Chapter 4
Dynamics: Force and Newton's
Laws of Motion
What is Force?
Force is “a push or a pull” which is exerted on an object by an
outside agent.
Therefore: For every force you should be able to identify the
outside agent that exerts it.
Force is a Vector Quantity,
it has both magnitude and direction!
Unit of Force is Newton or N
pull
push
If more than one force acts on an object, the resultant force
(or net force) is the vector sum of the individual forces!!!
The NET FORCE acting on an object is the vector sum of
all forces acting on that object.
𝑛
𝐹Ԧ𝑛𝑒𝑡 = 𝐹Ԧ1 + 𝐹Ԧ2 + ⋯ + 𝐹Ԧ𝑛 = ෍ 𝐹Ԧ𝑖
𝑖=1
To find the net force, or the vector sum of forces, select a suitable coordinate
system and decompose each force vector into its components
Common Types of Forces:
Force
Agent
Weight
normal
earth
solid surface
tension
rope or chain
(anything that pulls)
hard surface or fluid
friction
Contact or
Long-range?
long-range
contact
contact
contact
The result of applying a force
When a force is applied on an object, the state of the object changes.
In other words, its motion will change.
Newton’s First Law
“An object at rest will remain at rest and an object in motion will remain in
motion at a constant velocity unless it is acted upon by a net force.”
A frame of reference in which Newton’s First Law is
valid are called:
Inertial frame of reference
Examples of Non-inertial frames of reference:
•An airplane that’s accelerating down the runway
•A car braking to a stop
In this course, we will assume that the ground is an inertial frame of reference.
Newton’s Second Law
If a force F acts on an object, the object will accelerate
Its acceleration is given by:
𝐹Ԧ
𝑎Ԧ =
𝑚
Or:
𝐹Ԧ = 𝑚 ∙ 𝑎Ԧ
Where m is the mass of the object,
Which is a measure of how difficult it is to change the velocity of the object or its
inertia, and it reflects how much matter the object has.
In other words, the larger the object the more difficult it is to change its velocity
Weight Vs. Mass
g
W
y
Weight: The weight of a body is defined as
the magnitude of the force required to
prevent the body from falling freely.
mg
Fnet , y = ma y  W − mg = 0  W = mg
Important
The weight of an object is not its mass. If the object is moved to a location
where the acceleration of gravity is different (e.g., the moon, where gm = 1.7
m/s2), the mass does not change but the weight does.
Newton’s 3rd Law
When two bodies interact by exerting
forces on each other, the forces are equal
in magnitude and opposite in direction.
For example: The block is applying a force Fg downward on the table and
the table is applying a force FN upward on the block. And Fg=FN.
Mathematically:


Fg = − FN
Normal Force
When a body presses against a surface, the
surface deforms and pushes on the body
with a normal force perpendicular to the
contact surface. An example is shown in the
picture to the left. A block of mass m rests
on a table.
Fnet . y = ma y  FN − mg = 0  FN = mg
In this case FN = mg. This is not always the case.
Tension
It is the force exerted by a rope
or a cable attached to an object.
It has the following characteristics:
1. It is always directed along the rope.
2. 2. It is always pulling the object.
3. It has the same value along the rope.
In this course, the following assumptions are made:
a. The rope has negligible mass compared to the mass of the object it pulls.
b. The rope does not stretch.
If a pulley is used as in fig.(b) and fig.(c), we assume that the pulley is massless
and frictionless.
Friction
If we slide or attempt to slide an object over a surface, the motion
is resisted by a bonding between the object and the surface. This
force is known as “friction.”
Identifying the forces acting on an object:
• Since all real objects have a mass, they are attracted by the earth
and hence have weight
• Since all the other forces we will be dealing with at this stage of
the course are contact forces, just list the agents that contact the
object under consideration
• Ignore all forces that are internal to the object
Free-body Force Diagram:
• Represent the object by a point
The same force exerted on systems of different masses produces different accelerations.
Free-body Force Diagram:
• Draw an arrow for each force that acts on the object; the lengths
and directions of the arrows should correspond roughly to the
information you have about the various forces
• Make all arrows start at the object and point away from it
• Label each arrow with a symbol for the force
Example
Two children push a wagon with a child in it.
Arrows representing all external forces are
shown. The system of interest is the wagon
and its rider.
All of the external forces acting on the system add together to produce a net force, Fnet .
The free-body diagram shows all of the forces acting on the system of interest. The dot
represents the center of mass of the system. Each force vector extends from this dot.
Because there are two forces acting to the right, we draw the vectors collinearly.
Example
Since motion and friction are parallel to the
slope, it is most convenient to project all
forces onto a coordinate system where one
axis is parallel to the slope and the other is
perpendicular (axes shown to left of skier). N
is perpendicular to the slope and f is parallel
to the slope, but w has components along
both axes, namely w⊥ and w ∥ . N is equal in
magnitude to w⊥ , so that there is no motion
perpendicular to the slope, but f is less than
w ∥ , so that there is a downslope
acceleration (along the parallel axis).
Example
The weight of a tightrope walker causes a
wire to sag by 5.0 degrees. The system of
interest here is the point in the wire at
which the tightrope walker is standing.
When the vectors are projected onto
vertical and horizontal axes, their
components along those axes must add to
zero, since the tightrope walker is
stationary. The small angle results in T being
much greater than w .
Example 1:
The net force on a lawn mower is 51 N to the right. The lawn mower mass is 24kg.
At what rate does the lawn mower accelerate to the right?
A) 1.5 m/s2
B) 2.1 m/s2
C) 3.1 m/s2
D) 2.8 m/s2
Example 2:
θ = 30°
m = 10kg
m
θ
1) Identify all the forces acting on the mass
2) Find the magnitude of the acceleration of the mass along the incline
A) 9.8m/s2
B) 19.6m/s2
D) 3.6m/s2
E) 4.9m/s2
C) 2.45m/s2
Example 3:
θ1
𝜽2
θ1 = 30°
θ2 = 60°
m = 5kg
What is the tension in the two ropes?
Start by Identifying all the forces acting on the mass and then draw
the Free-body Force Diagram
A) T1=49N, T2=84.48N
B) T1=24.5N, T2=42.42N
C) T1=42.42N, T2=24.5N
D) T1=12.25N, T2=21.21N
Example 4:
m1
m1=12kg
m2=3kg
F=45N

F
m2
1) Find the acceleration of the two masses
2) Find the tension in the rope connecting the two masses
Answer to (1):
A) 2m/s2
B) 1.5m/s2
C) 6m/s2
D) 3m/s2
E) 1m/s2
B) 1N
C) 9N
D) 12N
E) 6N
Answer to (2):
A) 2N
Example 5:
What is the weight of a
person, whose mass is 75kg,
in an elevator as it
accelerates up at 1.2 m/s2.
A) 825 N
B) 735 N
C) 657 N
D) 915 N