Transcript Chapter 2 Summary

Nicholas J. Giordano
www.cengage.com/physics/giordano
Motion, Forces and Newton’s Laws
Mechanics
• Mechanics is one area of physics
• It is concerned with the motion of objects
• 2 questions need to be answered to understand
mechanics
• What causes motion?
• Given a particular situation, how will an object move?
Newton’s Laws are a cornerstone of physics
• They are the basis for nearly everything discussed
in the first part of the text
• They are based on ideas developed in centuries
before Newton.
Aristotle’s Mechanics is Wrong!!
• Types of motion identified by Aristotle
• Celestial motion
•
The motion of things like the planets, the Moon, and the stars
• Terrestrial motion
•
•
The motion of “everyday” objects
Objects move when acted on by forces
• Motions of celestial objects and terrestrial objects
look very different
• Mainly because terrestrial objects seem to come to a
stop and celestial objects do not
• The natural state of terrestrial objects was at rest
More About Aristotle’s Terrestrial Motion
 Motion is caused by forces
 Terrestrial objects move only
when acted upon by another
object
 In modern terminology, this
would say that an object moves
only when acted on by a force
 Forces are produced by contact with other objects
Forces
• A force is a push or a pull on an object
• Force is a vector quantity
• The magnitude of the force is the strength of the
push or pull
• The direction of the force is the direction of the
push or pull
• Denoted by
Motion
• One way to think about
motion is in terms of velocity
• Velocity is a vector quantity
• The magnitude is the
distance traveled in one
second
• The direction is the
direction of motion
Aristotle’s Law of Motion is WRONG!
• Aristotle thought the velocity of the object was
proportional to the force acting on it and inversely
proportional to the resistance to the motion
• This was incorrect!
• But does seem to explain many everyday motions
• Failures of Aristotle’s Mechanics
• Doesn’t work in all situations
• Examples: baseball, falling objects
• Lack of direct contact
• Force and velocity are not always in the same direction
• Newton’s Laws overcome the difficulties of Aristotle’s
Mechanics
Example of Failure of Aristotle’s Laws
• Falling object
• Aristotle’s prediction
• A heavy object will fall
faster than a light one when
both are dropped in the
same medium
• Galileo’s Experiment
• Light objects fall at the
same rate as heavy objects
What Is Motion?
• Defined in terms of various concepts
• Look at motion in terms of
• Position
• Velocity
• Acceleration
Section 2.2
Definition of Motion
• Start by considering one-
dimensional motion
• Can be shown by a motion
diagram
• Could be a multiple
exposure
• Sometimes is a sketch
• Shows the location of an
object at regularly spaced
time intervals
Section 2.2
Representations of Motion
• A shows a motion diagram
• Multiple images of a hockey puck
traveling across an icy surface
• B shows a position – time graph
of the motion
• The dots correspond to the images of
the puck
• C shows a velocity-time graph of
the motion
Section 2.2
Velocity and Speed
• The magnitude of the velocity is called the speed
• This is the distance traveled per unit of time
• Speed is a scalar quantity
• The direction of the velocity gives the direction of
the motion
• SI unit is meters / second (m/s)
• Remember that speed and velocity are not
the same
Section 2.2
Velocity and Speed, cont.
• One-dimensional motion
• Direction of velocity will be parallel to the x-
axis
• Will have only one component
• One-, two- or three-dimensional motion
• Velocity may be positive, negative, or zero
• Speed is equal to the magnitude of the velocity
•
Speed cannot be negative
Section 2.2
Displacement and Velocity
• An object’s change in position is its
displacement
• Displacement: Δx = xfinal - xinitial
• Average velocity is the displacement per
unit time:
Section 2.2
Velocity and Position
• In general, the
average velocity is
the slope of the line
segment that
connects the
positions at the
beginning and end of
the time interval
Section 2.2
Velocity Example
• A shows a multiple exposure
sketch of a rocket powered car
• B shows the position-time
graph
• C shows the velocity-time
graph
• In this case, the speed of the
car increases with time
Section 2.2
Instantaneous Velocity
• Average velocity doesn’t tell us
anything about details during the
time interval
• To look at some of the details,
smaller time intervals are needed
• The slope of the curve at the time of
interest will give the instantaneous
velocity at that time
• Will be referred to as velocity
in the text
Section 2.2
Velocity of a Bicycle (Example 2.1)
•
•
•
•
•
Need average velocity from 2.0 to 3.0 seconds
Draw a picture
Find displacement, Δx
Find average velocity, vave = Δx / Δt
Solve
Section 2.2
Graphical Analysis of Velocity (Example 2.3)
• To find the velocity graphically
• Find the slope of the line
tangent to the x-t graph at the
appropriate times
• For the average velocity for a
time interval, find the slope
of the line connecting the two
times
Section 2.2
Average Acceleration
• Acceleration is related to how velocity changes in
time
• Acceleration is defined as the rate at which the
velocity is changing:
• SI unit is m/s²
Section 2.2
Instantaneous Acceleration
 The instantaneous acceleration
can also be defined:
 The instantaneous acceleration
is the slope of the velocitytime graph at a particular
instant in time
 In this case, the average
acceleration equals the
instantaneous acceleration
Section 2.2
Finding Acceleration from a Graph
(Example 2.4)
• The acceleration is
the slope of the
velocity-time graph
• The slopes of the
tangent lines at
various locations on
the graph will give
the acceleration
Section 2.2
Velocity and Acceleration
• Acceleration and velocity do not necessarily reach
a maximum value at the same time
• Acceleration is the slope of the velocity-time
curve
• It is the rate of change of the velocity with
respect to time
Section 2.2
Motion: Summary
• Graphical
• Velocity is the slope of the position-time graph
• Acceleration is the slope of the velocity-time graph
• Position, displacement, velocity and
acceleration are all that are needed to formulate
a complete theory of motion
• Newton’s Laws of Motion explain why these
relationships are valid
Section 2.2
The Principle of Inertia
• Newton’s work was based largely on Galileo’s
• Galileo experimented on the motion of terrestrial
•
•
•
•
objects
The experiments showed an object can move even
with zero force acting on it
Galileo did not arrive at the correct laws of
motion
Galileo did discover the principle of inertia
Newton’s Laws incorporated the principle of
inertia
Section 2.3
Galileo’s Motion Experiments
• Experimented with balls on an incline
• When the ball was released from rest at the top of the
incline, its velocity varied with time
• The acceleration was constant and positive
• The slope of the line in b is the value of the
acceleration shown in c
Section 2.3
Galileo’s Motion Experiments, cont.
• Repeated the experiment by
rolling the ball up the incline
• Give the ball an initial velocity
• The slope of the velocity-time
graph is negative
• The slope of the v-t graph was
always constant and depended
upon the angle of the incline
Section 2.3
Galileo’s Motion Experiments, final
• The acceleration when a ball rolled up a particular
incline was always equal in magnitude, but
opposite in sign, when compared with the
acceleration when the ball rolled down the same
incline
• Reasoned that if the tilt of the incline was exactly
zero, the ball would move with a constant velocity
• Proposed that on a perfectly horizontal ramp, the
ball would roll forever
Section 2.3
Inertia
• The Principle of Inertia
• An object will maintain its state of motion
unless it is acted upon by a force
• The velocity is its state of motion
• Demonstrated by Galileo’s experiments
• Showed that one can have motion without a force
•
Broke Aristotle’s link between force and velocity
• Still did not explain exactly how the force is
linked to the motion
• Newton’s Laws provide this link
Section 2.3
Newton’s Laws of Motion
• The laws are three separate statements about
how things move
• Newton’s First Law is a statement about
inertia
• Newton’s Second Law gives the link
between motion and forces
• Newton’s Third Law explains where forces
come from
Section 2.4
Newton’s First Law
• If the total force acting on an object is zero,
the object will maintain its velocity forever
• If the total force is zero, the object will move
with a constant velocity
• Constant velocity means the same speed and in
the same direction
• Remember velocity is a vector
Section 2.4
Inertia and Mass
• Inertia is a measure of an object’s resistance to
changes in its motion
• This resistance to change depends on the object’s
mass
• The mass of an object is a measure of the
amount of matter it contains
• SI unit of mass is kg
• Mass is an intrinsic property of an object
• It is independent of the object’s location
• It is independent of the object’s velocity or
acceleration
Section 2.4
Newton’s Second Law
• In many situations, several different forces act on
an object simultaneously
• The total force on the object is the sum of these
individual forces,
• The acceleration of an object with mass m is then
given by:
• Newton’s Second Law is the link between force and
motion
• It tells us how an object will move when acted upon by
a force or a collection of forces
Section 2.4
Newton’s Second Law, cont.
 The acceleration of an
object is directly
proportional to the total
force that acts on it.
 Alternative statement
 Remember forces are
vectors so you need vector
addition techniques
 The direction of the
acceleration is parallel to
the sum of the forces
Section 2.4
Force Units
• The SI unit of force is the newton (N)
• Deriving the newton unit:
• Newton’s Second Law has many applications
Section 2.4
Falling Object (Example 2.8)
• The velocity graph is found from the position-time graph
• Slopes at various points to define velocity points
• The acceleration graph is found from the velocity-time graph
• The acceleration is constant and negative
• The force is negative and is proportional to the
acceleration
Section 2.4
Directions
• The direction of the acceleration
is always parallel to the
direction of the total force
• The velocity and the total force
do not need to be in the same
direction
• Example
• Initial velocity is upward
• The total force is downward
• The acceleration is downward
Newton’s Third Law
• When one object exerts a
force on a second object,
the second object exerts a
force of the same
magnitude and opposite
direction on the first object
• Often called the actionreaction principle
• Example
• Force on ball
• Force on bat
Section 2.4
Newton’s Third Law Consequences
• Forces come in pairs
• The two forces are always
equal in magnitude and
opposite in direction
• The forces act on different
objects
• Person exerts a force on the
refrigerator
• The refrigerator exerts a
force on the person
Section 2.4
Using Newton’s Laws
• Newton’s Second Law
• Tells about an object’s acceleration
• Looks at forces acting on one object
• Accounts for all the forces acting on the object
• Newton’s Third Law
• Forces always come in pairs
• For a force acting on one object, there must be a
corresponding reaction force acting on another
object
Section 2.4
Using Newton’s Laws, Example
• Multiple forces act on the
cell
• The force the cell exerts on
the water is equal and
opposite to the force the
water exerts on the cell
• For Newton’s Second Law,
you need to find the total
force acting on the cell
Section 2.5
Laws of Nature
• Ideas and theories can eventually lead to the
discovery of a “law” of physics
• The process by which Newton’s Law came
to be used to illustrate this
Section 2.6
Before Newton
• Aristotle’s Laws of Motion
• For a long time, were the “Laws of Physics”
• Didn’t explain some important observations
• Galileo’s work on motion and ideas of
inertia
• Trying to explain the discrepancies in
Aristotle’s Laws
Section 2.6
Newton
• Likely tested his ideas (hypotheses) by
comparing their predictions with experiments
by Galileo and others
• Reworked ideas until they described motion of
everything studied up to his time
• Laws applied to celestial motion as well as
terrestrial motion
• Others used the Laws to make predictions that
could be tested
Section 2.6
After Newton
• Newton’s Laws do not cover all areas involved
with matter and energy
• Found Newton’s Laws work in the classical
regime
• Wide range of phenomena
• Break down in the quantum regime
• The area of electrons, protons and neutrons
• Newton’s Laws don’t tell us anything about
energy
Section 2.6
Laws of Nature, Final
• All the presently known laws of physics are
known to fail or to be inadequate in some
regime or another
• A law of physics must correctly describe all
behavior in a particular regime of nature
• Newton’s Laws provide an accurate
description of all motion in the regime of
classical physics