Motion & Force: DYNAMICS
Force
A Force is “A push or a pull” on an object. Usually,
for a force, we use the symbol F. F is a VECTOR!
Obviously, vector addition is needed to add forces!
Classes of Forces
“Pulling”
1. “Contact” Forces:
Forces
“Pushing”
Forces
2. “Field” Forces:
Physics I: Gravity
Physics II:
Electricity & Magnetism
Classes of Forces
• Contact Forces involve physical
contact between two objects
–Examples (in the pictures): spring
forces, pulling force, pushing force
• Field Forces act through empty space.
–No physical contact is required.
–Examples (in the pictures):
gravitation, electrostatic, magnetic
The 4 Fundamental Forces of Nature
• Gravitational Forces
–Between masses
• Electromagnetic Forces
–Between electric charges
• Nuclear Weak Forces
–Certain radioactive decay processes
• Nuclear Strong Forces
–Between subatomic particles
Note: These are all field forces!
The 4 Fundamental Forces of Nature
Sources of the forces: In the order of decreasing strength
This table shows details of the 4 Fundamental Forces of
Nature, & their relative strength for 2 protons in a nucleus.
Sir Isaac Newton
•
•
•
•
1642 – 1727
Formulated the basic laws
of mechanics.
Discovered the Law of
Universal Gravitation.
Invented a form of
Calculus
Made many observations
dealing with light & optics.
Newton’s Laws of Motion
• The ancient (& wrong!) view (of Aristotle):
A force is needed to keep an object in motion.
The “natural” state of an object is at rest.
In the 21st Century, its still a common
MISCONCEPTION!!
• THE CORRECT VIEW
(Galileo & Newton):
It’s just as natural for an object to be in
motion at constant speed in a straight
line as to be at rest.
Newton’s Laws of Motion
• THE CORRECT VIEW (Galileo & Newton):
• It’s just as natural for an object to be in motion
at constant speed in a straight line as to be at rest.
• At first, imagine the case of NO FRICTION
Experiments Show
• If NO NET FORCE is applied to an object
moving at a constant speed in straight line, it will
continue moving at the same speed in a straight line!
• If I succeed in having you overcome the
wrong, ancient misconception & understand
the correct view, one of the main goals of the
course will have been achieved!
Newton’s Laws
• Galileo laid the ground work for
Newton’s Laws.
• Newton: Built on Galileo’s work
Now, Newton’s 3 Laws, one at a time.
Newton’s First Law
Newton was
born the same
year Galileo
died!
• Newton’s First Law (“Law of Inertia”):
“Every object continues in a state of rest or
uniform motion (constant velocity) in a
straight line unless acted on by a net force.”
Newton’s First Law of Motion
Inertial Reference Frames
Newton’s 1st Law:
• Doesn’t hold in every reference frame. In
particular, it doesn’t work in a reference frame
that is accelerating or rotating.
An Inertial Reference frame is one in which
Newton’s first law is valid.
• This excludes rotating & accelerating frames.
• How can we tell if we are in an inertial reference frame?
By checking to see if Newton’s
First Law holds!
Newton’s
st
1
Law
• Was actually stated first stated by Galileo!
Newton’s First Law
(Calvin & Hobbs)
Mathematical Statement of Newton’s 1st Law:
If v = constant, ∑F = 0 OR
if v ≠ constant, ∑F ≠ 0
Conceptual Example
Newton’s First Law.
A school bus comes to a sudden stop,
and all of the backpacks on the floor
start to slide forward.
What force causes them to do this?
Newton’s First Law
Alternative Statement
• In the absence of external forces, when
viewed from an inertial reference frame,
an object at rest remains at rest & an
object in motion continues in motion with
a constant velocity
– Newton’s 1st Law describes what happens
in the absence of a net force.
– It also tells us that when no force acts on an
object, the acceleration of the object is zero.
Inertia & Mass
• Inertia  The tendency of an object to
maintain its state of rest or motion.
• MASS  A measure of the inertia of a mass.
– The quantity of matter in an object.
– As we already discussed, the SI System quantifies
mass by having a standard mass = Standard
Kilogram (kg). (Similar to standards for length & time).
– The SI Unit of Mass = The Kilogram (kg)
• The cgs unit of mass = the gram (g) = 10-3 kg
• Weight is NOT the same as mass!
– Weight is the force of gravity on an object.
• Discussed later.
Newton’s Second Law (Lab)
• Newton’s 1st Law: If no net force acts, an object
remains at rest or in uniform motion in a straight line.
• What if a net force acts? That is answered by doing
Experiments!
• It is found that, if the net force ∑F  0 
The velocity v changes (in magnitude, in direction or both).
• A change in the velocity v (Δv).
 There is an acceleration a = (Δv/Δt)
OR
A net force acting on a mass produces
an Acceleration!!! ∑F  a
Newton’s 2nd Law
Experiments Show That:
• The net force ∑F on an object & the acceleration
a of that object are related.
• How are they related? Answer this by doing more
EXPERIMENTS!
Thousands of experiments over hundreds of
years find (for an object of mass m): a  ∑F/m (proportionality)
• The SI system chooses the units of force so that
this is not just a proportionality but an
Equation: a  ∑(F/m) OR (total force!)

Fnet  ∑F = ma
Newton’s 2nd Law: Fnet = ma
• Fnet = the net (TOTAL!) force acting on mass m
m = mass (inertia) of the object.
a = acceleration of the object.
OR, a = a description of the effect of F.
OR, F is the cause of a.
• To emphasize that F in Newton’s 2nd Law is the
TOTAL (net) force on the mass m, some texts write:
∑F = ma  Vector Sum of all Forces
on mass m!
∑ = a math symbol meaning sum (capital sigma)
• Newton’s 2nd Law:
∑F = ma (A VECTOR Equation!)
It holds component by component.
∑Fx = max, ∑Fy = may, ∑Fz = maz
Based on experiment!
Not derivable mathematically!!
ll
THIS IS ONE OF THE
MOST FUNDAMENTAL &
IMPORTANT LAWS OF
CLASSICAL PHYSICS!!!
Summary
• Newton’s 2nd Law is the relation between
acceleration & force.
• Acceleration is proportional to force and
inversely proportional to mass.
It takes a force to change either the direction
of motion or the speed of an object.
• More force means more acceleration; the same
force exerted on a more massive object will yield
less acceleration.
Now, a more precise definition of Force:
Force  An action capable of accelerating an object.
Force is a vector & ΣF = ma is true along each coordinate axis.
The SI unit of force is
The Newton (N)
∑F = ma, unit = kg m/s2
 1N = 1 kg m/s2
Note
The pound is a unit of
force, not of mass, & can
therefore be equated to
Newtons but not to kilograms.
Laws or Definitions?
• When is an equation a “Law” & when is it just an equation?
Compare
These are NOT Laws!
• The one dimensional constant acceleration equations:
v = v0 + at, x = x0 + v0t + (½)at2, v2 = (v0)2 + 2a (x - x0)
• These are nothing general or profound. They are valid for constant
a only. They were obtained from the definitions of a & v!
With ∑F = ma.
• This is based on EXPERIMENT. It is NOT derived
mathematically from any other expression! It has
profound physical content & is very general.
It is A LAW!!
This is based on
experiment!
definition Not on math!!
Also it is a
of force!
Example: Estimate the net force needed to accelerate
(a) a 1000-kg car at a = (½)g = 4.9 m/s2
(b) a 200-g apple at the same rate.
Example: The force to stop a car.
What average net force is required to bring a
1500-kg car to rest from a speed of 100
km/h (27.8 m/s) within a distance of 55 m?