Download Motion and Force

Motion and Force
Dynamics
4.1. Force
 A force is a push or a pull.
 Force is a vector
We must add all the forces acting on the body.
Forces do not necessarily cause motion.
5N
5N
5N
5N
10 N
5N
0N
10 N
5N
4.2. ARISTOTLE(384-322 B.C.)
ON MOTION
Aristotle believed that a
force was needed to continue
motion. He attempted to
understand motion by
classification.
Two Classes:
Natural and Violent
natural motion – motion that could maintain itself without the
aid of an outside agent. (pushing a rock off the
ledge and it falls to the ground, liquids falling or
running downhill, air rising, flames leaping upward)
violent motion – motion that forced objects to behave contrary to an
objects natural motion, meaning an external push or
pull was needed
Aristotle believed everything was made of four elements
Aristotle's
Periodic
Table
Fire
Air
Water
“Natural Motion”
(vertical)
Earth
“Violent Motion” (horizontal)
Aristotelian Universe
Terrestrial Realm
 Composition predicts motion
natural tendencies
Fire and Air tend to rise
Earth and Water tend to sink
 Overall tendency to seek rest
 Objects are corruptible (changing)
How things move on Earth
Aristotle's
Periodic
Table
water’s natural
resting place
is on top of earth
Fire
Air
“Natural Motion”
(vertical)
• Each element has its own
natural motion, and its own
place that it strives to be.
Water
Earth
“Violent Motion” (horizontal)
• Aristotle believed an object’s
natural motion was determined
by how much of each element
the object contained (rocks
sink in water because they
contain mostly earth, wood
floats because it contains
mostly air)
earth moves downward
because Earth’s center
is its natural resting place
•Motion not on earth followed a different set of rules. Motion in the
heavens had no beginning or end. Circular paths were considered
natural for the stars and the planets.
•Celestial objects were considered to be made of the 5th element –
ether (from the Greek word for to kindle or blaze) – Ether had no
weight, was unchangeable, and perfect in every way.
Stationary Earth according to Aristotle
 Earth is heavy.
 Easier to imagine the sky can move
 It looks like the sky is moving.
 We have no sensation of our motion.
 A rotating Earth would make objects fly off of the
surface.
 It would take a huge force to move the Earth so the
Earth must not be moving.
 The Earth must be the center of the universe.
Aristotle’s Laws of Motion –Summary
1.
Natural Motions are determined by the innate “desire” of the moving object to return
to it’s “natural resting place “. The proper state was “at rest”.
2. Violent Motions occur because outside influences give motion to the object. As soon as
force “runs out”, the object stops. This was the belief for 2000 years.
3. Objects composed of ether travel in gigantic, perfect circles centered on the Earth
which was assumed to be at rest.
Nicholas Copernicus
1473 - 1543
(Niklas Koppernigk)
Nicholas Copernicus
developed a mathematical
model for a Sun-centered
solar system based on
astronomical
observations.
Galileo Galilei
1564-1642
 He was among the first to turn a telescope to the
sky.
 He developed the Scientific Method.
 He believed in the popularization of science.
 He defined inertia as resistance to change in
motion.
Galileo Galilei helped overthrow Aristotelian physics.
Because of his radical ideas he was confined to house
arrest for the last 10 years of his life.
Galileo argued that only when friction is present is a
force needed to keep an object in motion. Friction is a
force caused by irregularities in the surfaces of objects
in contact. Friction acts in a way which opposes motion.
I do not feel obliged to believe that the same God who has endowed us with
sense, reason, and intellect has intended us to forgo their use. -Galileo
∞
Newton’s Laws
The
st
1
Law
Every object continues
to move as it has been
moving unless acted
upon by an external
force.
Law of Inertia – An object will move in a straight line at a
constant speed
UNLESS acted upon by an external force
- objects in motion stay in motion
- objects at rest stay at rest
UNLESS influenced in some way
YOU
you start turning here
•outside influence – tires on car
friction on tires
•outside influence – door on you
PASSENGER
Car begins turning here
Another example: “Canis Insanis”
you fastened to you seat belt
you stop too!
Jeep
Miss Pickles standing on the
console
apply brakes at
red light
trip to the
vet needed
Mass and Inertia
Inertia is a property of a body that resists
changes in motion.
Mass is a measure of the amount of matter
in a body.
Inertia and Mass are the same concept.
Units – Kg or slugs
Mass and weight are NOT the same concept
but they are proportional.
Mass and volume are NOT the same
concept but they are proportional.
Weight
Force of gravity pulling on the mass of
the body.
Units – Newtons or Pounds
A newton is about the weight of a small
apple.
One kg weighs 2.2 lbs.
W = mg
g = acceleration due to gravity at the surface
of the Earth
= 32 ft/s2 = 9.8 m/s2
Newton’s first law
Newton’s first law does not hold in all
reference frames.
It does not hold in an accelerating
reference frame.
A cup on the dash of a car moving as the
car accelerates.
It does hold in an inertial frame of
reference and is proof of such a frame of
reference.
Newton’s Second Law
Newton was the first to realize that the
acceleration produced when an object
moves depends not only on how hard it is
pushed or pulled but also on the object’s
mass.
The acceleration produced by a net force
on an object is directly proportional to the
magnitude of the net force, is in the same
direction as the net force, and is inversely
proportional to the mass of the object.
Force causes acceleration.
Recall that
acceleration = change in velocity/time
interval.
This chapter focuses on the cause of
acceleration: Force.
A force is a push or a pull.
Most often there is more than one force
acting on an object.
The combination of forces acting on an
object is the net force.
Force causes acceleration.
Acceleration is proportional to
net force.
F ~ a
To increase the acceleration of
an object you must increase the
net force on the object.
Mass resists acceleration.
More massive objects resist a
change in their motion. Inertia
prevents changes from occurring
without a net force present.
 a ~ 1/m
Thus acceleration and mass are
inversely proportional.
Newton’s Second Law
a = F/m
a = F/m
Or F = ma
Newton’s Second Law
Every force is a vector with magnitude and
direction.
Thus every rectangular coordinate may be
written in the form of Newton’s second
law.
Fx = Σmax
Fy = Σmay
Fz = Σmaz
Questions
Two forces act on a book resting on a
table: its weight and the support force
from the table. Draw a free body diagram
of the book. Does a force of friction act as
well?
Suppose a high-flying jet cruises with a
constant velocity when the thrust from its
engines is a constant 80 000 N. What is
the acceleration of the jet? What is the
force of air resistance acting on the jet?
 In SI the unit of force is the Newton (N) but in the
cgs system, the unit of force is the dyne, which
is 1 g cm/s2. A dyne is 10-5 N.
 In the British system the unit of force is the
pound. 1 lb = 4.45 N. The unit of mass is the
slug which is defined as that mass which will
undergo an acceleration of 1 ft/s2 when a force
of 1 pound is applied to it. So 1 lb = 1 slug ft/s2.
Newton’s Third Law
 Whenever one object exerts a force on a second
object, the second exerts an equal and opposite
force on the first. Just remember that the action
and the reaction forces are acting on different
objects. You must remember on what object a
given force is exerted and by what object the
force is exerted. Newton’s second law applied
only to forces exerted on an object.
 The partnered forces are called the action and
the reaction forces. It does not matter which is
which.
Gas pushes rocket and rocket
pushes against gas.
Questions
 Does a stick of dynamite
contain force?
 A car accelerates along a
road. Strictly speaking, what
is the force that moves the
car?
Does the
dog wag
the tail or
does the
tail wag
the dog?
When
Freddie
Force
jumps from
a boat onto
the dock,
what
happens to
the boat?
Newton’s Third Law
Do action-reaction forces cancel each
other out?
Action and Reaction
Remember that action-reaction forces act
on different objects and, as such, cannot
cancel each other out.
What is the reaction force to a cannon
propelling a cannonball from its muzzle?
Which one is greater, the force from the
cannon or the force from the cannonball?
Weight – the Force of Gravity and the
Normal Force
The force of gravity pulling down on an
object is its weight.
The force exerted by a support structure
such as the floor is called the contact
force.
When a contact force acts perpendicular
to the surface of contact, it is called the
normal force.
Do the normal force and the weight
constitute an action-reaction pair?
Weight – the Force of Gravity and the
Normal Force
To determine the resultant force, you must
have the resultant force in the x direction
and the resultant force in the y direction.
FN
Net force = 0 if FN = Fg
ΣFy = FN - mg
Fg
Vector Forces and Free-Body Diagrams
Include only vectors to indicate velocity,
force, acceleration, etc, and boxes to
indicate objects.
Must be drawn to scale and at correct
angles.
Simple example
Atwood’s machine
Friction and Inclines
Ff = µFN is the formula for static friction.
Friction exists between any two surfaces
in contact.
Kinetic friction is between two surfaces
that are moving.
Static friction is between two surfaces that
are not in motion.