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Forces and Newton’s Laws Unit
Lecture Notes - Forces
Part 1 Introduction to Newton’s Laws
The laws codified by Isaac Newton organize
our
understanding of why objects move (or do not move), (as
long as they are not very, very small and not moving too
close to the speed of light )
Newton wrote his laws as follows:
Law 1 Every body continues in its state of rest, or of
uniform motion in a right line, unless it is compelled to
change that state by forces impressed upon it.
Law 2
The change of motion is proportional to the motive
force impressed and is made in the direction of the right
line in which that force is impressed.
Law 3
To every action there is always opposed an equal
reaction: or the mutual actions of two bodies upon each
other are always equal and directed to contrary parts.
A. Newton’s Laws explained
1. First Law of Motion
- the law of inertia
Inertia – resistance to change in state of motion.
inertia, more resistance.
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Forces and Newton’s Laws Unit
If a body has more inertia, more force will be required to
“compel” it to
a) Speed up
b) Slow down
c) Change direction
Inertia is the same as mass. Inertia is a property of a body,
NOT a force that acts upon a body.
2. Second Law of Motion - A net force is the cause of a
change in motion.
a
a
force
mass
∑F = ma
What variables are held constant in each of these
plots?
3. Newton’s third Law
Forces come in action-reaction pairs.
Forces come in interaction pairs.
F1,2 = - F2,1
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B. What are forces?
Where do forces come from?
1. There are several different types of forces.
The
important skill is to sketch a free-body diagram, which
consists of:
a) The body
b) The forces acting upon the body
The forces are represented by arrows:
http://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams
2. Types of Forces
Forces come in two general types
Contact forces
and Non-contact or field forces
Contact forces include –
a) Normal force – surface support force; perpendicular to
the surface
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Forces and Newton’s Laws Unit
b) Friction force – sliding resistance between surfaces
in relative motion
c) Tension force
- pull from rope or similar
d) Applied force – direct push or pull
e) Drag or air resistance – mechanical resistance to a
body’s passage, provided by a low-density medium such
as air.
Non –contact forces include field forces:
a) Gravitational force
b) Electromagnetic force
And Nuclear forces:
a) Strong force
b) Weak force
These field forces are non-contact, however in the standard
model that explains their existence, they are considered to
be transmitted by particles called bosons.
Gravitational force – graviton
Electromagnetic force – photon
Strong force – gluon
Weak force – W, Z boson
3. Forces come from interactions
Recall that forces are always part of an interaction
pair. The forces in that pair are equal in magnitude and
opposite in direction, but importantly, they
Do not act upon the same object.
parts”.
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They act upon “contrary
Forces and Newton’s Laws Unit
Consider again the free-body diagram:
Where did each of the forces arise and what are the
pairs?
a) Fgrav is the field force of the earth’s gravitational
field acting upon the mass.
The interaction pair is the
mass’s gravitational field acting upon the Earth.
They
are EQUAL in magnitude.
b) FNorm is the support force of the table on the mass.
This
is the reaction force due to the mass’s force on the
table (NOT its weight) The table can do this due to its
intermolecular structure.
c) Fapp is the direct pull, which has an interaction pair
that would be the same force acting on whatever is doing
the pulling. That is why it might hurt your hand when
you pull something along.
d) Ffriction is the force of the ground on the mass due to
their relative motion.
The interaction pair is the
force of the mass on the ground, which would cause the
ground to be disturbed.
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Forces and Newton’s Laws Unit
4. The horse and cart problem:
How can a horse move a cart if whenever he pulls on the
cart, the cart pulls back on him with an equal and opposite
force?
C. What is Weight?
Weight is not mass.
Consider a mass in free-fall:
Assume no air
M
Weight = force due to position in Earth’s
gravitational field.
According to Newton’s second law: Fnet = ma
There is only one force, weight.
Therefore:
Weight = ma
In free- fall, the mass experiences acceleration equal to
a =
𝑊𝑒𝑖𝑔ℎ𝑡
𝑚𝑎𝑠𝑠
This ratio is defined as the gravitational field strength
‘g’.
Therefore:
g =
𝑊𝑒𝑖𝑔ℎ𝑡
𝑚𝑎𝑠𝑠
(no air resistance)
Weight is therefore defined as:
Weight = mg. (Close to the surface)
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While mass is a measure of inertia and unaffected by
gravitational force, weight is a function of the
gravitational field strength at the location of the mass.
D. Newton’s Second Law: Constant force and constant
acceleration
∑𝐹 = 𝑚𝑎
If the vector sum of the forces acting upon a body is
equal to zero (left side of the relation), then the
acceleration must always equal zero (right side of the
relation).
An object is in equilibrium when the vector sum of the
forces acting on the object is zero.
a = 0
Therefore, the object is either at rest or moving at
constant velocity (in straight line at constant speed)
1. Some statements to keep in mind!
-A body is in a natural state of motion when it is at rest,
or moving at constant velocity.
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Forces and Newton’s Laws Unit
-As a consequence of its inertia, it has a tendency to
remain at rest or to move at constant velocity.
- A body does not have a tendency to slow down or speed up!
- The more inertia (mass) the more force required to move a
body from its natural state of motion to a different state.
- A change in motion includes speeding up, slowing down or
changing direction
2.
Solve:
Newton’s Second Law.
F = ma problems
Two canoe paddlers paddle together in their 300-kg canoe.
One exerts 225 N, the other exerts 375 N.
What is the
acceleration of the canoe?
Suppose air resistance supplies 50 N of force to a freefalling, 50-kg object.
What is the resulting
acceleration?
E. Friction – force that acts between surfaces to impede
their relative sliding motion
1. Static friction – when the surfaces are stationary
with respect to each other
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Forces and Newton’s Laws Unit
2. Kinetic friction – when one or both surfaces are in
motion.
3. For a given pair of surfaces, usually static
frictional force is greater than kinetic.
4. Frictional force depends on two factors which are
characteristics of the system being analyzed:
Ff = µFN
Where µ
= the coefficient of friction, a measure of how
“sticky” two surfaces when in contact.
Typical coefficients of friction
Surface
µs
µK
Rubber tires on
0.80
0.65
0.60
0.40
0.78
0.58
0.15
0.06
dry concrete
Rubber tires on
wet road
Steel on steel,
dry
Steel on steel
with oil
Normal shoes on
0.68
concrete
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Shoes on
0.40 (less than
linoleum
0.5 is a slip
hazard)
Zitzewitz, Paul W., Todd George. Elliott, David G. Haase, Kathleen A. Harper, Michael R. Herzog, Jane Bray. Nelson, Jim Nelson,
Charles A. Schuler, and Margaret K. Zorn. Physics: Principles and Problems. New York: Glencoe/McGraw-Hill, 2005. Print.
Coefficients of friction can be greater than 1.0 for
objects that have some adhesion, such as with tape,
sticky surfaces and special tires used in drag racing.
FN = the Normal force that acts perpendicular to the
surfaces:
Normal Force
motion
Normal force
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mg
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