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Chapter 4
Forces and the Laws of Motion
Chapter Objectives
• Define force
• Identify different classes
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of forces
Free Body Diagrams
Newton’s Laws of Motion
Define Equilibrium
Identify different types of
everyday forces
Definition of Force
• Force is defined as the cause of acceleration.
• We often think of it as a push or a pull on some
object.
• Force causes a change in velocity.
• That could mean magnitude and/or direction.
Contact v Field Forces
• The first class of force that we
• The second class of force that
will talk about is contact.
• A contact force is a force that
arises from the physical contact
of two objects.
• This would include such forces
as a bat striking a baseball, a
receiver catching a football,
friction, etc.
we will talk about is field.
• A field force is a force that can
exist between objects, even in
the absence of physical contact
between the objects.
• This would include such forces
as gravity, magnetism, static
electricity, etc.
Free Body Diagrams
• Because force deals with acceleration, and acceleration is
a vector quantity, therefore force is a vector.
• To show the forces acting on a object we draw a free body
diagram.
• A free body diagram is a diagram of an object showing all
forces acting on that object.
• Free body diagrams are drawn of objects as they are
isolated from the rest of the objects in the system.
Things to Remember in a Free Body
Diagram
1.
2.
3.
4.
All forces originate from the center of mass of the object.
The vector to represent the force of gravity always points straight
down.
The vector to represent the force of friction always opposes applied
force.
When an object is in contact with a surface, there is a normal force
that is directed perpendicular to the surface.
Fn
Fa
Ff
Fg
Newton’s First Law
• An object at rest remains at rest, and an object in motion
continues in motion with constant velocity (that is constant
speed in a straight line) unless the object experiences a
net external force.
• We will shrink that down to say objects in motion tend to
stay in motion unless acted upon by an outside force.
• This is also called the Law of Inertia.
• Inertia is the tendency of an object to resist acceleration.
Newton’s Second Law
• The acceleration of an object is directly proportional to the
net external force acting on the object and inversely
proportional to the object’s mass.
• We will take that mess and shrink it down to one simple
formula: F = ma
• This will become our standard formula for calculating
force in this book.
Newton’s Third Law
• If two objects interact, the magnitude of the force exerted
on object 1 by object 2 is equal to the magnitude of the
force simultaneously exerted on object 2 by object 1, and
these two forces are opposite in direction.
• We will shrink that tongue twister down to for every
action, there is an equal and opposite reaction.
• Notice that the action-reaction is done by two different
objects.
• Example: You are pushing down on your chair and the
chair is pushing up on you.
Equilibrium
• Equilibrium is defined as the
state in which there is no
change in the body’s motion.
• Based on Newton’s First Law,
equilibrium is achieved when
the net external force on an
object is equal to 0.
• That means that the
acceleration of the object is 0.
Which means the velocity of the
object is constant.
• Constant as in at rest, or
constant as in moving at a
constant velocity.
Weight
• Weight is the name given to the magnitude of the force of
gravity acting on an object.
• Weight can change based on the acceleration due to
gravity.
• Since the acceleration due to gravity on Earth is assumed
to be constant, weight is constant on Earth.
• Weight would be less on the moon since the acceleration
due to gravity on the moon is less. (About 1/6 that of
earth.)
F = ma
Fg = mg
Normal Force
• Remember that the normal force is the force exerted on an object
perpendicular to the surface of contact.
• So this force exists when there is an object sitting on a table, floor,
ground, or an inclined plane.
• If the object is sitting on a level surface, then the normal force is equal
but opposite to the force of gravity, or weight of the object.
• If it is not on a level surface, then you need to break the force of
gravity vector must be broken down into components.
Fn
Fn
Fg
Fg
Θ
Inclined Plane
Fn
Θ
Fg
If we flip the force of gravity
vector and take advantage of a
trigonometry proof, we see that
the angle between the normal
force and the force of gravity is
equal to the angle of the incline.
Using trig properties, we can
calculate Fn by using the cosine
function of Θ.
Θ
Fn = Fgcos Θ
Facts About Friction
• Friction opposes the motion of an object, and the motion
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is created by the applied force. So friction opposes the
applied force.
The force of friction is proportional to the normal force.
Friction depends on the surfaces in contact.
The characteristics of the surfaces are taken into account
by assigning a coefficient of friction to the surfaces in
contact.
The coefficient of friction is represented by the Greek letter
“mu”…μ.
Air Resistance
• Air resistance (FR) is the resistive force that opposes
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relative motion of an object as it flows through the fluid
medium of air.
This is based on the surface area of an object, the density of
the fluid, and the speed at which the object is traveling
through the fluid.
At low speeds, the air resistance is roughly proportional to
the car’s speed.
At high speeds, the air resistance is roughly proportional to
the square of the car’s speed.
When the magnitude of FR is equal to the applied force,
that is when an object reaches terminal velocity.
Types of Friction
• Static friction is the resistive
• Kinetic friction is the resistive
force that opposes relative
motion of two contacting
surfaces that at rest with respect
to one another.
• This is measured with the least
amount of force necessary to
make an object move.
• Static friction is always greater
than kinetic friction.
• You will need to know the
coefficient of static friction.
force that opposes the relative
motion of two contacting
surfaces that are moving past
one another.
• This is measured as the least
amount of force necessary to
keep an object moving at
constant velocity.
• Static friction is always greater
than kinetic friction.
• You will need to know the
coefficient of kinetic friction.
Fs = μs Fn
Fk = μk Fn
Tension
• Tension is nothing more than the force exerted in
a string, spring, rope, etc.
• Symbolized as FT or just T.
– The tension vector is always drawn away from the
object.
– If there is a string connecting two objects, the tension is
directed away from both of them.
FT
T1
T2