FORCES IN ONE DIMENSION
Chapter 4
Chapter Objectives
Section 4.1
 Define force.
 Learn how to draw FBD’s
nd law to solve
 Use Newton’s 2
problems.
 Explain the meaning of
Newton’s 1st law.
Section 4.2
 Describe how the weight and
mass of an object are related.
 Differentiate between actual
weight and apparent weight.
Section 4.3
rd
 Define Newton’s 3 law.
 Explain the tension in ropes
and strings in terms of
Newton’s 3rd law.
 Define the normal force.
 Determine the value of the
normal force by applying
Newton’s 2nd law.
Force and Motion
Chapter 4 Section 1
Force


A force is a push or pull
exerted on an object.
Forces can cause an object
to speed up, slow down or
change direction.
 A forces causes a
change in an object’s
velocity.
 A force causes an object
to accelerate.




Symbol: F
Vector Quantity
Units: newtons (N)
 1 N = 1 kgm/s2
 1N ≈ ¼ lb
Forces are categorized in
two ways:


contact force vs. field force
the four fundamental forces
of nature
2 Main Types of Forces
Contact Forces


When an object from the
external world touches a
system and thereby exerts
a force on it.
Examples:
 Frictional force
 Tension force
 Applied force
Field Forces


Forces that are exerted on
an object without contact.
Examples:
 Gravitational force
 Magnetic force
 Electric force
4 Fundamental Forces of Nature
Although you can think of hundreds of different forces, physicists
group them all into just four categories.
1.
1.
Gravitational Force

An attractive force that exists
between all objects

The weakest of the four forces
3.
Electromagnetic Force


A force due to electric charges,
both static and moving.
3.
Strong Nuclear Force

Force of very short range that
holds the particles in the nucleus
together

The strongest of the four forces
Weak Force

Involved in the radioactive
decay of some nuclei.

Actually a form of the EM force
Second strongest of the forces
Agents and Systems
Since forces are caused by interactions (whether there is contact
or not), you should be able to determine the cause of the force
and what the force is acting on.
The Agent
The thing the causes the
force
The System
The thing that the force is
acting on.
You should be able to label the agent and the system.
Example – Labeling the Agent and System
If I push a book with my hand across a table…
System
Agent
…the book is the system and my hand is an agent.
Models of Forces
You can use a pictorial model
to help you analyze how force
affects motion.
Force of table
on book
Force of hand
on book
Don’t forget the force of gravity!
Steps for Making a Pictorial
Model:
1.
Sketch the situation.
2.
Circle the system.
3.
Identify every place
where the system touches
the external world. (This is
where contact forces are
exerted.)
4.
Identify the contact forces
and label.
5.
Then identify any field
forces on the system.
Free-Body Diagrams (FBD)




A physical model that
represents the forces
acting on a system.
The system is represented
using a particle model.
Represent all forces
acting on the system with
an arrow that points
away from the particle.
Label all forces.
Don’t
forget the
force of
gravity!
F table on book
F hand on book
F table on book
F hand on book
Fg
Assignment
We are going to do some practice
problems together on whiteboards.

For each problem do the following:
 Draw
pictorial model and FBD
 Specify the system in the pictorial model.
 Label all forces with their agents in both.
 Draw vectors of appropriate lengths in FBD.
Some Types of Forces
Please become familiar with these forces – you will see them often!
Force
Symbol
Definition
Direction
Friction
Ff
The contact forces 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
Fsp
The push or pull a spring
exerts on an object
Opposite the displacement
of the object at the end of
the spring
Spring
Some Types of Forces
Force
Tension
Weight
Applied
Symbol
Definition
Direction
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,
or cable at the point of
attachment
Fg
A field force due to the
gravitational attraction
between two objects,
usually Earth and an object
Straight down toward the
center of Earth - ALWAYS
FA
A generic term for a push
or pull exerted by a
person on an object.
In the direction of the push
or pull.
Please become familiar with these forces – you will see them often!
Newton’s Laws of Motion
st
1
Newton’s Law:
An object with no net force acting
on it remains at rest or moves with
a constant velocity in a straight
line.
Newton’s Laws of Motion
Newton’s 2nd Law:
The acceleration of an object is
directly proportional to the net
force on it and inversely
proportional to its mass.
a = Fnet / m
or
Fnet = ma
Newton’s Laws of Motion
Newton’s 3rd Law:
When one object exerts a force on
a second object, the second exerts
a force on the first that is equal in
magnitude but opposite in
direction.
Newton’s First Law
The motion of an
object will continue
as it was (at the
same speed and in
a straight line)
unless acted upon
by an unbalanced
force.
Balanced Forces


Balanced forces acting on an
object produce a net force = 0
The forces “cancel” each other out.
Unbalanced Forces


Unbalanced forces acting on an
object produce a net force ≠ 0
The forces do not “cancel” each
other out.
4-2 Newton’s First Law
Inertia

The tendency of an
object to resist change.
If an object is at rest, it
tends to remain at rest.
 If an object is in motion,
it tends to continue
moving as it was.
Equilibrium



Inertia is not a force.

When the net force on
an object is equal to
zero, the object is said
to be in equilibrium.
An object is at
equilibrium when it is:
at rest
OR
 moving at a constant
velocity

Combining Forces
Net Force (Fnet)
 The vector sum of all
of the forces acting on
a system.

Net force is equal to
the resultant
 can
be determined
graphically or
mathematically.
Graphically:
100 N
200 N
300 N
So the Fnet = 300 N to the right
Mathematically:
75 N
25 N
(-75 N)
+ (25 N)
-50 N
So the Fnet = 50 N to the left
You Try – Example 1

Two horizontal forces, 225 N
and 165 N, are both exerted
on a canoe to the right. Find
the net horizontal force on the
canoe.
You Try – Example 2

Two horizontal forces are exerted
in opposite directions on a canoe.
If 225 N is exerted to the left and
165 N to the right, find the net
horizontal force on the canoe.
You Try – Example 3

Three confused sled dogs are
trying to pull a sled across the
Alaskan snow. Snowball pulls
east with a force of 35 N,
Rudolf also pulls east but with a
force of 42 N, and big Diesel
pulls west with a force of 53 N.
What is the net force on the
sled?
Using Newton’s Second Law
Steps for Determining How Forces Effect the
Motion of an Object :
1.
2.
3.
4.
5.
Identify all forces acting on the object
(Pictorial Model is useful here)
Draw a free body diagram
Add forces to find the net force
Use Newton’s 2nd to find acceleration.
*Use constant acceleration equations from
chapter 3 (if necessary) to find displacement
or velocity.
Physics Theory - Bell Ringer
Consider a cart moving along a straight line, moving at a
constant speed…
Because the velocity is not
changing, does this mean
there are no forces acting
on the cart?
If identifiable agents are
exerting forces on the cart,
then why is there no
change in velocity?
No, the Earth and the track both
exert forces on the cart. There
are also forces due to air
resistance and friction.
The net force on the cart is
zero.
Practice Problems
Practice Determining Net Force:
 p. 93, # 6-8
Practice Using Newton’s 2nd Law:
 p. 113, #61
 p. 114, #86 + 87
Using Newton’s Laws
Chapter 4 Section 2
Using Newton’s Laws
What is the force of gravity?


The gravitational force
exerted by a large
body, usually Earth, is
called weight.
Weight is measured in
newtons like all other
forces.
How can you calculate weight?


You can you figure out
the weight of an object
with mass, m, if you
know the acceleration
due to gravity, g.
The weight of an object
can be found using
Newton's 2nd Law.
Weight
The weight of an object
can be found using
Newton's 2nd Law.
This force is called the
weight of an object and
given the special symbol
“W”. So,
F = ma
a=g
W = mg
The force of gravity is
given by the equation:
F = mg
*Remember, weight and mass
are not the same thing.
Mass is the amount of matter
something contains.
Weight is the gravitational pull
on an object. It depends on
mass and gravity.
Apparent Weight
What is Apparent Weight?


Whatever force is pushing
upward on us we interpret as
our "weight"- not our true
weight - that is the force due
to gravity ”mg".
This upward force is what we
interpret as our APPARENT
WEIGHT.
Does Your Apparent Weight Change?

If you accelerate in a vertical
direction, your weight will appear
different



Accelerating up, apparent weight
increases
Accelerating down, apparent weight
decreases
Why? Picture an Elevator…



N = mg if the elevator is at rest or
moving at constant velocity
N = mg + ma if the elevator has an
upward acceleration
N = mg - ma if the elevator has a
downward acceleration
Weightlessness
Definition
Weightlessness
Weightlessness

 When
an object has an
apparent weight of
zero due to the lack of
contact forces pushing
up on the object.

Remember - It is the
UPWARD FORCE that we
feel on us - not gravity!
All people/things who
are ONLY subjected to
gravity are freely
falling and feel
weightless.
Drag Force
Drag Force
Drag Force Example
The force exerted by a
fluid on an object
moving through the
fluid
 Depends
 object's
on:
properties
 object’s motion
 fluid’s properties
Terminal Velocity
Terminal Velocity

The constant velocity
of an object that is
reached when the
drag force equals the
force of gravity.
Terminal Velocity Pictorial Model
Drag
Force
Drag
Force
Fg
Body
released
from rest
Fg
Forces on
body during
acceleration
Fg
Forces on
body at
terminal
velocity
Homework

4.2 Section Review Questions
 p.
101
 #21 - 25
Interaction Forces
Chapter 4 Section 3
Interaction Forces



Remember Newton’s 3rd Law
Forces act in pairs
FA on B = - FB on A
Interaction Pair
 Two forces that are opposite in
direction and have equal
magnitude and act on different
objects.

Also called action-reaction pairs


One force does not cause the
other force.
They act together or not at all.
Fball on table
Ftable on ball
Action-Reaction Pairs

A block of mass m rests on a table. You apply a small force to
the block, but the block does not move. Which of the following
are action-reaction pairs according to Newton’s 3rd Law?
A.
The force due to gravity acting on the block and the normal force
acting on the block
B.
The block’s gravitational pull on Earth and Earth’s gravitational pull
on the block
C.
The applied force on the block and the frictional force on the block
D.
The block’s push on the table and the table’s push on the block
Normal Force
What is the Normal Force?
 It is the contact force
exerted by a surface on
another object.


The normal force is
ALWAYS perpendicular to
the surface.
Draw in the normal force for
each situation at the right.
Forces of Ropes and Strings
Tension Force

Tension is a specific name
for the force exerted by a
rope, string, or cable.
The tension in the rope is equal to
the weight of the object hanging
from it when the object is in
equilibrium.
The tension will not be the same as
the weight if the object is
accelerating.
Example
Draw a free body
diagram for this situation.
(The bucket is at rest.)
FT (rope on bucket)
Fg (Earth’s mass on bucket)
Tension Problems – Example
A 50.0 kg bucket is being lifted by a rope. The
rope will not break if the tension is 525 N or
less. The bucket started at rest, and after
being lifted 3.0 m, it is moving at 3.0 m/s. If
the acceleration is constant, is the rope in
danger of breaking?
Tension Problems – Example Solution
FT (rope on bucket)
Fg (Earth’s mass on bucket)
Given:
m = 50.0 kg
vi = 0.0 m/s
vf = 3.0 m/s
d = 3.0 m
g = 9.8 m/s2
FT = ?
Equations:
Fnet = FT - Fg
Fnet = ma
Fg = W = mg
vf2 = vi2 + 2ad
Calculations:
Fnet = FT - Fg
FT = Fnet + Fg
Fnet = ma
Fg = mg
FT = ma + mg
FT = m(a + g)
vf2 = vi2 + 2ad
vf2 = 0 + 2ad
a = vf2 / 2d
Calculations:
FT = m[(vf2 / 2d) + g]
FT = 50.0g [(3.0m/s)2 / (2)3.0m + (9.8m/s2)]
FT = 50.0g [(9.0m2/s2 / 6.0m) + 9.8m/s2]
FT = 50.0g [(1.5 m/s2) + 9.8m/s2]
FT = 50.0g (11.3 m/s2)
FT = 565 N
Max Tension of Rope = 525 N or more
So, yes, the rope is in danger of
FT = m(a + g)
breaking because the tension
FT = m[(vf2 / 2d) + g] exceeds 525 N.
Tension Problem – You Try!
You are fishing and catch a fish with a mass of 6 kg.
If the fishing line can withstand a maximum tension of
30.0 N, what is the maximum acceleration you can
give the fish as you reel it in?
Answer:
amax = 5 m/s2
Homework – Interaction Forces
Section Review Q’s:
pg. 107
#34-39
Practice Problem:
pg. 106
#32
Bell Ringer


1.
2.
3.
See the diagram on the board.
Two boys on roller skates are each holding the end
of a rope. If one boy pulls on the rope, what will
happen?
Will they accelerate?
In which direction will they accelerate, if any?
Who’s acceleration will be greater? Or will they
be equal?
Chapter 4 Review Problems
FYI - Ch 4 Test is Wednesday, Nov 5th!
Please complete the following problems to help you
review for the test.

p. 112-115 #53, 59-61, 64, 70, 73, 80, 84, 88(a&b)
 Note - This is an IN CLASS assignment – it will be checked
at the end of class today so that we may discuss all of the
answers tomorrow.
 You may work in groups – help each other work through
the problems, don’t just copy your classmates work.