Transcript Chapter 2, 4 &5 Newton`s Laws of Motion

Chapter 2, 4 &5
Newton’s Laws of Motion
Aristotle (384-322)BC
Aristotelian School of Thought
Natural Motion
Every Object in the universe has a proper
place, determined by its nature.
Heavier objects strive harder to be in
their proper place.
This implies that heavier objects fall
faster than lighter objects.
Violent Motion:
All motion results from a push or pull.
Except for celestial objects (the realm of the
Gods), the normal “natural” state of an object
was to be at rest.
The Earth does not move.
Aristotle’s school of thought dominated
western culture for the next 2000 years, until
the 16th century.
Celestial Spheres
Copernicus and the Moving Earth
Ptolemaic Model
• Copernican Model
Copernicus asserts that the Sun is
at the center of the solar system
instead of the Earth. This runs
contrary to the Aristotelian school
of thought.
1543 – Copernicus publishes
De Revolutionibus
Galileo Galilei
Galileo is considered to be the father of
experimental science.
Galileo demolished the Aristotelian model by
doing experiments and proving it wrong.
Inclined plane demo
Galileo’s Inclined Planes
Inertia
The tendency of a body to resist changes in
its motion.
Mass is a measure of inertia – A more
massive body has more inertia.
Chapter 3
Linear Motion
Description of Motion -Kinematics
dis tan ce
Speed 
time
Average Speed = total distance/time
Total distance = (Average speed) x (time)
Velocity
Speed in a particular direction
Examples
70mi/h due north --- is a velocity
70mi/h ----- is a speed
Approximate Speeds in Different Units
20km/h
12 mi/h
6 m/s
40 km/h
60 km/h
25 mi/h
37 mi/h
11 m/s
17 m/s
65 km/h
40 mi/h
18 m/s
80 km/h
50 mi/h
22 m/s
88 km/h
100 km/h
55 mi/h
24 m/s
62 mi/h
28 m/s
120 km/h
75 mi/h
33 m/s
Velocity is proportional to the time
velocity (m/s)
200
150
100
50
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
time(sec)
Acceleration
Acceleration = change in velocity/change in time
V
a
t
How quickly how fast changes
Constant Acceleration – Free Fall
Near the surface of the earth, all objects
fall with the same acceleration baring
effects from air friction.
In this case, a = g = 9.8m/s/s or 32 ft/s/s
or a = g = 9.8m/s2 or 32 ft/s2
Distance traveled
Assume a= 2 m/s/s and is constant.
1 sec
2 sec
3 sec
The distance traveled is
proportional to the time squared.
1 2
d  at
2
1 2
d  at
2
2d
t
a
Distance vs time
d = ½ gt2
distance (m)
2000
1500
1000
500
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
time (sec)
x d
V 

t t
V
a
t
If a is constant
V  at
V  at
V  Vo  a(t  to )
V  Vo  a(t  to )
If the particle starts with an initial velocity
of Vo at zero seconds (to = 0 sec) then:
V  Vo  at
V  Vo  at
Assume Vo = 1m/s and a = 10m/s2
t(sec)
V(m/s)
0s
1 m/s
1s
11 m/s
2s
21 m/s
3s
31 m/s
4s
41 m/s
5s
51 m/s
6s
61 m/s
7s
71m/s
8s
81 m/s
9s
91m/s
10 s
101 m/s
1  11  21  31  41  51  61  71  81  91  101
V 
 51m / s
11
Vo  V 1  101
V 

 51m / s
2
2
x d
V 

t t
V
a
t
Vo  V
V 
2
For free-fall
a  g
y d
V 

t t
x  y  d
Vo  V
V 
2
V
g 
t
Newton’s Laws of Motion
Newton’s First Law of Motion
Every object continues in its state of
rest, or of uniform motion in a straight
line, unless it is compelled to change
that state by forces impressed upon it.
Newton’s Second law of Motion
The acceleration of an object is
directly proportional to the net force
acting on the object, is in the direction
of the net force, and is inversely
proportional to the mass of the object.


Fnet  ma
Newton’s Third Law of Motion
For every action, there is always
opposed an equal reaction.
By “action”, we mean a force.
Action/reaction forces do not
act on the same object.
Types of Forces
Gravitational
Friction
Normal
Electromagnetic
Forces between masses
Contact force
Contact force
Forces between charges.
Nuclear
Forces between nuclear
particles (protons,
neutron)
Spring
Restoring Forces
When the acceleration is g
we have Free Fall
m
2m
F
2F
F
g
m
2F
g
2m
When acceleration is zero Equilibrium
N
Fnet  N  mg
Fnet  ma  0
N  mg  0
mg
N  mg
When acceleration is zero Equilibrium
N  mg
N
v = constant
Fa
f
mg
FH  Fa  f  0
Fa  f
Action/Reaction pairs
Action:
Reaction:
Tire Pushes on Road
Road pushes on Tire
Action/Reaction
Action: Rocket pushes on gas
Reaction: Gas pushes on rocket
Nonlinear Motion
Velocity : A vector quantity
A
B
A+B
Vector quantities have
magnitude and
direction
A
R=A+B
B
R is called the resultant
vector
The Pythagorean Theorem
R2 = A2 + B2
A
B
Projectile Motion
Any object that is projected by some
means and continues in motion under
the influence of gravity and air
resistance is called a projectile.
The path of a projectile is
called the trajectory
Projectile Motion
-g vector
Projectile Range
14
At 30 degrees
Vertical Distance (m )
12
10
8
6
At 15 degrees
4
2
0
0
20
40
60
Horizontal distance (m)
80
100
120
Fast Moving Projectiles
Satellites
The Earth’s curvature drops a vertical distance of
5 meters every 8,000 meters horizontally
Circular Motion
V=r

r