Chapter 4-Newton’s Laws of Motion

IntroductionDynamics-The study of the forces that

change or produce motion. The “why” of motion.

The work of Sir Isaac Newton, born in 1642 on Christmas day.

Born prematurely and not expected to survive.

Attended Cambridge in 1661, studying math and natural philosophy.

Invented calculus (fluxions) as a means of explaining gravitation.

Introduction

Published his work the Mathematical Principles of Natural Philosophy, commonly called the Principia, in 1687.

The work dealing with mechanics, gravity and astronomy is considered one of the most important books ever written.

Newton died March 20th, 1727.

Newton’s First Law of Motion

A body at rest will remain at rest, and a body in motion at a constant velocity will continue in motion at that constant velocity, unless acted upon by an unbalanced external force.

A force is a push or a pull that acts on a body.

The resistance to any change in motion is known as inertia.

More mass=more inertia

Newton’s First Law of Motion

Newton’s First Law is often referred to as the Law of Inertia.

The law holds true in an inertial coordinate system (also called an internal reference system), a system that is either at rest or moving at a constant velocity with respect to another coordinate system that is at rest or also moving at a constant velocity.

Newton’s Third Law of MotionIf body A exerts a force on body B, body B

will exert and equal but opposite force on body A.

“For every action, there is an equal, but opposite, reaction.”

BAAB FF FAB is the action force, FBA is the reaction force

Newton’s Second Law of Motion

The acceleration of a body is directly proportional to the unbalanced force applied to the object and inversely to its mass.

The acceleration is in the direction of the applied net force.

amFnet orm

a F net

Newton’s Second Law of Motion

The SI unit for force is the kg-m/s2 which is actually a newton (N).

The British unit of force is the slug-ft/ s2 which is the pound (lb).

Trivia: Why is the abbreviation for pound lb??

Once the acceleration of an object is determined from Newton’s Second Law, future position and velocity can be determined using kinematics equations.

Newton’s Second Law of Motion

Newton’s Second Law is consistent with his First Law.

If F=ma, and a=v/t, then F=m• v/t.Therefore, if F=0, then v must also be equal

to zero.The velocity of an object will not change

unless acted upon by an unbalanced external force.

Newton’s Second Law of Motion

A special case of Newton’s Second Law applies to a body near the surface of the earth.

Near earth, all objects are accelerated towards the center of the earth by gravity (g).

The force (ma) on an object near the surface is called the weight(w) of the object, and a=g.

w=mg and is also measured in Newtons or pounds.

Friction

Friction is a force that opposes the motion of an object as one body tries to slide over another.

Surfaces are never truly smooth, and the surfaces interact with each other to create this opposition.

Friction is a passive, not an active, force.Friction can be helpful or a detriment.

FrictionStatic Friction (fs)is the friction that holds an

object in place and keeps it from moving.The force of static friction increases, to a

maximum limit, as the force applied to an object increases.

The amount of static friction available is less than or equal to the product of the coefficient of static friction (s) and the normal or perpendicular force (FN).

Friction

The maximum value of static friction is often called starting friction.

Kinetic Friction, (fk)or sliding friction, is the force of friction that opposes the motion of a moving object.

Kinetic friction is usually less than the starting friction (maximum static).

Nss Ff

FrictionThe amount of kinetic friction available is

equal to the product of the coefficient of kinetic friction (k) and the normal or perpendicular force (FN).

Nkk Ff The coefficients of friction are a numerical

value comparing the relative amounts friction between surfaces.

FrictionThe coefficient of friction is based only upon

the nature of the surfaces.The surface area of the surfaces in contact have

no bearing whatsoever on the coefficient of friction.

A larger surface area results in less pressure (Force/area) but this does not effect the frictional force.

FrictionRolling friction is usually less than kinetic

friction and is the reason machines use wheels, ball bearings, etc.

Theoretically, there is no relative motion between the outer edge of the wheel and the surface that is rolls over. Any amount of friction that is present is due to the deformation of the wheel. Less deformation=less friction.

Why do ABS brakes work better than sliding?