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Physics – Forces
We will complete this chapter in two parts: first WITHOUT friction and then WITH
friction. If you understand without friction, adding friction in is very easy. If you do not
understand the chapter without friction, the concepts with friction only become harder!!!
I. Force
COULD
Force  any influence that
cause an object to accelerate.
IN OTHER WORDS: ACCELERATIONS ARE CAUSED BY FORCES
 Vector Quantity
 Units: Newton = 1 kgm/s2
Dyne = 1 g-cm/ s2
Pounds = 1 slug-ft/ s2
SAY WHAT???? Just because an
object doesn’t accelerate does NOT
mean there are no forces….it may mean
the forces are balanced!!
FYI – Pressure vs Strain  is the ratio of the force to cross sectional area
(Generally think of it as how the force is spread out)
P = σ = F/A
*this concept is very important to your bridge project that will be assigned next week.
Types of Forces
1) Contact Forces  forces that require direct physical contact
2) Field Forces  forces that act at a distance (requiring NO physical contact)
II Free Body Diagrams
Free Body Diagrams: is a simplified representation of all the forces acting on an object
Your diagrams will get complicated/cluttered quickly so it is best to keep it simple
EX 1) consider the forces on the cart.
Ground
Weight
Force of man
friction
Free Body Rules
1.
Draw the object as a box – Don’t care if it’s a
banana, car ball or whatever. Draw as a box 
2.
Use a vector to represent each separate force –
make sure it points in the appropriate direction!!
a. All vectors need to “touch” the center of the
free body to be considered an official free
body
b. DO NOT use numbers in the free body
diagrams
c. You can draw another working free body
diagram to put additional information on it
Free Body Views:
On the Ground/Surface
Can view Fweight
Can view FNormal
Can view FFriction (f)
Movement = left/right or up/down
(hint – if Fw or FN is given/shown then
ground view)
Overhead
Cannot view Fweight
Cannot view FNormal
Will not have to worry about FFriction (f)
Movement = vector analysis (x & y
chart)
III. Specific Forces
#1 Net Force (Fnet)
 vector* sum of all the forces (or components of the forces)
PARALLEL to the acceleration/motion
*yes force is a vector so magnitude and displacement rules apply
 Unit: Newton (N)
AKA: kgm/s2 pounds (the english unit)
EX 1) a force of 20N is applied to the east on a box. A second force of 30N is
applied to the west on the same box. What is the net Force?
Fnet = F1 + F2
F1
F2
*the negative indicates West
*in this case the forces are not balanced meaning they do not cancel out…….
this would result in an acceleration.
An Unbalanced Net Force (Fnet = 0) will result in an
acceleration
A Balanced Net Force is when the vector sum of all of the
forces is zero (the forces cancel each other out). When this
occurs the object will NOT accelerate, we say it is in
equilibrium
Static equilibrium is when the object is at rest (static) and not
accelerating (equilibrium)
EX 2) What if we now have a 20N Force North and another 30N force
West? What is the Fnet?
F2
F1
It might help if you look at the diagram another way.
F1
F2
F2
F1
F1
F2
All three diagrams show the same thing but some are easier to for vector addition
and other show the proper free body diagram
ϴ
Answer:
 Do not confuse the unit N (Newton) for the
direction N (north)
#2 Weight (Fw = mg)
 the force on an object due to the gravitational pull of the Earth*.
Unit : Newton
This force is always directed downward (toward the center of the
Earth*)
Calculated by multiplying mass (in kilograms) by the acceleration due
to gravity “g” (on Earth = “g” = “a” = 9.8m/s2. Other planets have
different accelerations due to gravity)
Weight is NOT the same as mass!
Mass is a physical property of the object and is constant,
regardless of the force of gravity (which varies with
location).
Weight CAN vary (with gravitational acceleration, “g”)
BUT mass is constant
It is good to know your own weight in Newtons: What weight (in
Newtons) is a 150lb person?
1Kg = 2.2 lbs
It’s a big value…….do not be confused by this! 1 Newton is a very
small amount of force. So you will typically deal with larger values.
*show newton scale
#3 Tension (T or FT)
 the force in a string, chain, wire, etc.
 tensile forces always act to pull objects.
Unit: Newton!
Nothing too special about tension. It’s just the force in a rope.
Typically we use it when we can’t directly pull something.
Ex. You pull on the rope with 120N of
force. The tension in the rope is 120N and
imparts your force to the box.
#4 Normal Force (FN)
 AKA: perpendicular force
 The support force that a surface exerts on the object
 If the object pushes on the surface the surface must be pushing back
otherwise the object would move the surface
 It always acts PERPENDICULAR to the SURFACE!!!
 What does this look like?
**do not confuse FN (normal force) with Fnet (net force). They are
VERY different!
Fnet: consider all forces (or components of forces) parallel to the
motion
FN: consider all the forces (or components of the forces)
perpendicular to the surface
FYI when you stand on a bathroom scale it actually indicates FN…….most
of the time FN = weight but not always. We will revisit this idea soon 
Solving for FN:
Method: Use forces up = forces down
EX 1) Let F= 150N and m = 15kg
Solve for FN
Solve for Fnet
Ex 2) Let F= 150N and m = 15kg
Solve for FN
Solve for Fnet
20°
#5 Force Friction (Ff or f)
 the force acting on a surface as two materials move past one
another. Friction always acts to impede the relative motion (or
attempt at motion) between two surfaces.
always acts OPPOSITE of the direction of
acceleration/motion
for now you can think of friction as the resistive force acting
between the surface and an object.
 We will come back to friction later – for now we will
continue to ignore it
IV. Newton’s Laws of Motion
Galileo (1564-1642) noticed that larger (more massive) objects
resisted changes in their motion. For example a cannon ball
rolling across the ground was harder to stop than an apple rolling
across the ground. He coined the term inertia to describe this.
Inertia is the natural tendency of an object to resist changes in
its current state of motion.
Inertia is measured in terms of an object’s mass.
In other words inertia and mass are proportionally
related. More mass = more inertia
Inertia is NOT a force. Forces are needed to overcome inertia
Newton (1643-1727) expanded on this concept of inertia and
developed his 3 laws of motion. These three laws are the
foundation for classical mechanics (that is the branch of physics
we are studying)
NEWTON’S LAWS OF MOTION
1st Law = Law of Inertia
Neglecting an outside net unbalanced force, an object at rest
will remain at rest and an object in motion will maintain its
current state of uniform motion* (in other words NO
acceleration)
*uniform motion = constant velocity = no acceleration = no
change in speed or direction
Science of football
Demos: 1) cart + PEZ (why wear a seat belt?)
2) Dollar and Bottles
3) table Cloth
4) eggs and glasses
2nd Law (this law quantifies how forces change motion)
The acceleration of an object is directly proportional to the
net force acting on the object and inversely proportional to
the object’s mass.
a  Fnet (a is proportional to Fnet)
AND
a  1/m (a is inversely proportional to mass)
SO
a  Fnet / m
THIS is the second law!
Proportions can only take us
so far, we can use a constant
of proportionality to find an
equation.
Newton defined the unit of
force (the Newton) as 1
kgm/s2, so the constant of
proportionality is 1 and we
have:
F = ma
Question…so why is weight = mg?
Science of football
Ex. #1 Mrs McGrath applies a eastward horizontal force of
270N to a 20kg crate. Ms. Boron applies a second westward
horizontal force of 380N to the same crate. Determine the
acceleration of the crate.
#2 Now Mrs. McGrath’s force is east and Ms Boron’s force is
south.
#3 Mrs McGrath pulls on a wagon via a rope. She pulls with a
force of 350N so that it makes an angle of 48° with the ground.
What is the acceleration of the wagon?
3rd Law = the law of action-reaction pairs
For every action (force) there is an equal* and opposite**
reaction (force)
These action/reaction pairs happen simultaneoulsy
* equal in magnitude
** opposite in direction
FAB = -FBA
This is NOT cause and effect!
It does not mean if a bat hits a ball then the ball will move
It does mean: if a bat hits a ball than a ball hits a bat
Science of foot ball
Example  if you slam on your breaks in your car, the seatbelt exerts a force on you and
you exert the same force in the opposite direction on the seatbelt.
Example: The picture to the right show a child hanging from a tree branch. Identify the
action-reaction pair.
The boy lets go of the branch and falls towards the ground. Identify the action-reaction pair
now.
Demo: scooters
CAUTION: Again this is NOT a cause and effect!!! Although
these forces ARE equal and opposite, the results can be
significantly different due to the different objects involved.
Question
If I push on an object and it pushes on me with the same force,
then why don’t they cancel out (giving no net force and thus no
acceleration)?
Answer – the forces act on different objects so they can’t cancel!
SAY WHAT????
For example……think about this
If the earth is pulling on me with a force and I am pulling on the
Earth with an equal but opposite force, then why doesn’t the
earth have the same acceleration as I do?
Answer – the masses are very different!
The forces are the same, but the results are VERY different!
FEme
= -FmeE
m Ea E
= mmeame
m a
m
a
a
(big
=
m
ass gives small acceleration)
(little mass gives big
cceleration)
V. SYSTEMS
V. Systems  Multiple objects moving together (via
ropes, chains).
METHOD
1) Assign positive direction for the
motion (figure out a direction of motion
or guess if you have no idea how it will
move)
2) Draw free-body diagram for EACH
object
3) Apply F = ma (to EACH object)
4.) Add the equations together
4) Solve
Ex.1 “horizontal system”
a. What is the acceleration of the system below?
b. what is the tension in the rope connecting the blocks?
25kg
200N
15kg
Ex 2 “vertical system” = Atwood)
Atwood machines are devices that consist of pulleys,
strings and masses. For the purpose of this class the
pulley and string will be considered mass-less and
for now we will not deal with friction.
*Since the objects are tied together they will move with the
same acceleration.
*use the system methodology you learned above to solve!
* make sure to assign each mass and tension a number!
20kg
50kg
Ex 3 Elevators
Elevator problems are problems in which an object is accelerated vertically.
Usually the problem involves an elevator with a person standing on a scale
or an object attached to a rope.
Therefore ...use the system methodology you learned above to solve!
(if no direction of motion is given you must assign a positive direction)
a. Elevator is standing still
When a person is standing on a scale, the scale shows the NORMAL
FORCE on the surface of the scale! At rest OR not accelerating on a
level surface the scale will read the weight of the person.
Lets prove this mathematically 
b. Now the elevator is traveling at a constant speed of 2m/s
When the person is accelerating either up or down, the scale will
show a different value.
c. Now the elevator is traveling at a constant acceleration of 2m/s2
upwards.
d. (last scenario) Now the elevator is traveling at a constant
acceleration of 2/m2 downward
Now you try some with some actual numbers!
Ex2. While conducting an experiment Ms. Boron stands on a bathroom scale in an elevator (weird
huh?) If Ms Boron has a mass of 58.0kg determine the reading on the scale in the elevator. *remember
the scale indicated the force normal!!
a.
The elevator is moving downward with a constant acceleration of 4.6m/s2
b.
The elevator is moving upward with a constant velocity of 4.6m/s.
VI. Equilibrium
Equilibrium – state of constant non-accelerating motion
Static equilibrium – state of constant non-accelerating motion
AND unchanging rest (v=0)
Vertical Motion
Horizontal Motion
Object is not accelerating
Object is not accelerating
∑Fup = ∑Fdown
∑Fleft = ∑Fright
Conditions for
Equilibrium
Remember
Constant velocity = No acceleration = Fnet is 0
Stopped
= No acceleration = Fnet is 0
Ex. A 70 kg sign is held from the ceiling (as shown below).
What is the tension in each of the ropes?
40°
30°
70kg
VII. Inclined Planes
1) Assign positive direction for the motion
(figure out a direction of motion or
guess if you have no idea how it will
move)
2) Draw free-body diagram for EACH
object
3) Apply F = ma (to EACH object)
4.) Add the equations together
4) Solve
mgcosΘ
the component of the
weight that is
perpendicular to the
motion/incline
Normal force
Fw (mg) always acts
straight down
Θ
mg
Θ
mgsinΘ
the component of the weight that
is parallel to the motion/incline
According to Fnet = ma. ONLY the forces that are
PARALLEL to the motion affect the acceleration!
Therefore PART of the gravitational forces affects the
acceleration (the parts parallel to the motion)
Ex. A 10kg box is placed on a 30° incline. Neglecting
friction, what is the acceleration of the block when it is
released from rest?
Ex2. The same block on the same incline, is subjected
to a 200N force up the incline and parallel to the
motion. What is the block’s acceleration now?
Want something a little more challenging???
100N
20kg
50kg
20°
98N
20°
VIII. Friction (f)
Friction is the force between two surfaces moving past one another. Friction always acts to
impede the relative motion (or attempt at motion) between two surfaces.
Types of Friction
1) Static Friction (fs)  the friction that must be overcome in order to initiate motion.
* Can vary from zero to some maximum value (depending on how hard you push/pull)
Fapp= 50N
Fapp= 100N
Fapp= 101N
If it doesn’t move then:
f = 50N
v = 0 and a = 0
To get it to move you
When Fapp is JUST
can push harder.
greater than friction the
If it doesn’t move then:
object will “break away”
f = 100N
v = 0 and a = 0
2) Kinetic Friction (fk)  the friction that opposes the motion of an object as it slides across a
surface.
Kinetic friction < Static Friction (for a given pair of materials)
Source of Friction
Friction depends on two factors:
1) Materials in contact
 indicated by the coefficient of friction (μ)
 this is a (unitless) value that varies for every
combination of materials
2) Normal Force
 the force with which the two surfaces are pressed together
f = μFN
But WHY does it exist?
Two schools of though:
1) Friction occurs due to asperities in the surfaces. These asperities cause the ridges
(in one material) to get hung up in the valleys (of the other material). According to this
theory, rough materials (which have more/deeper asperities) will have higher values for
friction.
2) Friction occurs at contact points due to “cold Welding.” The molecules of each
object exert (electromagnetic) forces on each other. This bonding is the source of friction.
This explains why highly polished (very smooth) objects can have enormous amounts of
friction.