The History of DynamicsThe History of Dynamics

Natural motion was caused by some internal quality of

an object that made it seek a certain “preferred” position without any application of

force.

The GreeksThe Greeks

Unnatural motion was anything else.

Unnatural motion was thought to require applied

force to be sustained.

The GreeksThe Greeks

Natural motions were divided into two categories:

Terrestrial (near the earth)Celestial (in the heavens)

The GreeksThe Greeks

Aristotle taught that an object’s “heaviness”

determined how “vigorously” it sought its natural place.

The GreeksThe Greeks

• began by collecting facts and establishing a description of motion

• This is called kinematics.• Galileo then inductively

developed workable theories of dynamics.

GalileoGalileo

• Experiments showed that the rate at which an object falls is not proportional to its size or mass.

• Astronauts later verified his theory on the moon.

GalileoGalileo

a hypothesis based on conjecture rather than

observation, usually in an attempt to explain a natural

phenomenon

Ad hocAd hoc

• Galileo’s experiments of “unnatural” motion indicated that the “natural” state of motion of an object could include moving as well as resting.

InertiaInertia

InertiaInertiaGalileo’s Principle of Inertia:An object will continue in its

original state of motion unless some outside agent

acts on it.

InertiaInertiaA moving object does not

require a continuous push to maintain a constant velocity!A push causes a change in

an object’s motion.

• built on the work of others• studied gravitation• Principia• only in recent decades have

scientists discovered any exceptions to his work

NewtonNewton

ForcesForces

Summing ForcesSumming Forces• Forces are often

described as “pushes” and “pulls.”

• Forces are vectors.• Forces can be added just

as vectors are added.

Summing ForcesSumming Forces• Notation:

ΣF ≡ F1 + F2 + ... + Fn

• The Greek capital letter sigma (Σ) is used to indicate a sum.

Summing ForcesSumming Forces• If forces are balanced...

ΣF = 0• ...and no change in

motion will occur.

ΣF = 0 ↔ ΣFx = 0 and ΣFy = 0

• will change an object’s state of motion

• there may be two, or more than two, forces which are unbalanced

Unbalanced ForcesUnbalanced Forces

• To find the sum of unbalanced forces, you add the force vectors acting upon the object.

• This usually involves finding and adding the vector components.

Unbalanced ForcesUnbalanced Forces

Equilibrant ForceEquilibrant Force• a force that balances one

or more other concurrent forces

Equilibrant ForceEquilibrant Force• a vector having the same

magnitude as the vector sum of the other unbalanced forces but pointing in the opposite direction

Fequil. = -ΣFother

Equilibrant ForceEquilibrant Force• If the sum of all forces on

an object is zero, then any unknown force must be the equilibrant of all the known forces.

WeightWeight• the force of gravity acting

on an object• a vector pointing straight

downward• often notated Fw

Types of ForcesTypes of Forces• All forces are classified

as either fundamental forces or mechanical forces.

• There are four fundamental forces.

Fundamental ForcesFundamental Forces• Gravitational force

• proportional to the masses of interacting objects

• can exert its influence over theoretically infinite distances

Fundamental ForcesFundamental Forces• Gravitational force

• all objects exert gravitational force on all other objects

Fundamental ForcesFundamental Forces• Electromagnetic force

• used to explain both magnetism and electricity

• a long-range force• a short-range force

Fundamental ForcesFundamental Forces• Strong nuclear interaction

force• Weak nuclear interaction

force

Classification of Forces

Classification of Forces

• Noncontact Forces• gravity• electromagnetic forces• sometimes called

“action-at-a-distance” forces

Classification of Forces

Classification of Forces

• Noncontact Forces• field theory attempts to

explain these• virtual particles have

been offered as an explanation

Classification of Forces

Classification of Forces

• Contact Forces• transmitted only by

physical contact between objects

• include the following:

Classification of Forces

Classification of Forces

tensile (pull things apart)compressive (push things

together or crush)torsion (twist)

Classification of Forces

Classification of Forces

friction (oppose motion between two objects in contact)

shear (cause layers within matter to slide past one another)

Measuring ForcesMeasuring Forces• instruments used include:

• spring scale• load cell• pressure gauge

Measuring ForcesMeasuring Forces• instruments used include:

• ballistic pendulum• accelerometer• force table

Newton’s Laws of Motion

Newton’s Laws of Motion

These are the central principles of dynamics.

Their proper use requires an understanding of what a

system is.

Newton’s LawsNewton’s Laws

In physics, a system is whatever is inside an

imaginary boundary chosen by the physicist.

It is isolated from its surroundings.

SystemsSystems

A system at rest will remain at rest, and a moving system will move continuously with a constant velocity unless

acted on by outside unbalanced forces.

Newton’s 1st LawNewton’s 1st Law

If all external forces on a system are balanced, then its

velocity remains constant; the acceleration is zero.

Newton’s 1st LawNewton’s 1st Law

If all forces acting on a system are not balanced, then a nonzero resultant

force exists and the velocity changes, resulting in an

acceleration.

Newton’s 1st LawNewton’s 1st Law

Stated mathematically:Newton’s 1st LawNewton’s 1st Law

ΣF = 0 ↔ a = 0

ΣF ≠ 0 ↔ a ≠ 0

or equivalently:

Friction is a force that causes motion to change.

Inertia is the tendency for a system to resist a change in

motion.

Newton’s 1st LawNewton’s 1st Law

Mechanical equilibrium occurs when the sum of all forces on a system is zero.Without unbalanced forces,

objects tend to move in straight lines.

Newton’s 1st LawNewton’s 1st Law

• the most general of the three laws

• gives a working definition of force and a way to measure such force

Newton’s 2nd LawNewton’s 2nd Law

Newton’s 2nd LawNewton’s 2nd LawThe acceleration of a system if directly proportional to the sum of the forces (resultant force) acting on the system and is in the same direction

as the resultant.

Newton’s 2nd LawNewton’s 2nd LawStated mathematically:

ΣF = ma

a =ΣFm

or equivalently:

Newton’s 2nd LawNewton’s 2nd LawA resultant force of 1 N,

when applied to a mass of 1 kg, produces an

acceleration of 1 m/s².

This is how the Newton, a derived unit, is defined.

Newton’s 2nd LawNewton’s 2nd Law

component equations:

ΣFx = max

ΣFy = may

ΣFz = maz

Newton’s 3rd LawNewton’s 3rd LawIf system X exerts a force on system Y, then Y exerts

a force of the same magnitude on X but in the

opposite direction.

FX→Y = -FY→X

Newton’s 3rd LawNewton’s 3rd Law• forces have four properties

that relate to this law:• All forces occur in pairs.• Each force in an action-

reaction pair has the same magnitude.

Newton’s 3rd LawNewton’s 3rd Law

• Each force acts in the opposite direction in line with the other force of the pair.

• Each force acts on a different system.

Weight and MassWeight and Mass• The force of planetary

gravitational attraction on an object is called its weight, Fw.

• Weight is directly proportional to mass.

• Fw = am

Weight and MassWeight and Mass• Since this gravitational

acceleration is downward:• Fw = mg

• g = -9.81 m/s²• The magnitude of an

object’s weight vector is |mg|.

Weight and MassWeight and Mass• The weight vector, like the

gravity vector, points straight down (toward the center of the earth).

• In scalar component form:• Fwy = mgy

Weight and MassWeight and Mass• Mass is measured on

scales and reported in units of kg or g.