Download Chapter 5

Forces and Newton’s Laws of Motion
CHAPTER 4
FORCE
A force is a push or pull. Forces are often
categorized as contact forces or at-a-distance
forces.
 Contact forces: arise from the physical contact
between two objects.
 At-a-distance forces: Gravity, electrical forces
 Forces are VECTOR QUANTITIES. We use
arrows to represent magnitude and direction.

MASS AND INERTIA
Mass is the amount of matter in an object.
 Mass is a scalar quantity.
 Inertia is a property of matter that depends on
mass.
 Inertia is a resistance to change in motion.
 Inertia is dependent on mass.
 Inertia is the “lazy factor.”

NEWTON’S 1ST LAW OF MOTION
An object continues in a state of rest or in a
state of motion at a constant speed along a
straight line, unless compelled to change that
state by a net force.
 Net force is the vector sum of all forces acting
on a body.
 Often called the Law of Inertia.
 This law helps explain why we fly over
handlebars and how and why seatbelts work.

NEWTON’S 2ND LAW OF MOTION
Acceleration is proportional to the net force
acting on an object.
 Again, net force is the vector sum of all forces.
 ΣF is used to signify net force.
 Also, for a given force, the magnitude of the
acceleration is inversely proportional to the
mass.

2ND LAW MATHEMATICS


 F  ma
SI unit of Force: a derived unit
kgm/s2 = Newton (N)
When a net external force acts on
an object of mass m, the
acceleration that results is directly
proportional to the net force and
has a magnitude that is inversely
proportional to the mass. The
direction of the acceleration is the
same as the direction of the net
force.
PROBLEM SOLVING HINTS
1.
2.
3.
4.
Start with a FREE BODY DIAGRAM!
Determine the net force. Remember force is a
vector quantity and may need to be broken
into x and y components to solve for ΣF.
You may need to use kinematics equations as
a means of solving for acceleration.
Substitute this information into F=ma.
Label everything clearly to eliminate
confusion.
VECTOR NATURE OF NEWTON’S 2ND LAW
When dealing with projectile motion, we
broke motion into x- and y- components.
 When dealing with forces, it is important to
realize we often need to do the same thing.
 ΣFx = max
 ΣFy = may
 After solving for the x- and y- components,
Net Force can be solved using pythagorean
theorem.

NEWTON’S 3RD LAW OF MOTION
Whenever one body exerts a force on a
second body, the second body exerts an
oppositely directed force of equal magnitude
on the first body.
 “Action – Reaction” law

TYPES OF FORCES

Common types of forces include:
 Gravitational
force
 Normal
force
 Frictional force
 Tension force

Each of these types of forces could be acting
on the same body. Newton’s Laws hold true for
ALL types of forces.
FUNDAMENTAL FORCES
These forces are the ones that are truly unique, in
the sense that all other forces can be explained in
terms of them.
 The three known fundamental forces are::

Gravitational Force
 Strong nuclear force – primary role in stability of
nucleus of the atom
 Electroweak force

 Electromagnetic
force – electrically charged particles exert on
one another
 Weak nuclear force – radioactive disintegration of certain
nuclei
NONFUNDAMENTAL FORCES
Except for gravity all forces dealt with in this
chapter are nonfundamental
 The rest are related to electromagnetic force
 Physicists are still trying to narrow the number
of fundamental forces!

THE GRAVITATIONAL FORCE

Every particle in the universe exerts an
attractive force on every other particle.
This equation is not perfect for
objects too large to be
considered particles. However,
assuming the objects are
spheres with uniform
distribution of mass, as long as
r is used as the distance
between the centers of the
spheres the equation is a good
approximation of gravitational
force.
m1m2
F G 2
r
G = 6.63 x 10-11 Nm2/kg2
G is the universal gravitational constant
WEIGHT






The weight of an object on or above the earth is the
gravitational force that the earth exerts on the object.
The weight always acts downward, toward the center of
the earth.
SI unit of Weight: newton(N)
On Earth Fw =mg
This equation works because the mass of the Earth and
the radius from the center are fairly constant and g can
be substituted in for constants in the universal
gravitation equation.
Of course, slight variations are expected and can be
easily solved for.
THE NORMAL FORCE
One component of the force that a surface
exerts on an object with which it is in contact –
namely, the component that is perpendicular to
the surface.
 The key part of the definition here is that the
normal force acts PERPENDICULAR to the
surface an object is in contact with.
 The normal force is consistent with Newton’s
3rd Law of Motion.

SPECIAL SITUATIONS :NORMAL FORCE
In “normal” situations, In “normal”
cases where an object is lying on a
horizontal surface, the normal force will
be equal and opposite to the weight of
the object.
However, if an additional downward
force is applied to the object, that force
must be included in determining the
normal force. Likewise, if an upward
force is applied to the object (not
causing motion) that force must be
subtracted from the weight.
APPARENT WEIGHT
Apparent weight is the force that the object
exerts on the scale with which it is in contact.
 Think about an elevator….

Accelerating up: apparent weight > true weight
 Accelerating down: apparent weight < true weight
 Constant velocity: apparent weight = true weight

FN  mg  ma
Always
Positive
STATIC FRICTION



When maximum static
frictional force is exceeded,
an object will move.
Not affected by surface area
Directly affected by normal
force
KINETIC FRICTION





Opposes the relative sliding
motion
Usually less than static
friction
Independent of area of
contact
Independent of the speed
(when small)
Proportional to the normal
force.
FRICTION: CONTACT FORCE ACTING PARALLEL
TO THE SURFACE
STATIC FRICTION
Fs   s FN
KINETIC FRICTION
FK   K FN
µ is the coefficient of friction (static or
kinetic). No units are associated with this
value. This value depends on the surfaces
in contact with one another.
If kinetic friction is exactly opposite the vector sum of applied
forces, the Net Force will equal zero. In these cases, there will
be no acceleration. However, an object could still be moving
with constant velocity.
FRICTION EQUATIONS
THE TENSION FORCE

Forces applied through ropes or cables.
For ease, we consider the
rope to be “massless. “
A Force is
applied to one
end of a rope.
Satisfying the
3rd Law, each
particle applies
the same force
to the next.
The original
force applied is
then applied to
the object.
EQUILIBRIUM APPLICATIONS OF NEWTON’S
LAWS OF MOTION

In physics, equilibrium is achieved when an
object has zero acceleration.
 Fx  0
1.
2.
3.
 Fy  0
4.
5.
Problem Solving Strategy
Select object to analyze. If necessary, treat two
or more objects separately.
Free body diagram for each object chosen.
Choose a set of x,y axes for each object and
resolve all forces in the free body diagram.
Apply equations at left.
Solve the two equations for the desired unknown
quantities. Remember, two equations can give
answers for only two unknowns at most.
NONEQUILIBRIUM APPLICATIONS OF NEWTON’S
LAWS OF MOTION
Net force does not equal zero so the object
is accelerating!
 We cannot set the forces equal to zero
according to the 2nd Law.

 Fx  ma x
 F y  ma y
Apply the same reasoning strategy
as in equilibrium problems.
However, use these equations in
step 4.
HINTS AND WEBSITES
Read this chapter and work through ALL sample
problems. They are helpful for developing
concepts and will reinforce notes.
 http://www.wiley.com/college/cutnell check out
Chapter 4 features
 http://wps.prenhall.com/esm_giancoli_physicspp
a_6/16/4351/1113925.cw/index.html great site
for extra practice
 www.physicsclassroom.com Forces and dynamics
