Transcript Normal Contact Force

Class Rules
1. Punctuality
a. The last person to come into the class later than me
will teach the class for 10 minutes
b. Homework to be returned during the first Theory
lesson of the week.
2. Cleanliness
3. Courtesy
a. If you need to speak, raise your hands.
4. Consistency
a. You must always have your notes with you.
Dynamics Part 1
Interactions & Forces
Topic Overview
CLASSICAL MECHANICS
Kinematics
Dynamics
Statics
Motion without
looking at its cause
HOW?
Motion and its
causes
WHY & WHAT?
Lack of Motion and
its causes
WHY & WHAT?
N
F
Ignore
Forces
Ff
W
Fundamental Interactions
When two bodies meet, we often find that
they may interact with one another.
For instance, when two like charges come in
proximity with one another, they repel.
When two unlike charges meet, they attract.
When two masses meet, they gravitate
towards one another.
All these motion, attraction or repulsion, are
all the effects or outcomes of underlying
INTERACTIONS between 2 bodies.
Fundamental Interactions
Bodies may only interact if there are more
than 1 of them involved (ie. 2 or more).
In the earlier example, we have already
seen two types of interactions:
Love
1) Electrostatic
2) Gravitational
Can you think of other kinds of
interactions?
3) Magnetic Interaction!
Electrostatic
Force and Motion
• Physicists describe the effect of these interaction (whether it is an
attraction or a repulsion) on ONE of the two interacting bodies as
the result of a FORCE.
• In any interaction, both objects are influenced equally.
• Hence, in any one interaction, there will always be a pair of
FORCES, with each of the two bodies bearing one of the pair of
forces.
Magnetic
Interaction
• A force is a vector.
• Like all vectors, it is represented by an
arrow, whose
1. Length proportional to magnitude of
the vector (ie. Strength of the force)
2. and the direction is that which the
arrowhead points.
• The unit for measuring Force is the
newton (N).
• One Newton is defined as the force
required to cause 1 kg of mass to
accelerate at 1ms-2.
Gravitational
Force
Force
Newton’s Third Law of Motion
• Also known a the Law of Reciprocal Actions.
• States that
Whenever a body A applies a force (known as the “action”) on
a body B, body B will exert another force (known as the
“reaction”) that is equal in magnitude, but opposite in direction
to the force applied by A. The two forces hence act on two
different bodies that are interacting with one another.
Magnetic Force acting on
Magnetic
Magnet A by Magnet B
Magnet B by Magnet A
Interaction
Magnetic Force acting on
Review of Newton’s Third Law
Let’s go back to the Earth-Moon example:
• What is the interaction that exist between
them?
• Is the gravitational force of the Moon on the
Earth stronger, weaker or the same compared
to that of the Earth on the Moon?
• Can you show some characteristics of actionreaction pairs in this example?
• An object may experience more than
one form of interaction simultaneously
Eg. a magnet experiences gravitational
influences and magnetic influences all
at once.
• This also suggest that the body is
interacting with several different
partners at the same time.
Gravitational
• Hence, there may be several forces
acting on the same body at any one
time.
Gravitational
Multiple Forces at Work
Characteristics of ActionReaction Pairs
• Action-reaction pairs of forces MUST ALWAYS BE TRUE
for the below characteristics:
1.
2.
3.
4.
5.
They are equal in magnitude
They are opposite in direction
They act on DIFFERENT bodies
They act along the same line of action.
They arise from the same type of interaction.
• If any of these characteristics are not satisfied, then the
two forces under examination are NOT action-reaction
pairs.
Characteristics of ActionReaction Pairs
• In the magnet example, are the following 5 characteristics
satisfied?
1. They are equal in magnitude
2. They are opposite in direction
3. They act on DIFFERENT bodies
4. They act along the same line of action.
5. They arise from the same type of interaction.
• WHAT DOES “SAME TYPE” MEAN?
Magnetic Force acting on
Magnetic Force acting on
MagneticMagnet B by Magnet A
Interaction
Magnet A by Magnet B
Types of Forces
What types of forces are there?
1.
2.
3.
4.
5.
6.
7.
8.
Gravitational Force
Magnetic Force
Electrostatic Force
Friction (Demo)
Air/Water Resistance
Normal Contact Force
Tension
Nuclear Forces in the nucleus of an atom
Normal Contact Force
• Normal Contact Force is a force that acts perpendicular to the surface of
contact between two bodies that are being pushed together.
Normal Contact Force appears between
the surface of contact when the two
bodies are subjected to external force
pushing them together.
No Normal Contact Force when the two
bodies are just placed next to each other,
touching but NOT pushed together.
Book on Table Example
Normal
Are you able to identify the forces acting on the book?
Normal Contact BOOK
force of the Table
acting on the Book
Weight
Weight =
gravitational force
of the Earth acting
on the Book
Are the Weight and
the Normal Contact
force an actionreaction pair?
Book on Table Example
• The reaction pair of the weight
of the book, which is in fact,
the gravitational force acting
on the book by theBOOK
Earth, is
the gravitational force acting
on the Earth by the book!
• If the book is only 0.5kg of
mass, which translate to 5N of
weight, then, the force of the
book on the Earth is also 5N.
• The Earth is as light as the
book!
Book on Table Example
• If the yellow arrow, the weight of the book, is NOT the
reaction pair of the red arrow, or the Normal Contact
force acting on the book, then… where is the reaction
pair of the normal contact force acting on the book?
• Discuss with your partner.
BOOK
Yes! The reaction is
the Force of the
Book on the Table!
Book on Table Example
Putting everything into perspective…
There is an action-reaction pair between the
Book and the Table. These are a pair of Normal
Contact Forces. With the book pushing against
the table downwards.
There is yet another action-reaction pair,
between the Earth and the book. These are a
pair of Gravitational Forces. With the Earth
pulling on the book and vice versa.
If we look at the book only, it so happens that
the Normal Contact Force caused by the Table
on the book, balances the Gravitational Force
(or Weight) caused by the Earth on the Book.
Can you analyze the forces acting on the table?
BOOK
Types of Forces
RECALL: What types of forces are there?
 1. Gravitational Force
 2. Magnetic Force
 3. Electrostatic Force
4.
 5.
 6.
 7.
8.
Friction (Demo)
Air/Water Resistance
Normal Contact Force
Tension (Practical)
Nuclear Forces in the nucleus of an atom
Friction
There are two types of Friction:
(1) Static Friction
- Increases up to a max
value given by:
Fstatic ≤ μsN
(2) Dynamic /Kinetic Friction
Fdynamic = μdN
Frictional forces are only
dependent on:
(1) The material of the two
bodies in contact (μ).
(2) The Normal acting on the
body of interest (N).
Normal
External
Pulling Force
Static
Friction
COMMON MISCONCEPTION!
Weight
1) Friction is NEVER dependent on
-1
= 0msArea
theVelocity
Surface
of Contact!
2)
Unlike Fluid Resistance,
Normal
External
Dynamic Friction is
also
NEVER
Pulling
Force
Dynamic dependent on the velocity of
Friction
the moving object.
Weight
Acceleration = a ms-2
Slope Example
What are the forces acting on the box on the slope?
There is an action-reaction pair between the Box
and the Slope. These are a pair of Normal
Contact Forces. Thus, the box experience a
NORMAL CONTACT FORCE caused by the slope.
There is yet another action-reaction pair,
between the Earth and the box. These are a pair
of Gravitational Forces. With the Earth pulling on
the box and vice versa. The gravitational force of
the Earth on the box is known as WEIGHT.
Net/Resultant
Force = 0
Friction
Normal
STATIC FRICTION also arises as the box
experience the component of the weight that is
parallel to the slope.
If we look at the book only, then there are just
three forces acting on the body: WEIGHT,
NORMAL and FRICTION.
Weight
Tarzan Example
Tension
What are the forces acting on Tarzan?
There is a force caused
by the Earth acting on
Tarzan known as
“Weight”.
There is also a force
caused by the Tree
Branches acting on
Tarzan (through the vine)
known as “Tension”.
Weight
Balances and Unbalanced Forces
• Who is the ugliest character from the Star Wars?
• Perhaps it’ll be JarJarBinks… (or maybe Jabba the Hutt)
• If Yoda and Darth Vader were each attempting to use the Force
to repel JarJarBinks away from themselves, who will be the more
unfortunate soul?
Force caused
by Darth
Vader on JJB
Force caused
by Yoda on
JJB
Balances and Unbalanced Forces
• Well Yes! Darth Vader will have to bear with all the irritation from
JarJarBinks.
• This is because of unbalanced forces. The repulsive force that
Yoda exerts on JJB is far greater than that of Darth Vader on JJB.
• Let’s revise Vector Addition.
• As in Vector Addition, the RESULTANT FORCE points to the right.
Ending
Point
Starting
Point
Force caused
by Darth
Vader on JJB
Force caused
by Yoda on
JJB
RESULTANT
FORCE
Balances and Unbalanced Forces
• If Yoda and Darth Vader are equally strong however, the two
forces are said to be BALANCED.
• BALANCED FORCES cancel each other out, and the RESULTANT
FORCE or NET FORCE is ZERO.
Force caused
by Darth
Vader on JJB
Force caused
by Yoda on
JJB
Newton’s 1st Law of Motion
• What happens when the Net/Resultant Force is zero (Forces are
balanced)?
Newton’s First Law of Motion states that, a body will remain in
its state of rest or uniform motion, unless acted upon by a NET force.
静者恒静，动者恒动
• Also known as the Law of Inertia.
Newton’s 1st Law of Motion
• Inertia is the reluctance for an object to change its state of
rest or uniform motion. Or put in another way, it is the
tendency to stay at rest or in uniform motion.
• Mass is a measure of inertia.
• Hence the larger the mass, the greater the inertia an
object has.
• Demonstration of classic cup of water and table cloth.
• Moon Hoax
Newton’s 2nd Law of Motion
• What happens when the Net/Resultant Force is Non-zero?
Newton’s Second Law of Motion states that: The net force acting on a body is
directly proportional to its rate of change of momentum.
OR
The net force acting on a body is directly proportional to its acceleration, given
that its mass remains constant. The resulting acceleration is in the same direction
as the net force applied.
F ∝ ma
F = kma (k being a constant of proportionality)
F = ma (when Force is measured in Newtons)
• The Newton is adjusted so that the acceleration produced by 1N of Force on 1 kg
of mass is 1 ms-2.
Simple Example 1
m = 5.0 kg
F = 10.0 N
By Newton’s Second Law of Motion,
𝐹𝑅 = 𝑚𝑎
𝐹𝑅
𝑎=
𝑚
10.0𝑁
𝑎=
= 2.0 𝑚𝑠 −2
5.0 𝑘𝑔
Simple Example 2
m = 5.0 kg
F1 = 10.0 N
By Newton’s Second Law of Motion,
F2 = 5.0 N
𝐹𝑅 = 𝐹1 − 𝐹2 = 𝑚𝑎
10.0 N – 5.0N
=
𝑎 = 1.0 ms-2
(5.0kg)
𝑎
Two-bodies System
ByAnalyzing
Newton’sthe
Second
smaller
Lawblock
of Motion,
only,
𝐹𝑅 =
𝑚𝑎
𝐹𝑅𝑁==𝑚𝑎
𝐹𝑒𝑥𝑡
𝐹𝑒𝑥𝑡 = (3𝑀)𝑎
𝐹𝑅 = 𝑁 = 𝑀
𝐹𝑒𝑥𝑡
𝐹
𝑒𝑥𝑡
𝑎
=
𝑁 = 3𝑀
3
3𝑀
Two-bodies System
T
0.20 kg
T
0.04 kg
W = mg = 0.40 N
Tension
Action- of
Acceleration
Reaction Pairs between
the
On the
whole
0.20kg
system,
trolley,
the two blocks.
FR==consider
ma
T = mathe
If we
entire
system
as a
0.40N
T = (0.20kg)(1.7ms
= (0.24kg)
a -2)
-2 these
single
body,ms
3.4
Nthen
aT = 1.7
forces will cancel each
other out.
0.24
kg
0.04 kg
W = mg = 0.40 N
The (Famous) Horse and Cart
Can you explain to the horse what’s wrong with his
argument?
Since Action and Reaction are equal in
magnitude and opposite in direction, there is
no point pulling the cart, as the two forces are
balanced and will cancel each other out.
Tension of
Cart on Horse
Tension of
Horse on Cart
The (Famous) Horse and Cart
Indeed, if we consider the whole system, the Tensions of
the Cart on the Horse, and the Horse on the Cart will cancel
out. But if we consider the Cart alone, the Tension provided
by the horse is the only force that can drive it forward.
Driving Force
from Horse’s
Muscles
Tension of
Cart on Horse
Tension of
Horse on Cart
The forces do NOT cancel out when you
consider them as Separate bodies!
The Case of the Lift
Tension =
40000
5000 NN
What is the acceleration when:
a) Cable is intact and has a
tension of 40000 N?
b) Cable has a tension of 5000
N?
c) Cable suddenly breaks?
1000 kg
Weight =
10000 N
Velocity/ ms-1
Revisiting Air Resistance
t1
t2
> t3
With air resistance however,
falling objects will decelerate
and reach terminal velocity.
Time/s
Revisiting Air Resistance
Velocity/ ms-1
Air Resistance
increases as velocity of
object increases
t1
t2
> t3
The force of air resistance
increases to a point where it
will balance the weight!
Time/s
Terminal velocity is the velocity at which an
object in free-fall ceases to accelerate
because the total resistive forces are
balancedBut
by the
downward
pull ofconstant
gravity.
Weight
remains
Momentum
By Newton’s Second Law of Motion,
𝐹𝑅 = 𝑚𝑎
Substituting with the definition of uniform acceleration,
𝑣−𝑢
𝑎 =
∆𝑡
Thus,
Law may
TheNewton’s
quantity Second
𝑚𝑣 is known
as be
restated
as:momentum, 𝑝.
(linear)
𝑣−𝑢
𝐹𝑅 = 𝑚
∆𝑡
TheItNET
force acting
on an object is
is a vector
quantity.
directly proportional to the rate of
change
of momentum.
Momentum
is the product of
the mass and velocity of a body.
The resulting acceleration is in the
same direction as the force applied.
𝑚𝑣 − 𝑚𝑢
𝐹𝑅 =
∆𝑡
End of Dynamics
May the Force be with you…
Especially for Next Week’s Test…
The (Famous) Horse and Cart
Some answers from the class:
“In Newton's third law, it is stated that: whenever a particle A exerts a force on
another particle B, B simultaneously exerts a force on A with the same magnitude in
the opposite direction. The strong form of the law further postulates that these two
forces act along the same line. This law is often simplified into the sentence, "To
every action there is an equal and opposite reaction." I believe the horse is wrong
because the horse and the cart are considered as one unit as long as there is
tension on the reins that hold the horse back. This would mean that Newton's third
law would not be applicable to the horse plus cart experiment as there is only one
"particle" (A) since the cart cannot and should not be counted as another particle
(B). Hence when the horse exerts energy to move forward, it must merely use more
energy to overcome the weight of the cart in order to get moving...not too sure
though...seems like the law is too vague by stating "interaction between the two
bodies" to me. Not too sure if there is a difference if it is on a vertical or horizontal
plane when this rule is applied. Basically I understand that the horse's argument is
wrong as the cart and itself should not be counted as two particles but one. “ JooErn
The (Famous) Horse and Cart
Some answers from the class:
“My concept: For the movement of a cetain object, we can only consider the forces
acting on the object, and in this case its the cart. assuming that the cart moves on a
flat surface and the horse is pulling it, the forces acting on the cart will be the
weight, the frictional force, the normal reaction force and the force of the horse
pulling the cart. since the cart did not move upwards or downwards,we can say the
gravitational force(weight) and the normal reaction force cancels each other out, so
we dont have to consider them anymore.Therefore we are left with the frictional
force and the force that the horse exerts on the cart. If the force of the horse
exerted on the cart is bigger than the frictional force of the cart against the ground,
the cart moves foward, otherwise it will remain stationary. basically it has nothing
to do with the cart pulling him back. hope i got it right!” - LiBo
The (Famous) Horse and Cart
Some answers from the class:
“In my opinion, i feel that firstly, there are a few forces present in this case. They are
the gravitational force from the earth on the cart and the horse, there is frictional
force and also of course the reaction force. Since the pulling force is equal to the
reaction force, I feel that as long as he uses a force greater than the frictional force
of the ground, he should be able to move the cart. And the reaction force does not
actually cancel out the initial pulling force, hence his argument is false... Erm, hope i
got my concepts right, i am also not very sure... “ – Andrew
“The argument is flawed as although the cart will indeed pull him back with a
reaction that is equal in magnitude but opposite in direction, the action and
reaction force acts on the two objects differently and do not cancel each other out.
There is also frictional force between the horse and the ground, and also between
the rope which ties the horse and the cart (assuming there is) as such, these forces
are able to overcome the force by the cart and thus the horse has now no more
excuses for not being able to pull the cart. “ - Benjamin
The (Famous) Horse and Cart
Some answers from the class:
“im not very sure but what i am thinking is that the cart can only exert X amount
of force while the horse can increase the amount of force exerted on the cart to
be larger and therefore pull the cart along?” – Nicholas Teng
“Because right.. The horse will be exerting a forward motion and the tension force
in the "connector" between the cart and the horse will be equal to the force of
the horse pulling the cart. As the horse exerts more force to move forward, the
cart will follow him. hence the horse's argument is flawwed (dk why he can
talk..)” – YangXi
“the pulling force exerted by the horse will be converted to kinetic energy in the
wheels of the cart, overcoming the reaction force exerted by the cart onto the
horse to pull it at opposite directions. ??not sure lol” - KaiYuen