Transcript SCI 111 - Onondaga Community College

Chapter 2: Motion
Overview
Description
Explanation
• Position
• Velocity
• Acceleration
• Forces
• Newton’s laws
Applications
Applications
• Horizontal motion on land
• Falling objects
• Compound (2-D) motion
• Momentum
• Circular motion
• Newton’s Universal Law of
Gravitation
Measuring Motion
• Two fundamental
components:
– Change of position
– Passage of time
•
Three important
combinations of
length and time:
1. Speed
2. Velocity
3. Acceleration
Speed
• Change in position with
respect to time
• Three common
“speeds”
– Constant Speed
– Average Speed
– Instantaneous Speed
distance
speed =
time
Th e bar m e an s "ave rage "
distan ce
d
v= t
Ave rage spe e d
tim e
Example: average speed
Fig 2.2
Calculate average speed between trip times
of 1 h and 3 h
150km
50km
50km
d
?
v=
v= t = =
h
2h
?
Example: average speed
How else could we determine v ?
150km
50km
v=
= 50km
h
2h
Fig 2.3
Example 2.1
Example 2.2
Velocity
• Describes speed (How fast is it going?)
AND direction (Where is it going?)
• Graphical representation of vectors:
length = magnitude; arrowheads = direction
Fig 2.4
Acceleration
•
•
Rate at which motion changes over time
Three ways (think of when you’re in the driver’s seat)
1. Speed can change
2. Direction can change
3. Both speed and direction can change
v f - vi
a=
t
Fig 2.6
Acceleration Fig 2.5
Constant speed: no acceleration
Change in speed: acceleration
Correct “5 s” to “4 s” in Caption
• This example shows that you
sometimes need to tie a
couple of relationships
together
• Approach it the same way:
“How to Solve Problems”
Forces – historical background
(FYI)
Aristotle
Galileo and Newton
• Heavier objects fall faster
• Objects moving
horizontally require
continuously applied force
• Relied on thinking alone
• All objects fall at the
same rate
• No force required for
uniform horizontal
motion
• Reasoning based
upon measurements
Force
• A “push” or a “pull”…
…capable of changing an
object’s state of motion
• Sum of all forces
acting on an object
– Net Force
• “Final Force“: after the
forces are “added”
Fig 2.8
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
– Related to its Mass
Balanced and unbalanced
forces
• Motion continues
unchanged w/o
unbalanced forces
• Retarding force
decreases speed
• Boost increases
speed
• Sideways force
changes direction
Galileo’s Breakthrough
Falling objects
• Free fall: falling under
influence of gravity
w/o air resistance
• Distance proportional
to time squared
• Speed increases
linearly with time
• “Acceleration” same
for all objects
m
a = "g" = 9.8 2
s
v f = at ft 2
= 32 2
s
1
d = at
2
Three laws of motion
• First detailed by Newton (1642-1727 AD)
• Concurrently developed calculus and a law
of gravitation
• Essential idea:
– Relationship of forces and changes of motion
Newton’s 1st law of motion
• “The law of inertia”
• Inertia resists any changes in motion
• Every object retains its state of rest or its state of
uniform straight-line motion unless acted upon
by an unbalanced force (bolded print)
Newton’s 2nd law of motion
(see bolded print)
• Relationship between:
Net Force, Mass, &
Acceleration
• Forces can cause
accelerations
• Units = Newtons (N)
• More force, more
acceleration
• More mass, less
acceleration
Fnet = ma
Fnet
a= m
Where a Newton (N)
is defined as [ kg · m / s2 ]
Rearrange
Fnet = ma
Fnet
a= m
Mass vs. Weight
• Mass = quantitative
measure of inertia;
the amount of matter
• Weight = force of gravity
acting on the mass
• Pounds and Newtons are
measures of force
• Kilogram is a measure of
mass
Newton’s 3rd law of motion
Rutger’s Homepage
• 3rd law - relates forces
between objects
– See bolded print
• “For every action, there is
an equal and opposite
reaction”
– But neither force is the
cause of the other
FA dueto B =FB dueto A
Momentum
Rutger’s Homepage
• Important property
closely related to
Newton’s 2nd law
• Includes effects of
both motion
(velocity) and
inertia (mass)
p = mv
Fig 2.24
Conservation of momentum
2 Movies
Conservation of momentum
Fig 2.25
• 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
• A force (F) acting on an object for some time, t
• An impulse produces a change in momentum (Δp)
• Applications: airbags, hitting a baseball, padding for
elbows and knees, orange plastic barrels on highways
impulse = Ft
Forces and circular motion
• Circular motion =
accelerated motion
(direction changing)
• Centripetal acceleration
present thus Fc present
• Centripetal force must be
acting (inward)
• Centripetal force ends:
motion = straight line
v
ac = r
2
v
Fc =ma c = m r
http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html#grvcon
2
Newton’s law of gravitation
• Attractive force between all
masses
• Proportional to product of the
masses
• Inversely proportional to
separation distance squared
• Explains why g = 9.8 m/s2
• Provides centripetal force for
orbital motion
Next:
Chapter 3 - Energy