Forces

A force is just a push or pull.
– an object’s weight
– tension in a rope
– a left hook to the schnozzola
– friction
– attraction between an electron and proton

Bodies don’t have to be in contact to
exert forces on each other, e.g., gravity.
System/Environment

System--is the object that is being
considered in situation…. p. 119 book
– Book on desk
– Ball hanging on rope
– Ball held in hand

Environment– is the world around
object that is exerting forces on the
system
Contact vs. Long Range forces

Contact Forces act on body by
touching it

Long Range Forces act at a distance,
without contact.
Examples of each kinds of
force…
Frictional Force
1. Contact--actual Tensional Force
Normal Force
Air Resistance
touching
Applied Force
2. Long-Range— Spring Force
forces acting at
A Gravitational
a distance
B. Electromagnetic
C. Nuclear
Forces that could cause accelerations
Force
Symbol
Definition
Direction
Ff
The contact force that acts to
oppose sliding motion
between surfaces
Parallel to the surface and
opposite the direction of
sliding
Normal
FN
The contact force exerted by a
surface on an object
Perpendicular to and away
from the surface
Spring
Fsp
A restoring force, the push or
pull a spring exerts on an
object
Opposite the displacement
of the object at the end of
the spring
Tension
FT
The pull exerted by a string,
rope, or cable when attached
to a body and pulled taut
Away from the object and
parallel to the
string/rope/cable at the point
of attachment
Weight
FW or Fg
Long range force due to
gravitational attraction
between two objects
(generally Earth and an object)
Straight down toward the
center of the earth
Friction
Fundamental Forces of Nature: Long
Range Forces

Gravity
– Attraction between any two bodies w/ mass
– Weakest but most dominant

Electromagnetic
– Forces between any two bodies w/ charge
– Attractive or repulsive
 Weak nuclear force – responsible for
radioactive decay
 Strong nuclear force – holds quarks
together (constituents of protons and
neutrons)
Agents

An Agent is a specific, identifiable,
immediate cause of a force
– Mass is the agent of gravity
– Examine diagrams in book, page 119.
– Identify the agents of each force
– Now you try it….Practice problem #1,
p. 119
Free Body Diagram
Diagram showing all forces acting on an
object.
 Shows object as a dot.

Try a few….
What forces are acting on a “little, red
wagon” as it is being pulled at a
constant velocity?
 What forces are acting on a steel anvil
as it falls through the air? (not at
Terminal velocity)
 What forces are acting on an airplane in
level flight, at a constant velocity?
 What forces are acting on a person in
an elevator that is accelerating upward?

Wagon
Anvil
FNormal
Fdrag
Fapplied
Ffriction
Fw or Fg
Airplane
Fdrag
Flift
Fthrust
Fw or Fg
Fw or Fg
Elevator
Fapplied (causing acceleration)
FNormal
Fw or Fg
Newton’s 3 Laws of Motion
Newton’s 3 Laws of Motion
1.
2.
3.
Inertia: “An object in motion tends to
stay in motion; an object at rest tends
to stay at rest.” (unless some force
acts upon the object)
Fnet = ma
Action – Reaction: “For every
action there is an equal but
opposite reaction.”
nd
2
Law: Fnet = ma
The acceleration an object experiences
is directly proportional to the net force
acting on it and is inversely proportional
to the mass of the object.
 For a given mass, if Fnet doubles, triples,
etc. in size, so does a.
 For a given Fnet if m doubles, a is cut in
half.
 Fnet and a are vectors and always point
in the same direction.

Units
Fnet = m a
1N
= 1 kg
2
m/s
The SI unit of force is the Newton.
A Newton feels like about a quarter pound.
1 lb = 4.45 N An apple weighs about 1N
What Newton was really saying…
Greater net forces cause greater
accelerations
 Greater masses require greater net
forces to accelerate at equal rates
 Greater accelerations can occur if an
object is smaller

What is Net Force?
F1
F2
F3
Fnet
Net force (resultant
force) is the vector sum
of all the forces, e.g.,
the “net effect.”
If Net force acting on object is
zero….forces are said to “balanced”
and the object will not experience a
change in velocity (will have a zero
acceleration)
 Newton’s 1st law
 If net force is zero, then object could
either be moving (with a constant
velocity), or stopped.

Net Force & the
nd
2
Law
When forces act in the same line, we can just add
or subtract their magnitudes to find the net force.
32 N
15 N
2 kg
10 N
Fnet = 27 N to the right
a = 13.5 m/s2
Net Force and Newton’s 2nd Law
10 kg
3N
5N
a=????
ttp://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/newtlaws/u2l3c.htm
4N
Fnet = 0
4N
3N
CD p16
4N
Fnet = 1
4N
4N
3N
Fnet = 5N
3N Fnet = 5N
4N
2N
4N
2N
3N 5N
Fnet = 5N
CD p16
3N
5N
Fnet = 5N
9.9
9.9
0
CD p16
7
R=133N, northeast
Find acceleration of the 10kg object…….
F =ma
net
B
50.N
80. °
Cx=0N
Cy=-75N
Rx=140N + -8.7N
Ry=51N + 49N +-75N
Rx2 + Ry2 = R2
C
R2=(131N)2 + (25N)2
A
20.°
a= F
m
= 133N
150N
10kg
=13.3m/s2!!
Ax=hypCos20° Ay=hypSin20 °
75N =150NCos20° =150NSin20°
=51N
=140N
Bx=hypCos100° By=hypSin100°
=50.NCos 100° =50.NSin100°
=49N
=-8.7N
W = mg, a specific application of
F=ma
Weight = mass  acceleration due to
gravity.
 This follows directly from F = m a.
 Weight is the force of gravity on a body.
 Near the surface of the Earth,
g = 9.8 m/s2.

Why, exactly, do heavier and lighter objects
fall with the same acceleration???? Isn’t
gravity pulling down on the heavier object
more?? Shouldn’t it accelerate faster as a
result of the larger force?
4. The force due to gravity on an
object is called? weight
The quantity of matter in an
object is called? mass
The amount of space an object
occupies is called? volume
CD p12
5. The force due
to gravity on
1-kg is 9.8 N
The force due
to gravity on
5-kg is 49 N
The mass with
a weight of 98
N is 10 kg
CD p12
w = mg
6. Find the weight of your
physics book. Then complete
the table.
CD p12
Object
Mass
Weight
Melon
1 kg
9.8 N
_____
Apple
0.1 kg
______
1N
Physics Book
______
______
Uncle Harry
90 kg
882 N
______
300
300
300
CD p13
150
100
CD p13
300
150
No!!!
300
150
No!!!
500
830
1000
CD p13
Newton’s First Law of Motion
Is a variation of the 2nd Law, for cases of
ZERO NET FORCE
 An object with no net force acting on it
is said to be in EQUILIBRIUM
 An object in equilibrium will be
stationary, or could be moving at a
constant velocity.

Inertia
“An object in motion tends to stay in motion;
an object at rest tends to stay at rest.”
 A moving
body will continue moving
in the same direction with the same
speed until some net force acts on it.
 A body
at rest will remain at rest
unless a net force acts on it.
 Summing
it up: It takes a net force
to change a body’s velocity.
What force acts on the ladder “in flight”?
Draw a free-body diagram of the forces acting on the ladder
Mass and Inertia
Mass is the “origin” of inertia
 If an object has a large mass, then it will
have a large inertia
 If an object has a small mass, then it will
have a small inertia

Inertia Example 1
An astronaut in
outer space will
continue drifting
in the same
direction at the
same speed
indefinitely, until
acted upon by an
outside force.
Inertia Example 2
If you’re driving at 65 mph and have an
accident, your car may come to a stop in
an instant, while your body is still moving
at 65 mph. Without a seatbelt, your inertia
could carry you through the windshield.
Inertia Demo
Inertia Demo
No Demo!!
1. An
The
astronaut
rock’s tendency
in outer to
space
do this
away
is called…
from allinertia.
forces throws a
rock.isWhat
will happen to the
What
inertia?
rock?
How
is it measured? grams /kg.
CD p11
What
the is
path
of the
rock at
2.
Theisrock
being
whirled
when
the string
breaks?
the end
of a string
in a
clockwise rotation.
A
B
C
D
CD p11
7. Hit lead plate with hammer
CD p12
3. The bus is traveling at 100 km/h.
Its horizontal
velocity
is100 km/h.
Relative
to the bus,
the pencil
is
As it drops,
horizontal
0 km/h.
traveling
at… its
velocity is 100 km/h.
Where
Where
will
will
thethe
pencil
strike
pencil
thestrike
floor?the
Directly
floor if
below
the bus
where
is
dropped.
at rest?
Directly below where
dropped.
CD p11
Newton’s 3rd Law…Action-Reaction
For every action force, there is an
opposite, but equal reaction force
Action - Reaction
“For every action there’s an
equal but opposite reaction.”

If you hit a tennis ball with a racquet,
the force on the ball due to the racquet
is the same as the force on the racquet
due to the ball, except in the opposite
direction.

If you drop an apple, the Earth pulls on
the apple just as hard as the apple pulls
on the Earth.

If you fire a rifle, the bullet pushes the
rifle backwards just as hard as the rifle
pushes the bullet forwards.
Earth Pulls down
On apple
Apple pulls up on earth
Forces are equal, but opposite
Earth / Apple 2
The products are the same, since the forces are the same.
m
a
Apple’s
little mass
=
Apple’s big
acceleration
m
a
Earth’s
big mass
Earth’s little
acceleration
Action Reaction force Pair????
The forces on
the ball
are…?
CD p15
Lost in Space
Suppose an International Space Station
astronaut is on a spacewalk when her tether
snaps. Drifting away from the safety of the
station, what might she do to make it back?
Demolition Derby
When two cars of
different size collide,
the forces on each are
the SAME (but in
opposite directions).
However, the same
force on a smaller car
means a bigger
acceleration!
Horse Cart Problem
As a horse pulls forward on a cart, according to
Newton’s Third Law, the cart must be pulling backward
on the horse.
Newton’s Law also says that each of these forces must
act in opposite directions, but be equal in magnitude
So…..it seems as if the forces are balanced, and that
the horse and cart should not move (or accelerate).
But they do….. Why???
Consider only the forces acting on the HORSE……
If net force is not zero, then horse will accelerate!!!
What about the wagon?? Consider only the
forces acting on it.
Misconceptions

If an object is moving, there must be
some force making it move. Wrong! It
could be moving without accelerating.

If v = 0, then a, and Fnet must be zero.
Wrong! Think of a projectile shot straight up at its
peak.

An object must move in the direction of
the net force. Wrong! It must accelerate, not
move, that way.

Inertia is a force.
False
Misconceptions 2

Heavy objects must fall faster than light
ones. Wrong! The rate is the same in a vacuum.

When a big object collides with a little
one, the big one hits the little one harder
than the little one hits the big one.
Wrong! The 3rd Law says they hit it each just as hard.

If an object accelerates, its speed must
change. Wrong! It could be turning at constant
speed.
Forces & Kinematics
1.
2.
3.
Find net force (by combining vectors).
Calculate acceleration (using 2nd law).
Use kinematics equations:
vf = v0 + a t
x = v0 t + a t2
vf2 – v02 = 2 a x
Sample Problem 1
Goblin
400 N
Ogre 1200 N
Treasure 300 kg
Troll 850 N
A troll and a goblin are fighting with a big, mean
ogre over a treasure chest, initially at rest. Find:
1. Fnet = 50 N left
2. a
= 0.167 m/s2 left
3. v after 5 s
= 0.835 m/s left
4. x after 5 s = 2.08 m left
6.2 Using Newton’s Laws
Apparent Weight
The weight of an object that is
sensed as a result of contact
forces on it.
Weightlessness
Means
there are NO contact
forces acting on the object
Scales
A scale is NOT a weight meter.
 A scale is a normal force meter.
 A scale might lie about your weight if

– you’re on an incline.
– someone pushes down or pulls up on you.
– you’re in an elevator.

Your actual weight doesn’t change in
the above cases.
Weight in a Rocket
U
S
A
You’re on a rocket excursion
standing on a purple bathroom
scale. You’re still near enough
to the Earth so that your actual
weight is unchanged.
The scale, recall, measures
normal force, not weight. Your
apparent weight depends on
the acceleration of the rocket.
Rocket:
At rest on the launch pad
U
S
A
a=0
v=0
N
m
mg
During the countdown to
blast off, you’re not
accelerating. The scale
pushes up on you just as
hard as the Earth pulls
down on you. So, the
scale reads your actual
weight.
Rocket:
Blasting Off
a 
U
S
A
v 
N
During blast off your
acceleration is up, so the
net force must be up (no
matter which way v is).
Fnet = ma
N - mg = ma
N = m (a + g) > mg
Apparent weight > Actual weight
mg
Cruising with constant velocity
U
S
A
a=0
v
N
m
mg
If v = constant, then a = 0.
If a = 0, then Fnet = 0 too. If
Fnet = 0, then N must be
equal in magnitude to mg.
This means that the scale
reads your normal weight
(same as if you were at rest)
regardless of how fast you’re
going, so long as you’re not
accelerating.
Rocket:
Engines on low
As soon as you cut way back on the
engines down, the Earth pulls harder on
you than the scale pushes up. So you’re
acceleration is down, but you’ll still head
upward for a while. Choosing down as
the positive direction,
Fnet = ma
mg - N = ma
N = m (g - a) < mg
Apparent weight < Actual weight
U
S
A
a
v
N
m
mg
Friction

Friction is the force bodies exert on each other
when in contact.
 The friction forces act parallel to the contact
surface
 Exerted against motion (opposite direction)
 The forces shown are an action-reaction pair.
Ffriction
Acme Hand
Grenades
Fapplied
constant v
Friction Facts

Caused by
– electrostatic attraction between the atoms
of the objects in contact
– microscopic particles banging into each
other.
Like any force, can cause acceleration.
 Often results in waste heat/wear and
tear on parts
 Comes in action-reaction pairs.

Good or Bad?
Two Kinds of Friction

Static friction
FA
Fs
– Must be overcome in order
to budge an object
– Present only when there is
no relative motion between
the bodies, e.g., the box &
table top

Kinetic friction
– Weaker than static friction
– Present only when objects
are moving with respect to
each other (skidding)
objects still or
moving together
Fk
FA
a to the right
v left or right
Coefficients of Friction
Static coefficient … s.
 Kinetic coefficient … k.
 Both depend on the materials in contact.

– Small for steel on ice or scrambled egg on
Teflon frying pan
– Large for rubber on concrete or cardboard box
on carpeting

The bigger the coefficient of friction, the
bigger the frictional force.
Surface
Rubber on asphalt, dry
Rubber on asphalt, wet
Rubber on ice
Rubber on concrete, dry
Rubber on concrete, wet
Steel on steel – dry
Steel on steel – lubricated
Steel on ice
μs
1.07
0.95
0.005
1.02
0.97
0.41
0.12
0.01
Lubrication

Reduces friction by
– separating two surfaces so
“high points” don’t hit each
other
– Changing coefficient of
friction to a lower value with
a different material
– Includes using oil, graphite,
teflon, etc.
Normal force
Force exerted between two surfaces in
contact, perpendicular to the surface.
 If level surface, and object is resting on
surface, then……..

FN
FN = mg.
m
and, Fnet = 0;
mg
hence a = 0.
Normal forces aren’t always up
“Normal” means perpendicular. A normal force is
always perpendicular to the contact surface.
N
But it isn’t always
equal to mg!!!!!
mg
Normal force directions

Up
– You’re standing on level ground.
– You’re at the bottom of a circle while flying a loopthe-loop in a plane.

Sideways
– A ladder leans up against a wall.
– You’re against the wall on the “Tom’s Twister” ride
when the floor drops out.

At an angle
– A race car takes a turn on a banked track.

Down
– You’re in a roller coaster at the top of a loop.
Cases in which N  mg
1. Mass on incline
2. Applied force acting on the mass
3. Nonzero acceleration, as in an elevator or
launching space shuttle
FA
N
N
a
N
mg
mg
mg
When does N = mg ?
If the following conditions are satisfied,
then N = mg:

The object is on a level surface.

There’s nothing pushing down or pulling
it up.

The object is not accelerating vertically.
Friction Magnitude
FF= FN
The magnitude of the friction force is
proportional to:
 how hard the two bodies are pressed
together (the normal force, N).
 the materials from which the bodies are
made (the coefficient of friction, ).
Attributes that have little or no effect:
 sliding speed
 contact area
Static Friction Force
Fs  s N
static frictional
force
coefficient of
static friction
normal
force
Fs, max = s N
maximum
force of static
friction
fs, max is the force you must
exceed in order to budge a
resting object.
Static friction force varies



Fs, max is a constant in a given problem, but Fs varies.
Fs matches FA until FA exceeds Fs, max.
Example: In the picture below, if s for a wooden
crate on a tile floor is 0.6,
Fs, max = 0.6 (10 Kg ) (9.8m/s2) = 58.8 N.
FS = 27 N
FA = 27 N
10 kg
Fs= 43 N
FA = 43 N
10 kg
FA = 66 N
Fk
10 kg
finally budges
Kinetic Friction
Fk = k N
kinetic
frictional force
coefficient of
kinetic friction
normal
force
Once object budges, forget about s.
 Use k.
 fk is a constant so long as the materials
involved don’t change.
 There is no “maximum fk.”

 values
Typically, 0 < k < s < 1.
 This is why it’s harder to budge an object
than to keep it moving.
 If k > 1, it would be easier to lift an object
and carry it than to slide across the floor.
 Dimensionless (’s have no units, as is
apparent from FF =  N).

Friction Example 1
You push a giant barrel o’ monkeys setting on
a table with a constant force of 63 N applied
sideways. If k = 0.35 and s =0.58, when
will the barrel have moved 15 m?
Never, since this force won’t even budge it!
answer:
63 < 0.58 (14.7) (9.8)  83.6 N
Barrel o’
Monkeys
14.7 kg
A desk has a mass of 30. kilograms.
If the coefficient of static friction
between the desk and the floor is
0.48, what force must be used to
move the desk from rest? 141N
Once the desk above is in motion,
what force must be used to keep it
moving at a constant velocity if the
coefficient of kinetic friction is
0.32?
94N

What will the acceleration of the box be
if a force of 120N is applied sideways to
the box?
First, calculate NET force acting on the box…
Then, use F=ma to find acceleration
0.87m/s2
Drag
Friction-like force exerted on objects
moving through a fluid such as air or
water.
 Acts in opposition to motion

Apollo 15
returning to
earth
Model of
Leonardo
da Vinci’s
parachute
Air Resistance

R depends on:
– Relative velocity (approximately
proportional to v2)
R
• Faster speed = greater drag
– cross-sectional area
• Larger area = greater drag
m
– air (fluid) density
– other factors like shape
mg

R is not a constant; it changes
as the speed changes
Turbulent flow
Streamlined/
laminar flow
a streamline is a line which is everywhere tangent
to the velocity of flow
Airplane wing in “stall”, which is a condition of loss of
Lift due to turbulence over wing instead of laminar flow
1921 Rumple, drag
coeff. .27, compared to
1984 average of .40
Traveling as fast as it can…..Draw a Free
Body diagram. Include engine thrust,
friction, drag.
Terminal Velocity
As an object falls faster, the amount of
drag force increases.
 When the drag force equals the force
due to gravity of the object, the object
will be in equilibrium
 The object ceases to accelerate, and
has reached “Terminal Velocity”

Period (Harmonic) Motion
Simple Harmonic motion is caused by a
“Restoring Force” that results from a
displacement of some object or material
from rest position.
 The distance of the displacement is
called the “Amplitude”
 The “period” is the length of time (T)
needed to complete one cycle of motion

Facts about the Simple Pendulum

The period is independent of the
mass.

The period depends only on the
pendulum’s length.

The period = T = 2
Don’t confuse the
symbol T, which is
used for both period
and tension.
L
g
Restoring
force on
pendulum is
gravity!
Mass on Spring

Spring Oscillator Applet
T = period
m= mass
k = spring constant (larger for
stiffer springs)
Harmonic Motion 1
Resonance

Sometimes, when small forces are
applied repeatedly to an object, the
object will vibrate with larger and larger
displacements….this is resonance
Tacoma Narrows Bridge video
The relatively new bridge over the
Tacoma Narrows collapsed in 1940 as a
result of mechanical resonance brought
on by wind blowing through
substructure of bridge.
 Wind caused eddy currents which
applied alternating forces which
ultimately destroyed the bridge.
