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Chapter 4: Newton’s Laws

Brent Royuk Phys-111

Concordia University

Introduction • Kinematics vs. Dynamics • Newton: Philosophiae Naturalis

Principia Mathematica (The Mathematical Principles of Natural Philosophy)

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

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?

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The First Law

•  The pen & hoop •  The penny & the

bottle •  The dinner table

The Second Law •  How would you define force? •  Do all forces cause accelerations? •  The Net Force:

•  What if you push harder? –  a � F

•  What if the object is more massive? –  a � 1/m

•  The Law: •  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?

€

! F net =

! F ∑

€

! F net = m

! a

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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?

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.

Newton’s Third Law •  For every _____ there is an equal and

opposite _____. •  The bathroom scale law. •  Force Pairs: F12 = -F21 •  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

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Newton’s Third Law

Newton’s Third Law 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 F1 of 7.0 N and Jill exerting a force of 11 N. Jill’s force is exerted at an angle of 28o with the vertical. At what angle with respect to the vertical should Jack exert his force if the pail is to accelerate straight upward?

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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 25o 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.

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Newton and the Big Picture •  Philosophiae Naturalis Principia Mathematica

(The Mathematical Principles of Natural Philosophy), (see below for year of publication)

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

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.