Introduction to Dynamics
Chapter 6
Forces
Sec 6.1
Force and Motion
► Objectives
 Define a force and differentiate between contact
forces and long-range forces
 Recognize the significance of Newton’s second
law of motion and use it to solve motion
problems
 Explain the meaning of Newton’s first law and
describe an object in equilibrium
Force
= a push
or a pull
FORCE
= a push or a pull
Metric Units for Force = Newtons (N)
1N=1
2
kg·m/s
= the force needed to give a 1 kg mass
an acceleration of 1 m/s2
Note: The English unit for force is the pound: 1 lb equals 4.48 Newtons
Force & Mass are Different
• Force is a push or pull that can change motion.
• Measured in newtons (N) or pounds (lbs)
• Weight is a force caused by gravity.
• Measured in newtons or pounds, because it is a force.
• Mass is the amount of matter in an object.
• Measured in grams and kilograms
Your mass is the same everywhere in the universe,
but your weight can be different.
Four Fundamental
Forces of Nature
GRAVITATIONAL
FORCE
• An attractive force
between two bodies
• The weakest of all forces
ELECTROMAGNETIC
FORCE
• Charged particles at rest exert
electric forces on each other
• Charged particles in motion
exert magnetic forces on each
other
STRONG NUCLEAR
FORCE
• Holds particles of the
nucleus together
• The strongest of all
forces
WEAK NUCLEAR
FORCE
• Form of an
electromagnetic force
•Happens when some
nuclei radioactively
decay
The Forces of Nature
I. Gravitational:
•attraction b/tw masses
•Ex: tides, weight
II. Electromagnetic:
•attraction or repulsion
b/tw charges
•Ex: friction, tension,
adhesion, lift, electrostatic ,
drag, buoyant, magnetic
III. Weak Nuclear:
•helps to explain
atomic collisions
IV. Strong Nuclear:
•binds atomic nuclei
Two Categories of Forces…
► Contact
Force
 Acts on an object only by touching it
► Long-Range
Force (aka “Field Force”)
 Exerted without contact
►Magnets
►Gravity
Agent: a specific, identifiable,
immediate cause of a force
Examples of Forces
► Ff
- - Friction (opposes sliding)
► FA - - Applied Force (an external push or pull)
► FN - - Normal (perpendicular to a surface)
► Fsp - - Spring (push or pull of a spring)
► FT - - Tension (spring, rope, cable)
► Fthrust - - Thrust (rockets, planes, cars)
► Fg - - Weight (force due to gravity)
Which of the four types of force are each of these?
….all of them but one is electromagnetic!
Weight Force, Fg
aka gravitational force
ON EARTH:…
• The weight force acts on all objects
• The direction of the weight force is always towards the center
of the earth
• The magnitude of the weight force is always equal to the
mass of the object (kg) multiplied by acceleration due to gravity
object
Fg
Fg = mg
(or FW )
W = mg or Fg = mg
The magnitude of an object’s
weight force is always equal its
mass times the acceleration it
would have if it were in free-fall.
Fg = mg
All Forces have an
Agent and an Object
Agent: the cause of a force
(what does the pushing or pulling)
Object: the ‘victim’ of a force
(what gets pushed or pulled)
Weight Force, Fg
ON EARTH:…
• The agent of the weight force is always the earth.
Fg = mg
object
Fg
(or FW )
Agents and Objects of
Forces
Example: A car is towed by a tow truck:
AGENT:
The tow truck
OBJECT:
The car
Conventional Notation:
FTYPE (AGENT, OBJECT)
FA (T,C)
Forces are Vectors
 Forces have magnitude and direction.
 We can represent forces by drawing arrows
 Example:
This diagram shows
all of the forces
acting on an object:
Drawing Force Vectors
► The
direction of the arrow represents the
direction of the force.
► The
length of the arrow represents the
magnitude of the force.
► We
always draw force vectors as ‘pulls’ on
objects, not pushes (arrow starts at object)
Free Body Diagrams
A picture of a ‘body’ with all the force
vectors acting upon it represented
graphically is called a
FREE BODY DIAGRAM
Free Body Diagrams
Rules for drawing free body diagrams:
1.
2.
3.
4.
5.
Draw the object as a dot
Only draw forces acting on that object
Draw all forces as ‘pulls’
(arrow point away from the dot)
Draw and label every force acting on the object.
Length of each arrow must reflect magnitude
(stronger forces  longer arrows!)
(equal forces  same arrow length.)
Try it...
Draw a picture of
your book sitting on
the desk. Identify
all the forces acting
on it.
Free Body Diagrams...
FN (normal force)
Book
Fg or FW (weight force)
Normal means perpendicular;
not ordinary or regular!
The “Normal” Force
FN (normal force)
Book
Fg or FW (weight force)
Normal means perpendicular;
not ordinary or regular!
Normal Force, FN
• The direction of the normal force is always
perpendicular to a surface (normal)
• The magnitude of the normal force varies depending
on the situation.
• The agent of the normal force is always the SURFACE.
Draw free body diagrams for the
following
► An
egg is free-falling from a nest in a tree.
Neglect air resistance.
► A skydiver is descending with a constant
velocity. Consider air resistance.
► Your physics book is sliding across the desk
at constant speed (no acceleration)
FN
Ff
FA
Physics
surface
W or Fw
Fw or W = Weight Force
FN
= Normal Force
FA
= Applied Force
Ff
Direction Matters!
= Friction Force
Net Force, Fnet or ΣF
• The net force on an object is the
SUM OF ALL FORCES acting on an object
• This is NOT just another force like FN or Fg !
• It must be determined by analysis.
Fnet = F1 + F2 + F3 … etc.
Net Force, Fnet or ΣF
• When the net force on an object is zero,
then the object is said to be in
equilibrium, and the acceleration of the
object must be zero.
If Fnet = 0 , then a = 0
Fnet
(Net Force) = ΣF
= the sum of all forces acting on an object
FN
Ff
FA
Physics
surface
W or Fw
Fw or W = Weight Force
FN
= Normal Force
FA
= Applied Force
Ff
Direction Matters!
= Friction Force
What is SF again? (aka Fnet)
• SF is called:
–the sum of the forces
–the net force
–the total force
• SF = F1 + F2
F1
• Remember though that
F2
– “Left” is probably negative
– “Down” is probably negative
You assign the coordinate system!
Sample Problems
1.What is the total force?
8N
12N
m
SF = F1 + F2
(Let’s make left be the negative direction, so the
12N force to the left is really -12N.)
SF = -12N + 8N
SF = -4N
Sample Problems
2.What is the total force?
F1 =
SF = F1 + F2
m
(Let’s make down be the negative direction;
so the 115N force is really -115N.)
SF = 158N + (-115N)
SF = 43N
158N
F2 =
115N
3 Possible Situations
F1
F2
m
F1 > F2
1. SF = F1 - F2
2. mass accelerates left
3 Possible Situations
F1
m
1.F1 < F2
2.SF = F2 - F1
3.mass accelerates right
F2
3 Possible Situations
F2
No! Does this block
have
a larger F2
The block was
already
moving. because its
moving
to the
So, if the force left
is equal
right?
to the force right then
the
block has no way to speed
up or slow down.
Balanced
m
Forces =
Equilibrium =
Constant
1.F1 = F2
Velocity
2.SF = 0
F1
3.mass stays at a constant velocity
Produce
NO
Acceleration
Produce
Acceleration
Free Body Diagrams...
What forces are acting on a
skier as she races down a hill?
The Answer...
FN
Ff (an)d Fd
Fg
The Answer...
FN
Ff
Hmmm…
What is Fnet ?
Fg
(and FAIR)
The Answer...
FN
Ff and Fd
W
Vector Resolution!
When does Fnet = 0 ?
Sir Isaac Newton
(1642-1727)
►
►
English physicist and
mathematician
Before the age of 30:
 Formulated basic laws
of mechanics
 Discovered the
universal law of
gravitation
 Invented Calculus
►
In 1687, published the
Principia.
 possibly the single most
important book in the history
of science!
Aristotle and Newton had different
ideas about forces and motion.
Aristotle's idea: For an
Newton's idea: An object
object to move at a constant
speed, a constant force
must be applied.
moving at a constant speed
will continue at that speed
without additional force
being applied.
Newton’s Second Law
F = ma
An unbalanced
force will cause
acceleration, but
mass will resist
acceleration.

a


SF
m
Example
►A
race car has a mass of 710 kg. It starts
from rest and travels 40.0 m in 3.0 s. The
car is uniformly accelerated during the
entire time. What net force is exerted on it?
Newton’s Second Law
SF = ma
or
Fnet = ma

a


a


SF
m

Fnet
m
Newton’s Second Law
SF = ma
First let’s clarify the variables and units
SF or Fnet
= Net Force (sum of forces) measured in N
a
= acceleration measured in m/s2
m
= mass measured in kg
Newton’s Second Law
SF creates the acceleration on a mass.
SF = ma
SF
m
a
So to find the
acceleration of
a mass, m, you
need to know
the forces.
Newton’s Second Law
Sample #1:
How much net force does it take to make
a 1.0kg block accelerate at 1.0m/s2?
m = 1.0kg
a = 1.0m/s2
SF = ?
1 N = 1 kg·m/s2
SF = ma
SF = (1.0kg)(1.0m/s2)
SF = 1.0 kg·m/s2
SF = 1.0N
Newton’s Second Law
1.
A monkey pulls on a banana on
a tree with a force of 25N and
the tree resists with a force of
25N. What is the total force on
the banana?
Newton’s Second Law
2.
Two kids pull on a toy. The
bigger girl pulls with 24.0N to
the right. The smaller boy pulls
12.0N to the left. If neither lets
go of the toy, then what will
their acceleration be if the total
mass of the boy, girl, and toy is
60.0kg?
Two kids pull on a toy. The bigger girl pulls with 24.0N to the right.
The smaller boy pulls 12.0N to the left. If neither lets go of the toy, then
what will their acceleration be if the total mass of the boy, girl, and toy
is 60.0kg?
Draw a diagram
12.0N
Write out
variables
60.0kg
24.0N
Pick equations and Solve
SF=F1 + F2
F1 = 24.0N
SF=24.0N + (-12.0N)
F2 = 12.0N
SF=12.0N
m = 60.0kg
a=?
a=?
SF= ma
a = SF
m
a = 12.0N
60.0kg
a = .200m/s2
Example Problems
1. What is the weight of a 75 kg person on
earth?
2. What is their weight in an elevator?
3. What is their weight in a falling elevator?
4. What is the mass of a person that weighs 865
N on earth?
5. What is the weight of a 75 kg person on the
moon where g = 1.6 m/s2 ?
Sec. 6.2
Using Newton’s Laws
► Objectives
 Describe how the weight and the mass of an object are
related
 Differentiate between the gravitational force weight and
what is experienced as apparent weight
 Define the friction force and distinguish between static
and kinetic friction
Mass and Weight
► The
weight force, Fg , is used to find the
downward force of an object.
► Both the weight force and acceleration due
to gravity are downward. (but the net force
on an object is not always equal to its weight
force!)
Weight Force = Fg = mg
Fg = mg
The magnitude of an object’s
weight force of is always equal its
mass times the acceleration it
would have if it were in free-fall.
Example Problems
1. What is the weight of a 75 kg person on
earth?
2. What is their weight in an elevator?
3. What is their weight in a falling elevator?
4. What is the mass of a person that weighs 865
N on earth?
5. What is the weight of a 75 kg person on the
moon where g = 1.6 m/s2 ?
Scale Problems
FN (Scale , Me)
The reading on a scale
is the magnitude of the
force of the scale on
the person or object
standing on the scale!
Scale Problems
F (S , O)
When a problems asks
you “what is the
reading on the scale”,
it is asking you to
determine the force of
the scale on the object.
Hmmm… will that ever differ from
the weight force of the object ?
(Yes, it can differ!)
Example Problems
FN (S,P)
A 75 kg person stands on a scale which
is in an elevator, accelerating upwards at 2.0
m/s2. What is the reading on the scale?
Fg (E, P)
F(S,P) = ?
Fnet = ma
m = 75 kg
Fnet = ΣF
a=
Fnet = F(S,P) + Fg(E,P)
+
2.0 m/s2
g = - 9.8 m/s2
Fg (E,P) = - 735 N
Fnet = 150 N
(“the sum of all forces”)
F(S,P) = Fnet - Fg(E,P)
= ma – (- 735 N)
= + 885 N
Example Problems
A 50.0 kg bucket is pulled by a rope. The rope is
guaranteed not to break if the tension force is
less than 500.0 N. The bucket is lifted from
rest, and after being lifted 3.0 meters, it is
travelling at 3.0 m/s. Is the rope in danger of
breaking?
Example Problem # 2
F (R , B)
A 50.0 kg bucket is pulled by a rope. The rope is
guaranteed not to break if the tension force is less than 500.0 N.
The bucket is lifted from rest, and after being lifted 3.0 meters,
it is travelling at 3.0 m/s. Is the rope in danger of breaking?
FT (R,B) = ?
m = 50.0 kg
a=?
v = 3.0 m/s
d0 = 0 m
d = 3.0 m
g = 9.8
Fg (E, B)
Fnet = ma = (50.0kg) (1.5 m/s2) = 75 N
v0 = 0
-
v2 = V02 + 2a(d-d0)
m/s2
Fg (E,P) = - 490 N
Fnet = ΣF
(“the sum of all forces”)
Fnet = FT (R,B) + Fg(E,B)
FT (R,B) = Fnet - Fg (E,B)
= 75 – (- 490 N)
= + 565 N
Newton’s First Law:
The Law of Inertia
Unless acted upon by
an unbalanced force,
objects at rest will stay
at rest and objects in
motion will stay in
motion.
Newton’s First Law
Unless acted upon by an unbalanced
force, objects at rest will stay at rest and
objects in motion will stay in motion.
Newton’s First Law
Unless acted upon by an unbalanced
force, objects at rest will stay at rest and
objects in motion will stay in motion.
Newton’s First Law
Unless acted upon
by an outside force,
objects at rest will stay
at rest and objects in
motion will stay in
motion.
Newton’s First Law of Motion
► “An
object that is at rest will remain at rest
or an object that is moving will continue to
move in a straight line with constant speed,
if and only if the net force acting on that
object is zero.”
Newton’s First Con’t
► Inertia—the
tendency of an object to resist
change.
► Equilibrium—object at rest or moving at a
constant velocity
Finally…Misconceptions about forces
►When
a ball has been throw, the force
of your hand remains on it. NO!
►A force is needed to keep an object
moving. NO!
►Inertia is a force. NO!
►The quantity ma is a force. NO!
Friction is a Force
► Friction
is a force that
resists motion.
► …it
is due to
microscopic
roughness on all
surfaces.
►…
it slows down all
moving objects.
Friction
► Static
friction force
 The force that opposes the start of relative
motion between the two surfaces in contact
►Friction
► Kinetic
force when object isn’t in motion
Friction Force
 The force that opposes relative motion between
surfaces in contact
►Friction
force when object is in motion
Calculating Friction
Kinetic Friction Force
(Ff ,kinetic) = (µkFN)
Static Friction Force
(Ff ,static) < or = (µsFN)
Typical Coefficients of Friction
Surface
µs
µk
Rubber on concrete
0.80
0.65
Rubber on wet concrete
0.60
0.40
Wood on wood
0.50
0.20
Steel on steel (dry)
0.78
0.58
Steel on steel (with oil)
0.15
0.06
Teflon on steel
0.04
0.04
Example Problems
 Balanced Forces:
You push a 25 kg wooden box across a wood
floor at constant speed. How much force do
you exert on the box? (μk = 0.20)
Example Problems
 Unbalanced Forces:
If you push the same 25 kg wooden box across a
wood floor with double the force, what is the
acceleration of the box?
Terminal Velocity
► The
constant velocity that is reached when
the drag force equals the force of gravity
► Objects can only fall so fast due to their size
and shape and density of the air/fluid




Ping-pong ball – 9 m/s
Basketball – 20 m/s
Baseball – 42 m/s
Skydiver: >62 m/s w/o chute
5 m/s w/ chute
THE END
Demo Time
► Demo:
Hanging Weights
► Question: Where will the string break if I
pull on the bottom string very quickly?
Demo Time
► Demo:
Hanging Weights
► Analysis: Why did the string break where
it did?
The string does not
stretch here, because
the large mass does not
move. A large mass
has lots of inertia. The
tension force in the
bottom of the string
does not accelerate the
large mass.
Demo Time
► Demo:
Paper cup and Marble
► Question: What will happen when the
card is flicked hard?
Demo Questions
1.
2.
Explain why the bottom string broke in the
demo
Explain why the ball fell down in the cup
demo.
Demo Questions Continued
4.
5.
6.
Why do groceries slide to the side when
you turn your car?
Why is it a bad idea to cut off a Hummer
and then slow down in your Mini Cooper?
If you have fuzzy dice hanging from your
rearview mirror, why does it swing when
you stop and start moving?
Periodic Motion
► Pendulums,
springs, strings
► Simple Harmonic Motion
 Motion that returns an object to its equilibrium position
as a result of a restoring force that is directly
proportional to the object’s displacement
► Period
(T)
 Time needed to repeat one complete cycle of motion
► Amplitude
 Maximum distance the object moves from equilibrium
Amplitude, Frequency, Period
The Amplitude is the displacement.
The Frequency is the number of cycles/sec.
The Period is the time for one cycle T = 1/f
Period of a Pendulum
Problems
► Pg.
136
► 17-19
Sec. 6.3
Interaction Forces
► Objectives
 Explain the meaning of interaction pairs of
forces and how they are related by Newton’s
third law
 List the four fundamental forces and illustrate
the environment in which each can be
observed.
 Explain the tension in ropes and strings in terms
of Newton’s third law
Interaction forces
► Two
forces that are in opposite directions
and have equal magnitude
► Newton’s
pairs
► FA on B
Third Law—all forces come in
= -FB on A