Ch. 4, 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
“Contact” Forces: “Pulling” forces
“Pushing”
forces
“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 objects
• Electromagnetic Forces
– Between electric charges
• Nuclear Weak Forces
– Arise in 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 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. In the 21st Century,
this is still a common
– The “natural” state of an object is at rest.
MISCONCEPTION!!!
• THE CORRECT VIEW (of Galileo & Newton):
– It’s just as natural for an object to be in motion at constant
Proven by Galileo
speed in a straight line as to be at rest.
– At first, imagine the case of NO FRICTION
in the 1620’s!
– Experiment: 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 (The “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 such 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 1st Law
• Was actually stated first stated by Galileo!
Newton’s First Law
(Calvin & Hobbs)
A Mathematical Statement of Newton’s 1st Law
If v = constant, ∑F = 0
OR
if v ≠ constant, ∑F ≠ 0
Conceptual Example 4-1:
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 a body to maintain its
state of rest or motion.
• MASS  A measure of the inertia of a body.
– The quantity of matter in a body.
– The SI System quantifies mass by having a standard
mass = Standard Kilogram (kg)
(Similar to the 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 in the chapter.
Newton’s Second Law (Lab)
• Newton’s 1st Law: If no net force acts, an object
remains at rest or in uniform motion in straight line.
• What if a net force acts? That question 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 body produces an acceleration!
∑F  a
Newton’s 2nd Law
Experiments Show That:
The net force ∑F on a body & the acceleration a of
that body 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, your text writes:
∑F = ma
 The Vector Sum
of all Forces
on mass m!
∑ = a math symbol meaning sum (capital sigma)
Based on experiment!
Not derivable mathematically!!
• Newton’s 2nd Law:
∑F = ma
A VECTOR Equation!!
It holds component by component.
∑Fx = max, ∑Fy = may, ∑Fz = maz
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 &
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
This is based on
physical content & is very general.
experiment!
It is A LAW!!
Not on math!!
Also it is a definition of force!
Examples
Example 4-2:
Estimate the net force needed to accelerate
(a) a 1000-kg car at a = (½)g
(b) a 200-g apple at the same rate.
Example 4-3:
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?