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An Introduction to Forces:
Student Learning Goal

The student will analyse, in quantitative terms,
the forces acting on an object, and use free-body
diagrams to determine net force on the object in
one dimension. (B2.9)
An Introduction to
Forces
SPH4C
A Definition
A force is a push or a pull.
A Definition
A force is a push or a pull.
It is a vector quantity and is symbolized by:
A Definition
A force is a push or a pull.
It is a vector quantity and is symbolized by:

F
A Definition
A force is a push or a pull.
It is a vector quantity and is symbolized by:

F
In the SI system, force is measured in Newtons (N).
1 N = 1 kg m/s2
Applied Force

Applied Force is a general term
FA
for any contact force, e.g.
Applied Force

Applied Force is a general term
FA
for any contact force, e.g.



Tension FT or T
Applied Force

Applied Force is a general term
FA
for any contact force, e.g.




Tension FT or T


Friction Ff or Ffr
Applied Force

Applied Force is a general term
FA
for any contact force, e.g.



Tension FT or T


Friction Ff or Ffr


Normal Force FN

Tension
Tension is the force exerted by
strings, ropes, cables, etc.
attached to an object.
Tension
Tension is the force exerted by
strings, ropes, cables, etc.
attached to an object.
The tension along the string is
constant.
Friction
Friction acts to oppose any (attempted) motion.
Friction
Friction acts to oppose any (attempted) motion.
 Static friction: the force that prevents a

Fs
stationary object from starting to move
Friction
Friction acts to oppose any (attempted) motion.
 Static friction: the force that prevents a
stationary object from starting to move
 Kinetic friction: the force that acts against an
object’s motion

Fs

Fk
Friction
Friction acts to oppose any (attempted) motion.
 Static friction: the force that prevents a
stationary object from starting to move
 Kinetic friction: the force that acts against an
object’s motion
 Air resistance (drag): friction on an object
moving through air

Fs

Fk

Fair
Friction
Friction acts to oppose any (attempted) motion.
 Static friction: the force that prevents a
stationary object from starting to move
 Kinetic friction: the force that acts against an
object’s motion
 Air resistance (drag): friction on an object
moving through air (many physics problems
will neglect this)

Fs

Fk

Fair
Normal Force
The normal force acts to keep objects apart.
Normal Force
The normal force is a force exerted by a surface
(or another object) on any other object at 90°
(perpendicular to the surface)
e.g. if you push on a wall, the wall will exert a
normal force on your hand
e.g. a table exerts a normal force on a textbook
Action-at-a-Distance Forces
There exist forces for which contact
between objects is not necessary.
These forces are called action-at-adistance forces.
Action-at-a-Distance Forces
There exist forces for which contact
between objects is not necessary.
These forces are called action-at-adistance forces.
Action-at-a-Distance Forces
There exist forces for which contact
between objects is not necessary.
These forces are called action-at-adistance forces.
One example is gravitational force, the
force of attraction between all objects
with mass.

Fg
Action-at-a-Distance Forces
There exist forces for which contact
between objects is not necessary.
These forces are called action-at-adistance forces.
Example 1:
Gravitational force - the force of
attraction between all objects with
mass.
(The gravitational force the Earth exerts
on an object is called its weight.)

Fg
Action-at-a-Distance Forces
Example 2:
Electrostatic force – the
attractive or repulsive
force between charged
objects (+ vs. +; + vs. -)

Action-at-a-Distance Forces
Example 3:
Magnetic forces – the
force between objects
with magnetic poles
(i.e. two magnets repel
with N-poles facing
each other; attract when
N-pole facing the Spole)

Free-Body Diagrams
Usually an object will have more than one force
acting upon it.
Free-Body Diagrams
Usually an object will have more than one force
acting upon it. A free-body diagram (FBD)
shows all the forces acting on an object
Free-Body Diagrams
Usually an object will have more than one force
acting upon it. A free-body diagram (FBD)
shows all the forces acting on an object – and
only the forces acting on the object.
Free-Body Diagrams
Usually an object will have more than one force
acting upon it. A free-body diagram (FBD)
shows all the forces acting on an object – and
only the forces acting on the object.
A representation of the object is drawn in the
centre of the diagram
Free-Body Diagrams
Usually an object will have more than one force
acting upon it. A free-body diagram (FBD)
shows all the forces acting on an object – and
only the forces acting on the object.
A representation of the object is drawn in the
centre of the diagram and the forces acting on it
are drawn as arrows pointing outwards.
Free-Body Diagrams
Usually an object will have more than one force
acting upon it. A free-body diagram (FBD)
shows all the forces acting on an object – and
only the forces acting on the object.
A representation of the object is drawn in the
centre of the diagram and the forces acting on it
are drawn as arrows pointing outwards. The
arrows must be labelled!
FBD: Example 1
A ball is falling downward through the air. Draw a
FBD for the ball.
FBD: Example 1
A ball is falling downward through the air. Draw a
FBD for the ball.
FBD: Example 1
A ball is falling downward through the air. Draw a
FBD for the ball.
Fg
FBD: Example 1
A ball is falling downward through the air. Draw a
FBD for the ball.
Fair
Fg
FBD: Example 2
A book is being pushed rightward across a table.
Draw a FBD for the book.
FBD: Example 2
A book is being pushed rightward across a table.
Draw a FBD for the book.
FBD: Example 2
A book is being pushed rightward across a table.
Draw a FBD for the book.
FA
FBD: Example 2
A book is being pushed rightward across a table.
Draw a FBD for the book.
Ff
FA
FBD: Example 2
A book is being pushed rightward across a table.
Draw a FBD for the book.
Ff
FA
Fg
FBD: Example 2
A book is being pushed rightward across a table.
Draw a FBD for the book.
Ff
FN
Fg
FA
An Introduction to Forces:
More Practice
Draw a free-body diagram
for each of the following
objects:
(a) A car engine being lifted
from a car by a rope
attached to a pulley
An Introduction to Forces:
More Practice
Draw a free-body diagram
for each of the following
objects:
(b) an car moving with
constant velocity on a
level road
An Introduction to Forces:
More Practice
Draw a free-body diagram
for each of the following
objects:
(c) an apple hanging from a
tree branch
An Introduction to Forces:
More Practice
Draw a free-body diagram
for each of the following
objects:
(d) a skydiver being slowed
by a parachute
An Introduction to Forces:
More Practice
Mr. Wong is pulling across level snow a sled on
which is sitting his daughter. Tied to the back of
his daughter’s sled is another tiny sled on which
his daughter’s baby doll is sitting.
Draw the free-body diagrams for (a) Mr. Wong
An Introduction to Forces:
More Practice
Draw the free-body diagrams for (b) his daughter
An Introduction to Forces:
More Practice
Draw the free-body diagrams for (d) his daughter’s
sled
An Introduction to Forces:
Answers to More Practice
Draw the free-body diagrams for
(d) the doll’s sled
Net Force
FBDs are drawn to help determine the net force
(the sum of all forces) acting on an object.
Resolve all vertical and horizontal vectors and
determine the resultant.
FBD: Example 2 with Numbers
A book is being pushed across a table with a force of 5 N
[right]. The force of friction is 2 N [left], the
gravitational force is 10 N [down], and the normal force
is 10 N [up]. Find the net force on the book.
FBD: Example 2 with Numbers
A book is being pushed across a table with a force of 5 N
[right]. The force of friction is 2 N [left], the
gravitational force is 10 N [down], and the normal force
is 10 N [up]. Find the net force on the book.
Ff = 2 N
FN = 10 N
FA = 5 N
Fg = 10 N
FBD: Example 2 with Numbers
A book is being pushed across a table with a force of 5 N
[right]. The force of friction is 2 N [left], the
gravitational force is 10 N [down], and the normal force
is 10 N [up]. Find the net force on the book.
Horizontal forces: FA + Ff = 5 N + (- 2 N) = 3 N
Vertical forces: Fg + FN = (- 10 N) + (10 N) = 0
The net force Fnet = 3 N [right]
INERTIA AND NEWTON’S FIRST
LAW OF MOTION
QUESTION:
When you are standing on the train and it suddenly
starts to move, what happens?
 You fall backwards.

What happens if you are standing on the train as it is
moving and it starts to slow down?
 You fall forwards.


What causes this movement?
INERTIA

A property of matter that causes an object to
resist changes in its state of motion; it is directly
proportional to the mass of the object.
 The greater the mass, the greater the
inertia an object possesses.



In physics we pretend that there is no friction for
some of our problems.
If the carpet of the train did not have any friction
and there was no air resistance, when the train
starts, you would stay in the same spot as the
train moves forward until the back wall hits you.
When the train slows down, you would continue
to move forward until you hit a wall.
NET FORCES
As we have already learned, several forces can
act on one object at the same time. The vector
sum of all the forces acting on the object is known
as the net force.
 The net force is not an actual force or a separate
force of nature; it is the sum of actual forces.

EXAMPLE:

1.
2.
A weight lifter holds a weight above the head by
exerting a force of 1.6 kN [up]. The force of the
gravity acting on the weight is 1.6 kN [down].
Draw a Free body diagram of the system.
Find the net force.
 Find
the net force.
=
1.6 kN [up] - 1.6 kN [down]
=
0
NEWTON’S FIRST LAW OF MOTION (LAW
OF INERTIA)
 If
the Net force acting on an object
is zero, the object will maintain its
state of rest or constant velocity.
THIS CAN BE STATED IN LAYMAN’S TERMS AS:

Objects at rest or moving with a constant velocity
maintain their state of rest or constant velocity
unless acted upon by a net force.
 The net force must be external in order to
change an objects velocity.
 Internal forces have no effect on an objects
motion.
This law of inertia helps us to understand the
principles behind using seatbelts and air bags.
Once an object is moving, it tends to keep moving
at a constant velocity because of its inertia.
 Air bags and seatbelts help to slow us down
safely.

EXAMPLE:


A 12 passenger jet aircraft of mass 1.6 x 104 kg is
travelling at a constant velocity of 850 km/h [E]
while maintain a constant altitude. Besides
gravity and air resistance, the aircraft also
experiences an upward force called “lift” and a
forward force of the engines called “thrust.”
Draw an FBD of the aircraft, and state the net
force acting on the aircraft.

What is the net force?
LAW OF INERTIA SUMMARY
1.
2.
3.
4.
Objects at rest remain at rest unless
acted upon by a net force.
Objects in motion remain in motion unless
action upon by a net force.
If the velocity of an object is constant (or
zero), the net external force acing it must be
zero.
If the velocity of an object is changing either
in magnitude, direction, or both, the change
must be caused by a net external force on the
object.
A THOUGHT EXPERIMENT

1)
2)
3)
4)
You are on a level ice field without boundary
Imagine slapping a hockey puck forward and it
travels 50 m.
What stops the hockey puck?
If you smooth out the ice field, what will happen
to the travelling distance of the puck?
Repeat the above until (theoretically) friction is
totally eliminated, what will happen to the
travelling distance of the puck?
What does that mean?