Download Physical Science, 6e Motion is.. Speed Measurements of Speed

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Motion is..
Physical Science, 6e
• A change of position along with the passage of time
• Defined with respect to something else, usually “at
rest”.
• The formal definition of motion is the act or process
of changing position relative to some reference
during a period of time.
• The change of position is called displacement
– Straight line distance between 2 points
– Distance is actual path between 2 points
Chapter 2
Motion
Homework: All the multiple choice
questions in “Applying the Concepts”
and Group A questions in “Parallel
Exercises”.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Measurements of Speed
Speed
• Change in position
with respect to time or
distance is covered per
unit time.
• Average speed - most
common measurement
• Instantaneous speed time interval
approaches zero
speed = distance
time
distance
The bar means "average"
v = dt
Average speed
time
• Instantaneous speed at any specific instant
is given by the speedometer in a car.
• Measurements such as speed with
magnitude ONLY are called scalar
quantities.
• The English system uses miles per hour
(mph or mi/hr)
• The metric system uses kilometers per hour
(km/hr) or meters per second (m/s)
Example: average speed
Calculate average speed between trip times of 1
h and 3 h
v = dt = ?
?
v = 150 km - 50km = 50km
h
2h
•Constant speed is difficult to maintain during driving;
average speed is used to describe the rate of travel.
Velocity
• Describes speed (How fast is it going?) and
direction (Where is it going?)
• Graphical representation of vectors: length =
magnitude; arrowheads = direction
Velocity
• Velocity is different from speed because it includes
both speed AND direction
• Measurements such as velocity with BOTH
magnitude AND direction are called vector
quantities.
• Velocity has the same numerical value as speed
but includes DIRECTION
• d = (vf +vi)/2 . t in which (vf +vi)/2= average
velocity under constant acceleration)
• d = (vf/2). t (for vi = 0)
Newton’s 1st Law of Motion
• Every object retains its state of rest or its state of
uniform straight-line motion unless acted upon by
an unbalanced force
• “The law of inertia”: tendency of an object to
remain in unchanging motion or at rest in the
absence of an unbalanced force.
Newton’s 2nd Law of Motion
F net = ma
Acceleration
F
a = mnet
• Acceleration is the change in velocity per unit time
and is commonly measured in m/s2.
f
i
• Speed can change
• Direction can change
• Both speed and direction can change
v - v
a=
t
•
•
•
•
Forces (F) cause accelerations (a)
Force = mass (kg) x acceleration (m/s2)
Units of force = kg-m/s2 = Newton (N)
The acceleration of an object is directly proportional to
the net force acting on it and inversely proportional to
the mass of the object.
• More force (F), more acceleration (a)
• More mass (m), less acceleration (a)
Weight and mass
Examples - Newton’s 2nd Law
• More mass, less
acceleration, again
• Focus on net force
– Net force zero here
– Air resistance + tire
friction match
applied force
– Result: no
acceleration;
constant velocity
•
•
•
•
•
•
Mass is not the same as weight
Mass = the amount of matter; measurement of inertia
Weight = force of gravity acting on the mass
Pounds and Newtons are units for measuring forces
Kilogram = measure of mass
Weight varies based on location but mass remains
constant.
Free Fall
• Any object dropped near the Earth’s surface, no matter how
heavy or light, falls with the same constant acceleration in
the absence of air resistance.
• The velocity of a falling object is proportional to the length of
the time that it has been falling.
• An object falling for 2 s reaches a velocity 2x that of an
object that has been falling for 1 s
• Speed increases each second it falls!
• The symbol for gravitational acceleration on Earth is “g” and
is equal to 9.8 m/s2 = 32 ft/s2
• Acceleration due to gravity, g, is independent of any motion
that the object may have.
Forces
• A push or pull associated with any change of
motion
• A force has magnitude and direction
• Forces are present in the interaction of two
planetary bodies over a distance or even the
interaction of electrons with protons in the
nucleus of an atom.
• An example is the gravitational attraction
between the moon and the Earth.
Falling Objects
• Free fall - falling under influence of gravity w/o air
resistance
• Distance (d) proportional to time squared because d = ½ at2
f
• Speed increases linearly with time
d = 1 at 2
• Trajectories exhibit up/down symmetries
2
• Acceleration same for all objects
v = at
Forces
• A push or pull capable of
changing an object’s state of
motion
• Forces have magnitude and
direction that can be added as
vectors to give a net force.
– Net force is sum of the 2
forces or vectors (Fig.
2.8a on Page 33)
– Net force = 0; balanced
force (Fig. 2.8b)
– 2000 units west if the
wind blowing west and
the ship traveling west
are both 1000 units. (Fig.
2 8c)
Forces - Historical Background
Aristotle
• Heavier objects fall
faster
• Objects moving
horizontally require
continuously applied
force
• Relied on thinking
alone
Galileo and Newton
• All objects fall at the
same rate
• No force required for
uniform horizontal
motion
• Reasoning based
upon measurements
Galileo’s Study of Motion
• Trial by the Inquisition and put on house
arrest
• Published book secretly in 1638 on motion
• Father of experimental science
• 1992 found “not guilty” by the Catholic
Church
• Motion will continue with balanced forces
• Motion will start or stop with unbalanced
forces
Galileo (1564 to 1642)
• Built telescope in 1609 to study celestial
bodies, solar system, mountains on Moon,
sunspots, rings around Saturn, and moons
revolving around Jupiter.
• Challenged the view that the Earth is center
of rotation for the universe and supported
sun-centered theory of Copernicus.
• Put on heresy trial for the alleged violation of
Catholic Church doctrine!
Sir Isaac Newton
• Born in 1642 (Galileo died in 1642)
• Studied at home during the bubonic plague
years
• Concurrently developed calculus and a law of
gravitation
• Also studied motion and gravity; optics, light,
and color; planetary motion.
• Shy and dedicated to his work
• Quote: “it was by standing upon the shoulders
of giants” (i.e. Galileo)
Balanced and Unbalanced Forces
• Motion continues
unchanged w/o unbalanced
forces
• Boost increases speed
• Retarding force decreases
speed
• Sideways force changes
direction
Falling Objects
• Galileo’s experiment on the
Leaning Tower of Pisa
• Dropping iron ball and wood
ball atop the tower; which will
hit the ground first? Both hit
at the same time!
• Velocity of a falling object
does NOT depend on its
weight
Newton’s 3rd Law of Motion
• For every action, there is an equal and opposite
reaction.
• The 3rd law relates forces between objects
• “Whenever two objects interact, the force exerted
on one object is equal in size and opposite in
direction to the force exerted on the other object.”
F A due to B =F B due to A
Horizontal motion on land
“Natural motion”
question: Is a
continuous force
needed to keep an
object moving?
• No, in the absence of
unbalanced retarding
forces
• Inertia - measure of an
object’s tendency to
resist changes in its
motion (including rest)
Projectile Motion
Compound Motion
Three types of motion:
1.
2.
3.
•
•
•
Vertical motion
Horizontal motion
Combination of 1. and 2 or compound motion
Throwing a football, discus, or shooting any projectiles
into the air is a form of compound motion.
Gravity acts on objects at all times and give rise to the
parabolic path of the projectile trajectory that can be
resolved into vertical and horizontal components.
An angle of 45° results in maximum angle of travel.
Example: Passing a Football
• Only force = gravity (down)
• Vertical velocity
decreases, stops and then
increases
• Horizontal motion is
uniform in the absence of
air resistance
• Combination of two
motions = parabola
Vertical projectile
Horizontal projectiles
•
•
•
•
• Horizontal velocity
remains the same
(neglecting air resistance)
• Taken with vertical motion
= curved path
Slows going up
Stops at top
Accelerates downward
Force of gravity acts
downward throughout
• Vertical motion of a falling
ball compared to the
compound motion of an
arrow that has both vertical
and horizontal component.
• They strike the ground at the
same time!
Momentum
• Momentum (p) involves both the
inertia/mass (m) and the velocity
(v) of a moving object as given by:
• p = mv where “p” has the unit of
kg-m/s
• The total momentum of a group
of interacting objects remains
the same in the absence of
external forces
• Applications: Collisions,
analyzing action/reaction
interactions
Impulse
• Impulse is defined as the product of a force (F)
and the time (t) during which the force acts upon
an object and is related to “follow through” when
hitting a ball.
• An impulse produces a change in momentum
(Up)
• Applications: airbags, padding for elbows and
knees, protective plastic barrels on highways
impulse = Ft
Forces and Circular Motion
• Circular motion =
accelerated motion
(direction changing)
• Centripetal acceleration
present
• Centripetal force must be
acting
• Centrifugal force - apparent
outward tug as direction
changes
• Centripetal force ends:
motion = straight line
2
a c = vr
2
F c = m a c = m vr
Centripetal Force
• Centrifugal force is the outward force on an
object in circular motion that is a
consequence of the third law of motion
• Center-seeking force or centripetal force
helps keep a ball swung from a string in a
circular path; when the string released, the
ball moves in a straight line at a right angle
to the radius at the point of release due to
outward centrifugal force.
• Centripetal force = (mv2)/r
Newton’s Law of Gravitation
• Gravitational force (F) is the
attractive force between
planetary bodies and is
proportional to the product
of their masses but
inversely proportional to the
square of the distance (d).
• Explains why g = 9.8m/s2
• Provides centripetal force
for orbital motion of planets.