the history of dynamics. natural motion was caused by some internal quality of an object that made...
TRANSCRIPT
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
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 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
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 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 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