PHYSICS UNIT 2: DYNAMICS
(Explaining Motion)
FORCES
Force
: a "push" or a "pull“
unit:
Newtons, N
(1 N is about ¼ lb)
vector

includes direction
contact forces
and
field forces
(act over a
distance)
net force
: total effect of all forces acting on
an object
FORCES
Typical Forces
gravity, F
G
:
object’s weight, always directed toward
center of earth (
F
G
=mg
mass
×
acceleration due to
gravity
)
normal force, F
N
: supporting force a surface exerts on an
object, always directed
upward perpendicular to the
surface
tension, F
T
: force transmitted by a rope or chain, directed
along the rope, constant throughout the rope
FORCES
Free body diagrams
: show just one object & the
forces acting
on the object
(NOT forces the object
is exerting on other things)
example: car hitting a
wall
Examples
Apple on a table
Rock under
water
Block on a hill
Water skier
Child pulled
forward at an
angle on a sled
NEWTON’S LAWS OF
MOTION
The Law of Inertia (1
st
Law):
an object’s
velocity stays constant
unless acted
upon by a net external force
inertia
: resistance to
change
in motion
(mass is a measure of inertia, more mass
= more inertia)
Example of
Newton’s
1
st
Law
NEWTON’S 2
nd
LAW OF
MOTION
The Law of Acceleration (2
nd
Law):
a net force
causes an acceleration
proportional to the force, in
the same direction, and inversely proportional to
mass.
F
net
= ma
F
net
: sum of all forces or net force (N),
m: mass (kg),
a: acceleration (m/s
2
)
1 N = 1 kg∙m/s
2
Second
The
greater
the force, the greater the
acceleration
The greater the
mass
, the greater the force
needed
for the
same
acceleration
Calculated by:
F = ma
(F = force, m = mass, a = acceleration)
NEWTON’S 2
nd
LAW OF MOTION
NEWTON’S 3
rd
LAW OF
MOTION
The Law of Interaction (3
rd
Law):
for
every action force
from one object on
another,
there is an equal magnitude,
opposite direction reaction force
from
the 2
nd
object back on the 1
st
action: hammer
hits anvil
reaction: anvil
hits hammer
NEWTON’S 3
rd
LAW OF
MOTION
Law of Interaction (3
rd
Law)
action & reaction forces do not balance
each other

they are on different bodies
(ex: car pulling a trailer)
equal force does not mean equal
acceleration

depends on mass
(ex:
person jumping off the ground)
Examples of Newton’s 3
rd
law
FORCES
Finding the Net Force
(total of all forces on an object)
draw a free body diagram
identify & label
x & y axes
separate forces into x and y parts
–
F
x
=Fcos
q
F
y
=Fsin
q
add all x forces, add all y forces
equilibrium
: no net force
–
x forces add up to zero, y
forces add up to zero
Example
LAB 2.3
–
Elevator Scene 1
LAB 2.3
–
Elevator Scene 2
LAB 2.3
–
Elevator Scene 3
LAB 2.3
–
Elevator Frame 1
LAB 2.3
–
Elevator Frame 2
LAB 2.3
–
Elevator Frame 3
LAB 2.3
–
Elevator Frame 4
LAB 2.3
–
Elevator Frame 5
LAB 2.3
–
Elevator Frame 6
LAB 2.3
–
Elevator Frame 7
QUIZ 2.1
Joe rolls a ball down a hill. The ball has
a mass of 0.500 kg. The force pulling
the ball down the hill is 6.00 N. The hill
is 100.0 m long. (a) What is the ball’s
acceleration? (b) How fast is the ball
going at the bottom of the hill, if it
started at rest at the top? (c) If the
force on the ball doubled, what would
happen to the ball’s acceleration? (d) If
instead the mass of the ball doubled,
what would happen to its acceleration?
12.0 m/s
2
49.0 m/s
doubles (24 m/s
2
)
halves (6 m/s
2
)
PHYSICS
UNIT 2: DYNAMICS
(Explaining Motion)
NEWTON’S LAWS OF
MOTION
Law of Inertia (1
st
Law)
objects slow & stop, or require continued
force to keep moving, due to
friction
FRICTION
Friction Force, F
f
:
resistance to motion
between objects in
contact with each
other
acts
parallel to contact
surface, opposite to
motion
caused by uneven
surfaces, molecular
attraction
FRICTION
static friction
: resistance to starting
motion (at rest)
beneficial
(walking, building, eating,
wheels rolling)
kinetic friction
: resistance to continued
motion (sliding)
undesirable
(machines, moving furniture,
wheels skidding)
kinetic
friction <
static friction
FRICTION
coefficient of friction,
m
: constant that
depends on type of surfaces in contact
m
s
: coefficient of static friction
m
k
: coefficient of kinetic friction
F
f
=
m
F
N
(friction force =
m
×
normal
force)
FRICTION
F
f
FRICTION
on
horizontal
surface:
mg
F
N
F
N
= mg
(normal force = body weight)
so
F
f
=
m
mg
FRICTION
on
tilted
surface:
q
mg
mgcos
q
F
N
F
f
F
N
= mgcos
q
so
f =
m
mgcos
q
PHYSICS
UNIT 2: DYNAMICS
(Explaining Motion)
QUIZ 2.2
A 1200 kg car sits on a horizontal road.
(a) How much force does Joe need to
push the car at a constant speed if the
coefficient of kinetic friction is 0.600?
(b) How much will the car accelerate if
Joe uses a force of 10,000 N?
a) 7060 N
b) 2.45 m/s
2
PHYSICS
UNIT 2: DYNAMICS
(Explaining Motion)
PROJECTILE MOTION
Projectile motion:
parabolic trajectory
(path)
Two dimensions of motion:
horizontal (x),
vertical (y)
v
y
v
x
q
v
v
x
= vcos
q
v
y
=
vsin
q
if a bullet was fired horizontally, and
another bullet was dropped from the
same height at the same time, which
would hit the ground first?
PROJECTILE MOTION
Vertical
Motion
constant vertical
acceleration
due
to gravity
(2
nd
Law)
PROJECTILE MOTION
A monkey hangs from a tree branch. A
hunter aims his tranquilizer gun barrel
straight at the monkey. When the hunter
fires his gun, should the monkey keep
holding on to the branch, or let go?
PROJECTILE MOTION
Vertical Motion
position:
y = h + v
i
sin
q
i
t
–
½gt
2
a. for ground launch, h=0,
y = v
i
sin
q
i
t
–
½gt
2
b. for horizontal cliff launch,
q
0
=0,
y = h
–
½gt
2
speed:
v
y
= v
i
sin
q
i
–
gt
flight time, T
: t when y=0
ground: cliff:
A tank moving at constant speed fires a
shell straight up into the air. Where will
the shell come back down?
PROJECTILE MOTION
Horizontal
Motion
constant
horizontal
speed
due to no
horizontal
force
(1
st
Law)
PROJECTILE MOTION
A snowmobile fires a flare, then slows
down. Where does the flare land? If
the snowmobile speeds up instead,
where does the flare land?
PROJECTILE MOTION
Horizontal Motion
position:
x = v
i
cos
q
i
t
for horizontal cliff launch,
q
i
=0,
x = v
i
t
speed:
v
x
= v
i
cos
q
i
range, R
: x when t = T
ground: cliff:
PROJECTILE MOTION
Example: A projectile is launched from ground level with a
velocity of 50 m/s at an angle of 30 degrees. What is its
position and velocity 2 seconds later? What is its flight
time? What is its range?
PHYSICS
UNIT 2: DYNAMICS
(Explaining Motion)
A plane moving at constant speed
drops a flare. Describe the path of
the flare.
RELATIVE MOTION
Reference
Frames
:
projectile motion
in
one reference frame
can be
vertical free
fall
in another
reference frame
(and
vice versa)
PHYSICS
UNIT 2: DYNAMICS
(Explaining Motion)
QUIZ 2.3
Circle your answers! Watch sig. fig's & units!
1. Joe throws a ball from ground level at an angle of 41º and a speed
of 19 m/s. (a) Find the ball's vertical position after 1.5 seconds. (b)
Find the ball's horizontal speed after 1.5 seconds.
2. Jane throws a ball off a 95

m tall building horizontally at 19 m/s.
(a) Find the ball's flight time. (b) Find the ball's range.
y = h + v
i
sin
q
i
t
–
½gt
2
v
y
= v
i
sin
q
i
–
gt
x = v
i
cos
q
i
t v
x
= v
i
cos
q
i
7.67 m
14.3 m/s
4.40 s
83.6 m
PHYSICS
UNIT 2: DYNAMICS
(Explaining Motion)
UNIT 2 REVIEW
Newton's Laws (Memorize!):
1st Law: velocity stays constant unless
acted upon by a net force
2nd Law: net force = mass x acceleration
3rd Law: for every action force, there is an
equal and opposite reaction force
UNIT 2 REVIEW
S
F = ma
F
G
= mg
F
f
=
m
F
N
v
f
= v
i
+ at
D
x= v
i
t + ½at
2
v
f
2
=v
i
2
+ 2a
D
x
y = h + v
i
sin
q
i
t
–
½gt
2
x = v
i
cos
q
i
t
v
y
= v
i
sin
q
i
–
gt
v
x
= v
i
cos
q
i
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