Chapter 4: Newton s Laws. Brent Royuk Phys-111 Concordia University

Transcription

1 Chapter 4: Newton s Laws Brent Royuk Phys-111 Concordia University

2 Introduction Kinematics vs. Dynamics Newton: Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy)

3 The First Law Aristotelian Mechanics Natural vs. Violent Motion Impetus Scholasticism Galileo The tendency to stop is overstated Empiricism and idealization Outer space & air tracks

4 The First Law The Law Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare. Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed. Inertia: What is it? What keeps Earth moving in its orbit around the sun? So what s the big deal? Isn t this law obvious?

5 The First Law The pen & hoop The penny & the bottle The dinner table 7

6 The Second Law How would you define force? Do all forces cause accelerations?!! The Net Force: Fnet = F What if you push harder? a F What if the object is more massive? a 1/m!! = ma The Law: Fnet The Force Unit Example: Push a 15-kg cart with a net force of 36 N. How fast is it going in 3.0 seconds?

7 Weight W = mg A newton-weight Mass vs. weight: how are they different? A weightless hammer in the space shuttle. Galileo and the Tower of Pisa again Two kinds of mass? Example You are holding a 5.0-kg mass in your hand, upon which you are exerting an upward force of 79 N. What happens to the mass?

8 Free-Body Diagrams An accounting system for forces Let a system of masses be a point, draw all vectors tail-to-tail so you can see what s going on. What is a system? Internal vs. External Forces What would a FBD look like for a car coasting down a (real) highway? Example: A box that weighs 49 N (and therefore has a mass of 5.0 kg) is pushed sideways with a force of 8.6 N. This push is resisted by a frictional force of 4.3 N. Find the acceleration of the box.

9 Newton s Third Law For every there is an equal and opposite. The bathroom scale law. Force Pairs: F 12 = -F 21 Example: Let s say you apply a 50-N force to a car in neutral on a level surface. The car pushes back on you with a 50-N force as well. These forces are balanced, so no acceleration takes place, right? Aka the Horse and Cart Paradox

10 Newton s Third Law 19

11 Newton s Third Law

12 Forces in 2-D When forces act in 2 dimensions, use a FBD with a convenient coordinate system and treat the components separately. Example Jack and Jill lift upward on a 1.3-kg pail of water, with Jack exerting a force F 1 of 7.0 N and Jill exerting a force of 11 N. Jill s force is exerted at an angle of 28 o with the vertical. At what angle with respect to the vertical should Jack exert his force if the pail is to accelerate straight upward?

13 Normal Forces Forces exerted by surfaces are always normal to the plane of the surface. Flat surfaces Draw a FBD for a mass on a flat table. Example: Find the normal force for a 15-kg box pulled by a rope inclined 25 o above horizontal with a force of 12 N. What is the box s acceleration? Inclined surfaces Find the normal force and acceleration for a mass on a frictionless plane inclined at angle with respect to horizontal.

14 Newton and the Big Picture Philosophiae Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy), (see below for year of publication) 26

15 Newton s Greatness The work that Newton undertook in the years between 1684 and 1686 presents the biographer and psychologist with an ineradicable mystery, one that goes beyond the sheer and irrefutable fact of genius, a fact that we may recognize but that we cannot explain. The Principia is without question our greatest work of pure thought; it is now one of humanity s collective treasures. It brings to completion the great scientific revolution initiated by Kepler and Galileo; it contains a matchless combination of mathematical argument and profound physical intuition. And it constitutes a crucial demonstration of the power of certain mathematical methods in natural philosophy. Before Newton, no one quite believed that those methods could provide a comprehensive system of the world; after Newton, no one doubted it. -David Berlinski

16 Newton s Greatness Nature and nature s laws lay hid in night; God said, Let Newton be, and all was light -Alexander Pope Newton was not only the greatest genius that ever existed, but also the most fortunate, inasmuch as there is but one universe, and it can therefore happen to but one man in the world s history to be the interpreter of its laws. -Pierre-Simon de LaPlace I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.