force on the other. That is, the total change of momentum of a pair of interacting bodies is zero. Equations 0 Change of momentum of object 1 caused by its interaction with object 2, etc. 0 0 4
Section 2 A Problem Independence of x & y Let s look at a problem where there are only horizontal and vertical forces. Forces applied to an object in the x-direction only affect motion in the x-direction. Normal Forces The forces of objects pushing against each other are called normal forces. The direction of a normal force is perpendicular to (or normal to) a surfaces. What normal forces are in this problem? Remember that forces always come in pairs! Tension The force exerted by a rope is called tension. What pair of forces is associated with tension? Kinetic Friction Kinetic friction is the force that opposes the motion of objects sliding over each other. The amount of force that friction produces depends on two things: The type of surfaces The normal force pushing the sliding object into the surface. μ k ( mu-k ) is called the coefficient of kinetic friction. Static Friction If we pull on the block with the string, but the frictional force keeps the block from moving, there is still a frictional force. This is called static friction and its equation is: μ s ( mu-s ) is called the coefficient of static friction. The inequality means that the static friction will balance out the tension until the tension is large enough to start the block moving. μ s > μ k Why?? 5
The Problem Identify the Bodies To solve a force problem: 1. Identify the bodies 2. Draw a free body diagram for each/identify all the forces 3. Remember forces always come in action reaction pairs. 4. Write down force equations in each direction (x and y) Draw a Free Body Diagram Write Equations Notes: There is a normal force whenever objects are in contact. There may also be a frictional force. Every object experiences a gravitational force. The reaction forces for the gray arrows are on other bodies not drawn. (Which bodies?). :. : 0... :. :.. The symbols for each of the forces represent magnitudes, so they are positive numbers. We determine the signs from the drawings. g=+9.80 m/s 2 Do the Algebra :. : 0... :. : 0... :. :... :.. :. Section 3 Fundamental Forces 6
Fundamental Forces All particles in nature are subject to four fundamental forces: Strong force Electromagnetic force Weak force Gravitational force Strong Force The "color force" is responsible for the tight binding of the quarks to form neutrons and protons. The strong force is the residual force between colorless particles. The strong force is the force between nucleons. Strongest of all the four basic forces Very short-ranged -- about 1 fm Electromagnetic Force Is responsible for the binding of atoms and molecules About 1/100 the strength of the strong force A long-range force that decreases in strength as the inverse square of the separation between interacting particles Weak Force Is responsible for beta decay A very short-ranged force -- about 0.001 fm Its strength is about 10 --6 times that of the strong force We now believe the weak and electromagnetic forces are two manifestations of a single force, the electroweak force Gravitational Force Holds the planets, stars and galaxies together Its effect on elementary particles is negligible It is a long-range force I It is about 10 --43 times the strength of the strong force What Causes Forces? Forces between particles are often described in terms of the virtual "field" particles that mediate the force For electromagnetic force, the photon is the field particle 7
Forces and Mediating Particles Interaction (Force) Mediating Field particle (gauge bosons) Color (strong) Gluon Electromagnetic Photon Weak W + W Z 0 bosons Gravity Graviton?? Gravity Gravity can t yet be described by a virtual particle model. Gravity is only successfully understood in terms of matter/energy changing the curvature of space-time. Section 4 Fundamental Particles Antiparticles For every particle, there is an antiparticle An antiparticle has the same mass as the particle, but the opposite charge, etc. The positron (electron s antiparticle) was discovered in 1932 Every known elementary particle has an antiparticle Some, such as the photon and 0 are their own antiparticles Particle Families Leptons light, spin 1/2, weak EM electron, neutrinos, etc. Mesons medium, spin 0,1, weak, EM, strong made of quark+antiquark pions, etc. Baryons heavy, spin ½,3/2, weak, EM, strong made of three quarks protons, neutrons, etc, Section 5 Recap 8
Big Ideas Newton s Laws Natural motion is rectilinear at constant speed Force is defined to be the rate of change of momentum Forces are binary and co nserve momentum We have two types of theories that explain fundamental interactions: virtual particle and geometrical theories The fundamental interactions are gravity, weak, EM, strong Leptons are fundamental Mesons are composed of quark + antiquark Baryons are composed of three quarks Schedule Do Post-Class Quiz #9 Do Pre-Class Quiz #10 HW #8 is due Friday Lab #4 is due Monday 9