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, FG: object’s weight, always directed toward
center of earth (FG=mg mass × acceleration due to
gravity)
 normal force, FN: supporting force a surface exerts on an
object, always directed upward perpendicular to the
surface
 tension, FT: 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 (1st 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
1st Law
NEWTON’S
MOTION

nd
2
LAW OF
The Law of Acceleration (2nd Law): a net force
causes an acceleration proportional to the force, in
the same direction, and inversely proportional to
mass.
Fnet = ma
Fnet: sum of all forces or net force (N),
 m: mass (kg),
2
 a: acceleration (m/s )
2
 1 N = 1 kg·m/s

NEWTON’S 2nd LAW OF MOTION
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
MOTION

rd
3
LAW OF
The Law of Interaction (3rd Law): for
every action force from one object on
another, there is an equal magnitude,
opposite direction reaction force from
the 2nd object back on the 1st
action: hammer
hits anvil
reaction: anvil
hits hammer
NEWTON’S
MOTION

rd
3
LAW OF
Law of Interaction (3rd 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
rd
3
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 – Fx=Fcosq Fy=Fsinq
 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
12.0 The
m/s2 hill
the ball down the hill is 6.00 N.
49.0What
m/s
is 100.0 m long. (a)
is the ball’s
acceleration? (b) How fast is the ball
2)
doubles
going
at (24
them/s
bottom
of the hill, if it
2)
halves(c)
(6 m/s
started at rest at the top?
If the
force on the ball doubled, what would
PHYSICS
UNIT 2: DYNAMICS
(Explaining Motion)
NEWTON’S LAWS OF
MOTION

Law of Inertia (1st Law)

objects slow & stop, or require continued
force to keep moving, due to friction
FRICTION

Friction Force, Ff:
resistance to motion
between objects in
contact with each
other

acts parallel to contact
surface, opposite to
motion
FRICTION
kinetic
friction <
static friction

static friction: resistance to starting
motion (at rest)


beneficial (walking, building, eating,
wheels rolling)
kinetic friction: resistance to continued
FRICTION

coefficient of friction, m: constant that
depends on type of surfaces in contact
ms: coefficient of static friction
 mk: coefficient of kinetic friction
 Ff = mFN
(friction force = m × normal
force)

FRICTION
FRICTION

FN
on horizontal surface:
Ff


FN = mg
(normal force = body weight)
so Ff = mmg
mg
FRICTION

on tilted surface:
FN
Ff
mgcosq
q mg
FN = mgcosq
 so f = mmgcosq

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) 7060
N a force of 10,000 N?
b) 2.45 m/s2
PHYSICS
UNIT 2: DYNAMICS
(Explaining Motion)
PROJECTILE MOTION

Projectile motion: parabolic trajectory
(path)

Two dimensions of motion: horizontal (x),
vy
v
vertical (y)
vy =
vsinq
q
vx
vx = vcosq
PROJECTILE MOTION

Vertical
Motion
constant vertical
acceleration due
to gravity
(2nd Law)
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

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 + visinqit – ½gt2
 a. for ground launch, h=0, y = v sinq t –
i
i
½gt2
 b. for horizontal cliff launch, q =0, y = h
0
– ½gt2
 speed: v = 2
vvisinq
–
gt
2h
sin
q
y
i
i
i
T
T
g
 flight time, T: t g
when y=0

PROJECTILE MOTION

Horizontal
Motion
constant
horizontal
speed
due to no
horizontal
force
(1st Law)
A tank moving at constant speed fires a
shell straight up into the air. Where will
the shell come back down?
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 = vicosqit
 for horizontal cliff launch, q =0, x = v t
i
i
 speed: v = v cosq
x
i
i
 range, R: x when t = T
2
2h
v
sin(
2
q
)
i
 ground:
Rcliff:
 vi
R i

g
g
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)
RELATIVE MOTION

Reference
Frames:
projectile motion in
one reference frame
can be vertical free
fall in another
reference frame (and
vice versa)
A plane moving at constant speed
drops a flare. Describe the path of
the flare.
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 7.67
a speed
of 19 m/s. (a) Find
m
the ball's vertical
14.3 m/s position after 1.5 seconds.
(b) Find the ball's horizontal speed after 1.5
seconds.4.40 s
83.6 m
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.
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
SF = ma
FG = mg
Ff = mFN
vf = vi + at
Dx= vit + ½at2
vf2=vi2 + 2aDx
y = h + visinqit –
½gt2
x = vicosqit
vy = visinqi – gt
2h
vx =2vvi isin
cosq
qi i
T
T
g
vi2 sin(2qi )
R
g
g
2h
R vi
g