Download Forces and the Laws of Motion

Forces and the
Laws of Motion
Chapter 4
4-1 Changes in Motion

Objectives
 Describe
how force affects the motion of an
object
 Interpret and construct free-body diagrams
Changes in Motion

Dynamics is an area of mechanics which
seeks to explain why objects move as they
do
 This
involves studying how forces affect
motion

force – an action exerted on an object that
may change the object’s state of rest or
motion
Changes in Motion

Often times a force acting on an object will
cause the object’s velocity to change with
respect to time – it’s accelerating
 Examples:
baseball
throwing a baseball vs. catching a
Changes in Motion

A newton is the SI unit of force
(N) – the amount of force required to
accelerate a 1 kg mass at 1 m/s2
 Therefore, 1 N = 1 kg x 1 m/s2
 newton
Changes in Motion

Forces can act through contact or at a
distance
 Contact
forces are forces that result from the
physical contact between objects (push/pulls)

Examples: pushing a cart, kicking a football, etc.
 Field
forces are force that do not involve the
physical contact between objects

Examples: gravitational force, electromagnetic
force, etc.
Force / Free-body Diagrams

Force is a vector quantity
 Both
the magnitude and the direction of the
force will influence how it affects the motion of
an object.
 The acceleration will be in the same direction
as the force.
Force / Free-body Diagrams
Drawing Free-body Diagrams

Drawing Free-body Diagrams
Identify the forces acting on the object and
the direction of the forces.
2) Draw a diagram to represent the isolated
object.
3) Draw and label vector arrows for all external
forces acting on the object.
1)
4-2 Newton’s First Law

Objectives:
 Explain
the relationship between the motion of
the object and the net force acting on the
object
 Determine the net force acting on an object
 Calculate the force required to bring an object
to equilibrium
Newton’s First Law

It is a common misconception that if there
are no forces acting on an object it will be
at rest
 Consider
what happens when push a book
along a table vs. pushing it along a sheet of
ice.
 What happens? Why?
Newton’s First Law
Galileo correctly concluded that it is an
object’s nature to maintain its state of
motion or rest
 Newton further developed this idea into
what has come to be known Newton’s
First Law of Motion

Newton’s First Law

Newton’s First Law of Motion:
An object at rest remains at rest, and an
object in motion continues in motion with
constant velocity (constant speed in a
straight line) unless the object experiences
a net external force.
 Sometimes
referred to as the law of inertia
Newton’s First Law
inertia – the tendency of an object to resist
being moved or, if the object is moving, to
resist a change in speed or direction
 Mass is a measure of inertia of a body

 The
more mass that an object has, the harder
it is to change its state of motion (requires a
greater force)
Pushing a car vs. a truck (starting from rest)
 Stopping a baseball vs. a bowling ball (same velocity)

Newton’s First Law

Any object that is accelerating has to have a net
force acting on it
force (ΣF) – the vector sum of all of the forces
acting on an object
 net

If the net force is equal to zero, the object will
have a constant velocity (acceleration = 0)
a book being slid at a constant velocity –
Why is it not accelerating?
 Example:
Newton’s First Law
Newton’s First Law

Objects that are either at rest or moving
with a constant velocity are said to be in
equilibrium
– the state in which the net force
on an object is zero
 equilibrium
Newton’s First Law
4-3 2nd & 3rd Laws of Motion

Objectives:
 Describe
an object’s acceleration in terms of
its mass and the net force acting on it.
 Calculate the direction and magnitude of the
acceleration caused by a known net force.
 Identify action-reaction pairs
Newton’s Second Law
Newton’s Second Law of Motion:
The acceleration of an object is directly
proportional to the net force acting on the
object and inversely proportional to the
object’s mass.
Equation:
ΣF = ma
net force = mass x acceleration

Newton’s Second Law

Acceleration is inversely proportional to
mass.
 If
the same force is applied to objects of
different masses:
The object with the greater mass will experience a
smaller acceleration.
 The object with less mass will experience a greater
acceleration.

Newton’s Second Law

Acceleration is directly proportional to net
force.
 When
mass is constant:
Increasing the force increases the acceleration by
the same factor.
 Decreasing the force decreases the acceleration
by the same factor.

Newton’s Second Law

Sample Problem C:
Roberto and Laura are studying across
from each other at a wide table. Laura
slides a 2.2 kg book toward Roberto. If the
net force acting on the book is 1.6 N to the
right, what is the book’s acceleration?
Newton’s Second Law
U: a (m/s2)
K: m = 2.2 kg
ΣF = 1.6 N to the right
ΣF = ma
1.6 N = (2.2 kg)a
a = 0.73 m/s2 to the right
Newton’s Third Law

Newton recognized that a single isolated
force cannot exist
 Consider
what happens when a person
wearing ice skates pushes on the wall of an
ice rink…

Forces always exist in pairs – Newton
described this in his third law of motion
Newton’s Third Law

Newton’s Third Law of Motion:
Whenever one object exerts a force on a
second object, the second object exerts an
equal and opposite force on the first object.
 Equal
magnitude, opposite direction
Newton’s Third Law

Generally stated: For every action there is
an equal and opposite reaction.
 The
objects exerting the forces on each other
are referred to as the action-reaction pair

These forces occur at the same time and act on
different objects
Newton’s Third Law

Consider the following examples:
 What
are the action-reaction forces involved
when a person hammers a nail into a piece of
wood?
 How does a rocket work?
Newton’s Third Law

Field forces also exist in pairs
 When
an apple falls from a tree it accelerates
toward the Earth because the Earth exerts a
gravitational force on the apple.
 If this is the action force, what is the reaction
force?
4-4 Everyday Forces

Objectives:
 Explain
the difference between mass and
weight.
 Find the direction and magnitude of normal
forces.
 Describe air resistance as a form of friction.
 Use coefficients of friction to calculate
frictional force.
Weight
weight (Fg) – a measure of the magnitude of
the gravitational force exerted on an object
 Since
weight is the magnitude of the
gravitational force acting on an object, it is a
scalar quantity
 Will the weight of an object be constant?
Weight vs. Mass
Since the gravitational force between
objects varies by location, weight will vary
by an object’s location.
 Mass does not vary by location - it is an
inherent property of the object.

 Example: A 1.5
kg hammer will have a weight
of 14.7 N near the Earth’s surface, but it will
weigh 2.4 N on the Moon (it’s mass is 1.5 kg in
both locations)
Weight
The force of gravity can be calculated by
the following equation:
Fg = mag
 ag represents the acceleration due to
gravity


Near Earth’s surface ag = g = 9.8 m/s2, so:
Fg = mg
Weight

What is the weight of an astronaut on
Earth (g = 9.8 m/s2) and on the Moon
(ag = 1.6 m/s2) if the astronaut’s mass is
81.6 kg?
The Normal Force

A television set is at rest on a table.
 The
force of gravity is constantly acting on the
TV.
 Is the TV in equilibrium? If so, how is it in
equilibrium?
The Normal Force

normal force (Fn) – a force that occurs
when objects come in contact with each
other and acts perpendicular to the
shared surface
 In
the absence of other forces, Fn is equal
and opposite to the component of Fg that is
perpendicular to the contact surface.
Fn = mg cos θ
The Normal Force
The Force of Friction

Friction is a force that resists motion
(static friction) or opposes the motion of
objects that are in contact (kinetic friction)
Is there any friction acting
on the jug of orange juice
pictured to the right?
The Force of Friction
static friction (Fs) – the force that resists
the initiation of sliding motion between two
surfaces that are in contact and at rest
The Force of Friction

When a force is applied to an object that
remains at rest, the Fs is always equal an
opposite to the component of the applied
force that is parallel to the surface
 If
the applied force increases, Fs increases
 If the applied force decreases, Fs decreases
The Force of Friction

Once the applied force is as great as it
can be without causing the object to
move, the static friction is at its
maximum value (Fs,max)
Increasing the applied force further
will cause the object to move and it
then be experiencing kinetic friction
The Force of Friction
kinetic friction (Fk) – the force that opposes
the movement of two surfaces that are in
contact and are sliding over each other
 The
force of Fk is less than Fs,max
 The net force acting on the object is equal to
the difference between the applied force and
the force of kinetic friction
ΣF = Fapplied - Fk
The Force of Friction

The force of friction is approximately
proportional to the normal force
 Example:
It is easier to push a chair across
the floor at a constant speed than it is to push
a heavier desk at the same speed
The Force of Friction
The force of friction can only
be approximately calculated

This is because it is a macroscopic
effect caused by a complex interaction
of forces at the microscopic level.
The Force of Friction

In addition to the Fn, the force of friction
also depends on the surfaces in contact
 The
quantity that expresses this concept is the
coefficient of friction
coefficient of friction (μ) – the ratio of the
magnitude of the force of friction between
two objects in contact to the magnitude of
the normal force acting on the objects
The Force of Friction

The force of friction can be calculated with
the following equations:
Static Friction:
Fs ≤ μsFn
Kinetic Friction: Fk = μkFn
The Force of Friction
Air Resistance


Whenever an object moves through a fluid
substance, such as air or water, the fluid
provides a force that opposes the objects motion
Air resistance will increase on an object in free
fall as the objects speed increases
 When
the upward force of air resistance is equal in
magnitude to the downward force of gravity the object
reaches terminal velocity
Fundamental Forces

The four fundamental forces are all field
forces
 Electromagnetic
Force
 Gravitational Force
 Strong Nuclear Force
 Weak Nuclear Force
Fundamental Forces
The strong and weak nuclear forces have
very small ranges and are not directly
observable
 The electromagnetic and gravitational
forces act over long ranges

 The
strong nuclear force is the strongest of
the fundamental forces; gravity is the weakest