Chapter 4 Forces and the Laws of Motion Changes in Motion ...

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Chapter 4

Forces and the Laws of Motion

Changes in Motion

Objectives:

1. Describe how force affects the motion of an object.

2. Interpret and construct free
-
body diagrams.

The Force is Strong With You

Force

is an action exerted on an object which may change the object's state of rest or motion.

Force may cause a change in an object's velocity with respect to time (acceleration.)

Forces can cause objects at rest to move, cause objects in motion to stop, and
cause objects to
change direction.

The Force is Strong With You

The SI unit of force is the Newton (named for Sir Isaac Newton.)

The amount of force that, when acting on 1 kg of mass, produces an acceleration of 1 m/s
2

.

1 Newton = 1 kg


1 m/s
2

Weight is

a measure of the gravitational force exerted on an object.

1 lb = 4.448 N

1 N = 0.225 lb

Contact Forces


Contact forces

result from the physical contact between 2 objects.

Pushing, pulling, throwing, catching

Field Forces

Field forces

do not involve physi
cal contact between objects, rather they are forces that act at a
distance.

Gravitational force, electrical forces (attraction or repulsion)

Masses create gravitational fields in the space around them.

Charged objects create electromagnetic fields in the s
pace around them.

Field Forces

All macroscopic contact forces occur as a result of microscopic field forces.

All contact can be examined on a microscopic atomic level and related to the interactions of
atomic particles.

Force Diagrams (Draw a Good
Picture!)

Force is a vector since it has both a magnitude and a direction.

Force diagrams are diagrams that show force as vectors.

A force vector's tail is attached to the center of gravity of the object.

A force vector points in the direction of the force

and its length is proportional to the
magnitude of the force.

Free
-
Body Diagrams

A free
-
body diagram is a representation of a single object and all the forces acting on that
object.

The forces exerted by the object isolated on other objects are not includ
ed in a free
-
body
diagram because they do not affect the motion of the object.

Free
-
body diagrams are constructed and analyzed like vector diagrams.


Concept Check

A truck pulls a trailer on a flat stretch of road. The forces acting on the trailer are th
e force
due to gravity (250 000 N downward), the force exerted by the road (250 000 N upward),
and the force exerted by the cable connecting the trailer to the truck (20 000 N to the
right.) The forces acting on the truck are the force due to gravity (80
000 N downward),
the force exerted by the road (80 000 N) upward, and the force exerted by the car's engine
(26 400 N to the right.) Draw and label free
-
body diagrams of both the trailer and the
truck.

Newton's First Law

Objectives:

1. Explain the relati
onship between the motion of an object and the net external force acting
on the object.

2. Determine the net external force on an object.

3. Calculate the force required to bring an object into equilibrium.

Inertia

Inertia

is the tendency of an object to

resist being moved or, if the object is moving, to resist a
change in speed or direction.

Galileo theorized about the nature of an object to maintain its state of rest or motion.

Newton furthered Galileo's conclusions by developing
Newton's first law of m
otion

An object at rest remains at rest, and an object in motion continues in motion with
a constant velocity (that is, constant speed in a straight line) unless the object
experiences a net external force.

Inertia

Inertia, therefore, is the tendency of an

object not to be accelerated.

Newton's first law thus states that
when the net external force on an object is zero, the object's
acceleration (or the change in the object's velocity) is zero.

Net Force

A car is traveling at a constant velocity.

The net ex
ternal force on the car is zero.

There are many forces acting on the car (
F
forward,
F
resistance
, F
gravity
, F
normal
)

The individual external forces acting on the car are not zero, but the net external force is zero.

An external force is a force that acts on

an object as a result of the interaction between the
object and its environment.

Net Force

All four forces acting on the car are external forces.

The net force is the sum of all the forces acting on the car.

Net force

is a single force whose external effe
cts on a rigid body are the same as the effects of
several actual forces acting on the body.

When all external forces acting on an object are known, the net force can be found.

Concept Check

A gust of wind blows an apple from a tree. As the apple falls, t
he gravitational force on the
apple is 2.25 N downward, and the force of the wind on the apple is 1.05 N to the right.
Find the magnitude and direction of the net force on the apple.

Concept Check

2.48 N at 25.0
˚
counterclockwise from straight down.

Equili
brium

Equilibrium

is the state in which the net force on an object is zero.

An object that is at rest or moving with a constant velocity is in equilibrium.

To determine whether an object is in equilibrium, determine the net force.

If the net force is zero,

the object is in equilibrium.

If there is a net force, a second force equal and opposite to the net force will put the body in
equilibrium.

Concept Check

Can an object be in equilibrium if only one force acts on the object?

Concept Check

No. Either no
force or two or more forces are required for equilibrium.

Newton's Second and Third Laws

Objectives:

1. Describe an object's acceleration in terms of its mass and the net force acting on it.

2. Predict the direction and magnitude of the acceleration caus
ed by a known net force.

3. Identify action
-
reaction pairs.

Newton's Second Law

Consider a situation in which you are trying to push a heavy piece of furniture across the room.

If you try to move it by yourself, the acceleration will be so small it will t
ake a long time to
notice a change in velocity.

If you get your friend to help you, the acceleration will be larger and the furniture will soon be
moving very quickly.

Newton's Second Law

A heavier piece of furniture accelerates less than a lighter piece o
f furniture.

It requires less force to accelerated a low
-
mass object than a high
-
mass object.

Newton Second Law

The acceleration of an object is directly proportional to the net forces acting on
the object and inversely proportional to the object's mass.

Σ
F=
m
a

Net force = mass x acceleration

Concept Check

Space
-
shuttle astronauts experience accelerations of about 35 m/s
2

during takeoff. What
force does a 75 kg astronaut experience during an acceleration of this magnitude?

Concept Check

2600 N

Concept C
heck

An 8.5 kg bowling ball initially at rest is dropped from the top of an 11 m building. The ball
hits the ground 1.5 s later. Find the net force acting on the falling ball.

Concept Check

83 N

Newton's Third Law

A single isolated force cannot exist.

Forces always exist in pairs.

Newton's third law of motion

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 o
pposite in direction.

For every action, there is an equal and opposite reaction.

Newton's Third Law

The forces two interacting objects exert on each other form an action
-
reaction pair.

The action force is equal in magnitude and opposite in direction from t
he reaction force.

Action and reaction forces occur simultaneously.

Action and reaction forces do not cancel each other such that an object does not move since
each force acts on different objects.

Newton's Third Law

The motion of an object is affected onl
y by the forces acting on that object.

To determine whether an object will accelerate, draw a free
-
body diagram of the object and
determine whether there is a net force acting on the object.

Action
-
reaction forces are equal and opposite, but either object
may still have a net force acting
on it.

Newton's Third Law and Field Forces

Newton's third law also applies to field forces.

Consider the gravitational force exerted by the Earth on an object.

The object will also exert a force on the Earth.

Since the mas
s of the Earth is greater than the mass of the object, the acceleration of the Earth
towards the object will be negligible when compared with the acceleration of the object
towards the Earth.

Everyday Forces

Objectives:

1. Explain the difference
between mass and weight.

2. Find the direction and magnitude of normal forces.

3. Describe air resistance as a form of friction.

4. Use coefficients of friction to calculate frictional force.

Weight

The weight of an object is calculated by
F
g
=
m
a
g
.

Since the acceleration due to gravity (
a
g
) varies with location of an object in the universe:

Weight

is a measure of the gravitational force exerted on an object; its value can
change with the location of the object in the universe.

Normal Force

The force
of gravity is constantly acting on all objects on Earth, since objects are not
continuously falling towards the center of the Earth there must be a force opposing the
force of gravity to keep them in equilibrium.

This force is the
normal force

A force that

acts on a surface that is perpendicular to the surface.

Normal means perpendicular.

Normal Force

The normal force is always perpendicular to the contact surface, not necessarily directly
opposite the force due to gravity.

In the absence of other forces,
F
n

is equal and opposite to the component of
F
g

that is
perpendicular to the contact surface.

If the angle
Θ

is the angle between the normal force and the vertical line and also the angle
between the contact surface and the horizontal, then
F
n

=
m
a
g
cos
Θ
.

Friction

Static friction

is the force that resists the initiation of sliding motion between two surfaces that
are in contact and at rest.

As long as the object does not move, the force of static friction is equal and opposite to the
component of the applie
d force that is parallel to the surface.

When the applied force is as great as it can be without causing the object to move, the force of
static friction has reached its maximum value (
F
s,max
)

Friction

Frictional forces occur because of microscopic interac
tions between contact surfaces.

When viewed at the microscopic level, surfaces only contact at a few points.

At these points, surfaces adhere together because of the electrostatic forces between molecules
of the two surfaces.

Friction

Kinetic friction

is the force that opposes the movement of two surfaces that are in contact and
are sliding over each other.

Kinetic friction is less that the maximum static friction.

F
n
=
F
applied
-
F
k


Friction

Heavier objects require more force to slide across the same sur
face.

This is so because the force of friction is proportional to the normal force of a surface on an
object.

Note that the normal force is equal and opposite to the vertical component of the gravitational
force of an object on a surface.

Friction

Friction

can be approximated if we know the normal force and
F
s,max
.

This is the
coefficient of friction

The ratio of the magnitude of the force of friction between two objects in contact to the
magnitude of the normal force with which the objects press against e
ach other.

μ
k
=
F
s, max


F
n


Concept Check

A 24 kg crate is set into motion on a horizontal floor. Once the crate is in motion, a
horizontal force of 53 N keeps the crate moving with a constant velocity. Find the
coefficient of static
friction, between the crate and the floor.

Concept Check

0.22

Concept Check

Two students are sliding a 225 kg sofa at a constant speed across a wood floor. One student
pulls with a force of 225 N at an angle of 13
˚

above the horizontal. The other student

pushes with a force of 250 N at an angle of 23
˚

below the horizontal. What is the
coefficient of friction between the sofa and the floor?

Concept Check

0.25

Air Resistance is a Form of Friction

Whenever an object moves through a fluid medium, such as air

or water, the fluid provides a
resistance to the object's motion.

When the magnitude of the force applied equals the magnitude of air resistance, the net force is
zero and the object moves at a constant speed.

When an object in free
-
fall accelerates, its
velocity increases.

As the velocity increases, the resistance of the air to the object's motion increases.

Air Resistance is a Form of Friction

When the upward force of air resistance is equal to the downward gravitational force, the net
force is zero and
the object moves at a constant velocity.

The object has reached terminal velocity.

Four Fundamental Forces

Electromagnetic forces
-
interactions between protons and neutrons. Acts over long ranges.

Strong nuclear forces
-
strongest of the forces.

Weak nuclear

forces

Gravitational forces
-
weakest of the forces. Acts over long ranges.

All four are field forces.