# PHYSICS UNIT 2: DYNAMICS (Explaining Motion)

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31 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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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