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Chapter 5
Force and Motion
What do we learn in this chapter?
•  Newtonian Mechanics
–  Newton’s three laws
•  Applications
–  Normal force
–  Gravitational force
–  Friction
–  Tension
–  Bouyancy
•  Some basic concept
–  Force (Interaction)
–  Mass
–  Their relation with motion
5.2 Newtonian Mechanics
Newtonian Mechanics:
Knowledge about the relation between force and
motion of an object with mass
5.2 Newtonian Mechanics: Historic remarks
Aristotle: All objects have a natural place in
the universe.
Ø  Heavy objects wanted to be at rest on the
Earth.
Ø  Light objects wanted to be at rest in the sky.
Ø  Stars wanted to remain in the heavens.
Ø  A body was in its “natural state” when it was
at rest.
Ø  Moving body (including in a straight line at a
constant speed) needs to be propelled by
force.
Aristotle (384 BC-322
BC). Greek philosopher
and polymath.
Galileo Galilei: Motion and inertia
ü  A force is necessary to change the velocity of
a body.
ü  No force is needed to maintain its velocity.
ü  This insight was refined by Newton, who
made it into his first law, the "law of inertia”.
Galileo Galilei: 1564-1642.
Italian physicist, mathematician,
astronomer, and philosopher
5.2 Newtonian Mechanics: Historic remarks
The three laws of motion were first
compiled by Sir Isaac Newton in his book
“Philosophiæ Naturalis Principia
Mathematica” ("Mathematical Principles
of Natural Philosophy") in 1687.
Newton used these laws to explain and
Newton's
own physical
first
investigate the motion
of many
edition
of his
objects and systems,
suchcopy
as planetary
Principia.
motion.
Quite successful! Kepler’s three laws of
planetary motion.
Isaac Newton (1643-1727)
English poet Alexander Pope’s famous epitaph:
Nature and nature's laws lay hid in night;
God said "Let Newton be" and all was light.
Newton himself:
“If I have seen further it is by standing on the shoulders of
giants.”
Newton another memoir – quite famous all over the world:
“I do not know what I may appear to the world, but to myself I
seem to have been only like a boy playing on the sea-shore, and
diverting myself in now and then finding a smoother pebble or
a prettier shell than ordinary, whilst the great ocean of truth lay
all undiscovered before me.”
Importance and range of validity
•  Newton's laws were extensively verified by experiment and
observation, with excellent approximations at the scales and
speeds of everyday life.
•  Newton's laws of motion, together with his law of universal
gravitation and the mathematical techniques of calculus,
provided for the first time a unified quantitative explanation
for a wide range of physical phenomena from what going on
the Earth to what going on in the Heaven.
•  These three laws hold to a good approximation for
macroscopic objects under almost everyday conditions.
•  However....
Importance and range of validity
•  Newton's laws (with universal gravitation and classical
electrodynamics) are inappropriate at
–  very small scales
–  very high speeds
–  very strong gravitational fields.
•  Another big difference: In quantum mechanics concepts
such as force, momentum, and position are defined by linear
operators that operate on the quantum state.
–  It is a completely different picture.
Mechanics of All
5.3 Newton’s First Law
Newton’s First Law:
If no net force acts on a body , the body’s velocity
cannot change; that is, the body cannot accelerate
Scenario-1: If the body is at rest, it stays at rest.
Scenario-2: If it is moving, it continues to move
with the same velocity (same magnitude and
same direction).
5.4 Force: What is it?
Ø A force is measured by the acceleration it
produces (one definition)
Ø Forces have both magnitudes and directions.
Ø When two or more forces act on a body, we can find
their net, or resultant force, by adding the individual
forces vectorially.
Ø The net force acting on a body is represented with the
vector symbol
!
Fnet
5.4 Force: Simplest operation
Which of the following
figures
correctly show the vector
!
!
addition of forces F1 and F2 to yield! the third vector, which is
meant to represent their net force Fnet ?
5.4 Force
The force that is exerted on a standard mass of
(1 kg) to produce an acceleration of (1 m/s2)has
a magnitude of (1 Newton) (abbreviated as N)
Newton: SI, derived units.
5.3 Newton’s First Law: Simple but with critical rich information.
•  Newton placed the first law of motion to establish frames of
reference for which the other laws are applicable.
•  It postulates the existence of at least one frame of reference (to
be called a Newtonian or inertial reference frame), relative to
which the motion of a particle not subject to forces is a straight
line at a constant speed.
•  The first law can also be restated as: In every material universe, the
motion of a particle in a preferential reference frame is determined
by the action of forces whose total vanished for all times when and
only when the velocity of the particle is constant in the frame.
•  Newton's laws are valid only in an inertial reference frame. Any
reference frame that is in uniform motion with respect to an inertial
frame is also an inertial frame.
Inertial Reference Frames: Where are they?
An inertial reference frame is one in which Newton’s laws hold.
(a) The path of a puck sliding from the north pole as seen from a stationary
point in space. Earth rotates to the east. (b) The path of the puck as seen from the ground.
If the puck is sent sliding along a long ice strip extending from the north pole,
and if it is viewed from a point on the Earth’s surface, the puck’s path is not a
simple straight line.
The apparent deflection is not caused by a force, but by the fact that we see the
puck from a rotating frame. In this situation, the ground is a noninertial frame.
Foucault pendulum
A simple device conceived as an experiment to
demonstrate the rotation of the Earth.
There is one in Fermilab:
https://www.youtube.com/watch?v=h8XWefHBh7s
Feb. 20
5.5: Mass: One definition
Mass is an intrinsic characteristic of a body
The mass of a body is the characteristic that relates a force
on the body to the resulting acceleration.
Empirical observations: The ratio of the masses of two bodies
is equal to the inverse of the ratio of their accelerations when the
same force is applied to both.
5.5: Toward Newton’s 2nd Law
mxax = m0a0
mxax = m0a0 = m1a1= m2a2 =…
mxax = m0a0 = m1a1= m2a2 =… =Constant
What is this constant?
•  Cannot be the shape of the object.
•  Cannot be the material of the object.
•  Cannot be the smell of the object.
It has to be the cause of the acceleration, the force!
5.6: Newton’s Second Law:
Newton’s Second Law:
The net force on a body is equal to the product of the
body’s mass and its acceleration.


Fnet = ma
In component notation,
The acceleration component along a given axis is caused only
by the sum of the force components along that same axis, and
not by force components along any other axis.
5.6: Newton’s second law
Again, the SI unit of force is Newton (N):
1 N =(1 kg)(1 m/s2) = 1 kg m/s2.
5.6: Newton’s second law: Free body diagram
One of the most important steps in Newtonian Mechanics
ü In a free-body diagram, the only
body shown is the one for which we
are summing forces.
ü Each force on the body is drawn as
a vector arrow with its tail on the
body.
ü A coordinate system is usually
included, and the acceleration of the
body is sometimes shown with a
vector arrow (labeled as an
acceleration).
The figure here shows two
horizontal forces acting on a
block on a frictionless floor.
Example
Example
Example
Example
Example, 2-D forces:
Example, 2-D forces:
Example, 2-D forces:
5.7: Some particular forces
The weight, W, of a body is equal
Gravitational Force:
to the magnitude Fg of the
gravitational force on the
A gravitational force on a body is
body.
a certain type of pull that is
directed toward a second body.
W = mg (=F)
Suppose a body of mass m is in
free fall with the free-fall
acceleration of magnitude g. The
force that the body feels as a
result is:
Fg = mg.
5.7: Some particular forces
Normal Force:
When a body presses against a surface, the
surface (even a seemingly rigid one) deforms
and pushes on the body with a normal force,
FN.
Direction: FN is always perpendicular to the
surface.
In the figure, forces Fg and FN and are the
only two forces on the block and they are
both vertical. Thus, for the block we can
write Newton’s second law for a positiveupward y axis, (Fnet, y= may), as:
The free-body diagram
for the block.
5.7: Some particular forces
Friction
If we either slide or attempt to slide a
body over a surface, the motion is
resisted by a bonding between the body
and the surface.
The resistance is considered to be
single force called the frictional force, f.
Direction: This force is directed along
the surface, opposite the direction of the
intended motion.
5.7: Some particular forces
Friction
1. Static friction: between non-moving surfaces.
2. Kinetic friction: between moving surfaces.
Force︎
The (static) friction increases as the applied force increases until the
block moves. After the block moves, it experiences kinetic friction,
which is less than the maximum static friction.
5.7: Some particular forces
Tension
When a cord is attached to a body and pulled taut, the cord pulls on the body
with a force T.
Direction: T directed away from the body and along the cord.
(a) The cord, pulled taut, is under tension. If its mass is negligible, the cord pulls on the body
and the hand with force T, even if the cord runs around a massless.
(b), (c) Frictionless pulley.
February 23rd
5.7: Some particular forces
Buoyancy
-  The magnitude of buoyancy is proportional to the difference in the pressure between
the top and the bottom of the column.
-  It is equivalent to the weight of the FLUID that would otherwise occupy the
column, i.e. the displaced fluid. (The Archimedes' principle)
Let’s looks at an example that requires some
thoughts on the “system” and “force analysis”
T0
W1
N0
W2
5.7: Some particular forces
Buoyancy
Two systems & The forces exerting on them
- Option-1
Tension
Normal force
T
N
B
Buoyancy
Weight of water
W1
Weight of the object
W2
T+B-W1=0
N-B-W2=0
5.7: Some particular forces
Buoyancy
Two systems & The forces exerting on them
- Option-2
Normal force
N
T
T
Tension
Weight of water
Weight of the object
T+N-W1-W2=0
T = W1-B
W2
W1
5.7: Some particular forces
Buoyancy
T+B-W1=0 à T=W1-B
N-B-W2=0 à N=W2+B
T+N-W1-W2= 0 à T = W1+W2-N
T = W1-B
T0=W1 , N0=W2
T0=W1 , N0=W2
T0-T=W1-(W1-B) = B >0
N0–N=W2- (W2+B) = -B <0
W1-B = W1+W2-N
N = B+W2
T0-T=W1-(W1+W2-N ) = N-W2 =B
N0–N=W2- (B+W2) = -B
5.8: Newton’s Third Law
The minus sign means that these
two forces are in opposite directions
5.8: Newton’s Third Law
Varying
ere
h
w
y
An
Ju s t d
is
h
t
y
r
t
o not
Newton’s Third Law:
When two bodies interact, the forces on the bodies from each
other are always equal in magnitude and opposite in
direction.
The forces between two interacting bodies are called a third-law force pair.
Think Deep
•  Newton used the third law to derive the law of conservation
of momentum p=mv (p and v are vectors);
•  However from a deeper perspective, conservation of
momentum is the more fundamental idea
–  It connects with Galilean invariance: the laws of motion are the
same in all inertial frames.
•  Conservation of momentum holds in cases where Newton's
third law appears to fail, for instance in quantum mechanics.
5.9: Applying Newton’s Laws
Sample problem
Figure 5-13 shows a block S (the sliding block) with mass M =3.3 kg. The
block is free to move along a horizontal frictionless surface and connected, by
a cord that wraps over a frictionless pulley, to a second block H (the hanging
block), with mass m 2.1 kg. The cord and pulley have negligible masses
compared to the blocks (they are “massless”). The hanging block H falls as
the sliding block S accelerates to the right. Find:
(a)  the acceleration of block S
(b)  the acceleration of block H
(c)  the tension in the cord
5.9: Applying Newton’s Laws
Sample problem, cont.
Key Ideas:
(1) Forces, masses, and accelerations are involved,
and they should
!
!
suggest Newton’s second law of motion: F = ma
!
!
(2) The expression F = ma is a vector equation, so we can write it as
three component equations.
(3) Identify the forces acting on each of the bodies and draw free body
diagrams like this:
5.9: Applying Newton’s Laws
Sample problem, cont.
(1) From the free body diagrams, write Newton’s Second Law in the unit
vector form,
(2) Assuming a direction of acceleration for the system.
(3) Identify the net forces for the sliding and the hanging blocks:
5.9: Applying Newton’s Laws
Sample problem, cont.
For the sliding block, S, which does not
accelerate vertically.
Also, for S, in the x direction, there is only
one force component, which is T.
Combine (1) and (2), we have:
Ma-mg = -ma
Ma+ma = mg
(M+m)a = mg
Divide both sides by (M+m),
(1)
For the hanging block, because the
acceleration is along the y axis,
Since FgH=mg, so this can be written as:
(2)
Insert this a into (1) to get:
February 25rd
(fraction operation)
a c
±
b d
a
log
b
a c
×
b d
a
b+c
e
d+
f
g+h
a c
÷
b d
The greatest common factor (GCF)
4
4
The least common multiple of the denominators
(the lowest common denominator)
5.9: Applying Newton’s Laws
Sample problem
In the figure to the right, a cord
pulls on a box of sea biscuits up
along a frictionless plane inclined
at θ= 30°.The box has mass m
=5.00 kg, and the force from the
cord has magnitude T =25.0 N.
Q: What is the box’s acceleration
component a along the inclined
plane?
5.9: Applying Newton’s Laws
Sample problem
(1) Choose a coordinate system
(2) Draw a free-body diagram
(3) The positive direction of the x axis is up the plane.
(4) Force analysis: Force from the cord & gravitational force.
(5) Projection to x- and y-axis: using θ
5.9: Applying Newton’s Laws
Sample problem
Using Newton’s Second Law, we have :
That is, a = (T - mg×sinθ)/m
We were given θ = 30°, the box mass m =5.00 kg, and the force from
the cord has magnitude T =25.0 N.
which gives: a = (25.0-5.00×9.8×0.5)/5.0 = 0.100 m/s2.
The positive result indicates that the box accelerates up the plane.
5.9: Applying Newton’s Laws
Sample problem
We don’t specify the motion:
It can be with any velocity or
acceleration: v(t), a(t) !
5.9: Applying Newton’s Laws
Sample problem
The free-body diagram
Reference system
Attention: We can use Newton’s 2nd
Law only in an inertial frame. If the
cab accelerates, then it is not an
inertial frame.
5.9: Applying Newton’s Laws
Sample problem
Let’s choose the ground to be our inertial frame and make
any measure of the passenger’s acceleration relative to it.
Relative to the ground!
5.8: Applying Newton’s Laws
Sample problem, cont.
5.8: Applying Newton’s Laws
Sample problem, cont.
Pay attention to +/- sign for the accelerations !
5.8: Applying Newton’s Laws
Sample problem, cont.
1. Fg of the gravitational force does not depend on the
motion. So, from Question (b) Fg = 708 N in the cab
frame.
2.  From Question (c), the normal force is upward, Fn=
939 N as one can read in the cab frame.
3.  So, the net force on the passenger in the cab frame is:
Fnet = FN-Fg = 939 – 708 = 231 N.
5.8: Applying Newton’s Laws
Sample problem, cont.
But the passenger’s acceleration ap,cab relative to
the frame of the cab is ZERO!
Fnet ≠ map,cab
Newton’s second law is valid
only in inertial frames!
Where we are now …