Projectile Motion
A projectile is an object on which the only force
acting is ______ and the direction of this force
is always _____.
(In real life, a projectile will also have ______ or
___________ acting on it and the direction of
this force is always _____________________.)
Projectile Motion
A projectile is an object on which the only force
acting is gravity and the direction of this force
is always down.
(In real life, a projectile will also have friction or
air resistance acting on it and the direction of
this force is always opposite the direction of
motion.)
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
with neglect this)

Fs

Fk

Fair
Normal Force
The normal force acts to keep objects apart.
Normal Force
The normal force acts to keep objects apart.
i.e. if you push on a wall, the wall will exert a
normal force on your hand that prevents your
hand from pushing through the wall.
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.
One example is 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
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
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]
More Practice
Estimating and Measuring Forces