Download Newton`s Laws

8/2/2013
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http://teachertech.rice.edu/Participants/louviere/Newton/law1.html
http://www.physchem.co.za/Vectors/Addition.htm
Newton’s Laws
Andrea Vig
PreMed course
31.07.2013.
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Kinematics-Dynamics
Kinematics: doctrine of motion
It investigates the parameters of body’s motion
(e.g. - velocity, acceleration, displacement, time).
Dynamics: doctrine of forces
It investigates effects of the forces on the body
(e.g. - motion, deformation, interaction).
It reveals the causes of motion.
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Given a particle
- We know the characteristic (mass, charge, magnetic dipole ……)
- We place it with known initial velocity into an environment from
which we have the complete description
Question:
What is the subsequent motion of the particle?
To be able to answer:
-we introduce the concept of force and define it with the acceleration
experienced by the particle
- We assign mass, to every particle
- We try to find ways of calculating the forces that act on the particle
from the properties of the particle and the properties of the
environment.
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Sir Isaac Newton
He was born in England on 25 December,
1642. He was born the same year that
Galileo Galilei died.
Isaac Newton was raised by his grandmother. He went
on to Trinity College Cambridge. While at college he
became interested in math, physics, and astronomy.
Newton had new ideas about motion,
which he called his three laws of motion.
He also had ideas about gravity, the
In this lesson you will develop
diffraction of light, and forces. Therefore
an understanding of each of
Queen Anne knighted him in 1705.
Newton's Three Laws of Motion
Sir Isaac Newton died in 1727, he lived for
and Newton’s Fourth Law.
85 years.
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Mass and Inertia
It may be more difficult to change the speed of an object than an another one
→ their mass is different.
All objects resist changes in their state of motion. All objects have this
tendency - they have inertia. The tendency of an object to resist changes in
its state of motion varies with mass.
Inertia: the resistance an object has to a change in its state of motion.
The mass is the degree of the object’s inertia („resistance against motion”).
Mass is that quantity that is solely/only dependent upon the inertia
of an object.
The more inertia that an object has, the more mass that it has. A more
massive object has a greater tendency to resist changes in its state of
motion.
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Exercise
Fred spends most Saturday afternoons at rest on the sofa,
watching football games and consuming large quantities of
food. What effect (if any) does this practice have upon his
inertia? Explain.
Fred's inertia will increase!
Fred will increase his mass if he makes a habit of this. And if his mass
increases, then his inertia increases.
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Mass and Weight
Mass
The mass is a scalar quantity. It
means that has magnitude
only.
Symbol of mass: m
Unit of mass: kg
Weight
The weight is a vecor quantity. It
has both magnitude and direction.
Weight is the name given to the force
on an object due to gravity.
Symbol of weight: G
G=m*g
The mass of one brick:
1 kg
m – mass
g- gravitational acceleration or gravitational field
strength. On earth's surface g is 9.8 N/kg (often
approximated as 10 N/kg or m/s2), on the Moon it
is 1,6 m/s2.
The weight of one brick (m=1 kg):
brick
1 kg*10=10 N
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Example
A dog was sent to the moon.
Mass of the dog: 10 kg
g on the On earth's surface - 9.8 N/kg
g on the Moon -1.6 m/s2.
How much is the dog's weight on the Earth and on the moon?
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Force
A force is a push or pull upon an object resulting from the object's interaction
with another object.
Action of force:
An effect that can change the state of motion of bodies.
Force:
It gives the magnitude and direction of the force action.
Vector quantity.
Symbol of force [unit]: F [N]
1 N - it is equal to the amount of net force required to accelerate an
object with mass of 1 kilogram at a rate of 1 m/s2.
Line of action (of force)
1 N= 1 kg*(m/s2)
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Two categories of forces
I. Contact Forces
Contact forces are those types of
forces that result when the two
interacting objects are perceived to
be physically contacting each
other.
1.
2.
3.
4.
5.
Frictional Force
Tension Force
Resistance Force
Applied Force
Spring Force
II. Action-at- a Distance Forces
Action-at-a-distance forces are those
types of forces that result even when the
two interacting objects are not in physical
contact with each other, yet are able to
exert a push or pull despite their physical
separation.
1. Gravitational Force
2. Electrical Force
3. Magnetic Force
A force is a vector quantity. It means that it has both magnitude and direction.
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The net force:
It is the vector sum of all the forces that act upon an
object. That is to say, the net force is the sum of all
the forces, taking into account the fact that a force is
a vector and two forces of equal magnitude and
opposite direction will cancel each other out.
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Balanced and unbalanced
force
1. Balanced forces
2. Unbalanced forces
3. Forces on the slope in the absence of friction
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Addition/decomposition of
vectors
1.
3.
If two vectors have the same direction, their
resultant has a magnitude equal to the sum of
their magnitudes and will also have the same
direction.
Parallelogram method
In the parallelogram method for vector addition,
the vectors are translated, (i.e., moved) to a
common
origin
and
the
parallelogram
constructed as follows:
2.
The Pythagorean Theorem
b
a
a2+b2=c2
90°
c
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Newton’s First Law of Motion
An object at rest stays at rest and an object in motion stays in
motion with same speed and in the same direction unless acted
upon by an unbalanced force.
This law is often called "the law of inertia".
Forces are Balanced
Objects at Rest
(v=0 m/s)
Objects in Motion
(v≠ 0 m/s)
a=0 m/s2
a=0 m/s2
Stay at Rest
Stay in Motion
(same speed and direction)
„ Every body persist in its state of
rest or uniform motion in a
straight line unless it is
compelled to change that state
by forces impressed on it.” Newton
(Philosophiae Naturalis Principia Mathematica)
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Newton’s First Law
What does this mean?
This means that there is a natural tendency of objects to keep on
doing what they're doing. All objects resist changes in their state of
motion. In the absence of an unbalanced force, an object in motion
will maintain this state of motion.
Newton's Laws hold only with respect to a certain set of
frames of reference called inertial reference frames.
The Newton’s Laws are true only in Inertia frames.
Inertia: the resistance an object has to a change in its state of motion.
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Notice!!!!!
- There is no distinction between a body at rest
and one moving with constant velocity.
Both motions are natural in the absence of forces.
- There is no distinction in the first law between
the absence of all forces and the presence of
forces whose resultant is zero.
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Examples
1.
There is a ball on top of the slope. We
lose hold of it. The ball would never
stop. It would roll forever if friction
were absent.
slope
2.
This law is the same reason why
you should always wear your
seatbelt.
3.
Physics
book
Force of Friction
Table
As a book slides across a table from left
to right, the force of friction acts on the
book to slow it down and bring it to rest.
In the absence of a force of friction, the
book would continue in motion with the
same speed and direction - forever!
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Exercise
1.
A 2-kg object is moving horizontally with a speed of 4 m/s. How much net
force is required to keep the object moving at this speed and in this
direction?
Answer: 0 N
An object in motion will maintain its state of motion. The presence
of an unbalanced force changes the velocity of the object.
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Newton’s Second Law of motion
Acceleration is produced when a force acts on a mass.
The greater the mass (of the object being accelerated) the greater
the amount of force needed (to accelerate the object).
What does this mean?
Everyone unconsiously knows the Second Law. Everyone knows that heavier
objects require more force to move the same distance as lighter objects.
The Second Law gives us an exact relationship between force, mass, and
acceleration. It can be expressed as a mathematical equation:


F  ma
F – force
m – mass
a - acceleration
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Exercises
1.
Mike's car, which mass is 1,000 kg, is out of gas. Mike is trying to push the
car to a gas station, and he makes the car go 0.05 m/s2. Using Newton's
Second Law, you can compute how much force Mike is applying to the car.
0,05 m/s2
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Exercises
2.
Determine the accelerations that result when a 12 N net force is applied
to a 3 kg object and then to a 6 kg object.
A 3 kg object experiences an acceleration of 4 m/s2.
A 6 kg object experiences an acceleration of 2 m/s2.
3.
A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at
a rate of 5 m/s2. Determine the mass of the encyclopedia.
Use Fnet= m * a with Fnet = 15 N and a = 5 m/s2.
So (15 N) = (m)*(5 m/s2)
And m = 3.0 kg
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Newton’s Third Law of motion
For every action there is an equal and opposite reaction.
• Same magnitude (size)
• Reversed directions
First object (force) act to the second object and vice versa.
between A and B objects:


FA   FB
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Newton third law
(action-reaction)
For every action there is an equal and opposite reaction.


FA   FB
Action and reaction forces:
N – The table holds the object.
m
G
Weight
 N  Fw
G Earth  G object
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Exercise
1.
While driving down the road, a firefly strikes the windshield of a bus and
makes a quite obvious mess in front of the face of the driver. This is a clear
case of Newton's third law of motion. The firefly hits the bus and the bus hits
the firefly. Which of the two forces is greater: the force on the firefly or the
force on the bus?
Tricky Question!
Each force is the same size.
For every action, there is an equal ... (equal!). The fact that the firefly splatters only means
that with its smaller mass, it is less able to withstand the larger acceleration resulting from
the interaction.
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Newton’s Fourth Law
(independency of forces)
The forces with different origin acting on the same object
can be treated separately and can be added together
following the rules of vectorial addition:
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Quiz
1.Who was the scientist who gave us the Laws of Motion?
Sir Isaac Newton
2. How many Laws of Motion are there?
Three
3. What is another name for the first law of motion?
The law of Inertia
4. Which law explains why we need to wear seatbelts?
The First law
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5. Which law says that force is equal to mass times acceleration (F=m*a)?
Second Law of Motion
6. Which law says that heavier objects require more force than lighter objects to
move or accelerate them?
Second Law of Motion
7. Which law explains how rockets are launched into space?
Third Law of Motion
8. Which law says that for every action there is an equal and opposite reaction?
Third Law of Motion
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Exercises
1.
Under constant force a body with 25 g travels in 1 sec 25 cm.
How much is the force?
F=m*a
d = a / 2 * t2
Answer:
F=1,25*10-2 N
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Exercises
2.
Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is
tripled and the mass is halved, then what is the new acceleration of the sled?
Answer: 12 m/s2
The original value of 2 m/s/s must be multiplied by 3 (since a and F are
directly proportional) and divided by 1/2 (since a and m are inversely
proportional)
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Exercises
3.
• F=8N
• m1=2kg
• m2=3 kg
• g=10m/s2
m2
m1
F
How much force does the strand stretch ( there is not friction)?
Answer:
F=4.8 N
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Exercises
4.
In the top picture (below), Kent Budgett is pulling upon a rope that is
attached to a wall. In the bottom picture, the Kent is pulling upon a
rope that is attached to an elephant. In each case, the force scale
reads 500 Newton. Kent is pulling ...
a. with more force when the rope is attached to the wall.
b. with more force when the rope is attached to the elephant.
c. the same force in each case.
Kent is pulling with 500 N of force in each case. The rope transmits the force from Kent to
the wall (or to the elephant) and vice versa. Since the force of Kent pulling on the wall and
the wall pulling on Kent are action-reaction force pairs, they must have equal magnitudes.
Inanimate objects such as walls can push and pull.
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Exercises
5.
Many people are familiar with the fact that a rifle recoils when fired. This recoil is the
result of action-reaction force pairs. A gunpowder explosion creates hot gases that
expand outward allowing the rifle to push forward on the bullet. Consistent with
Newton's third law of motion, the bullet pushes backwards upon the rifle. The
acceleration of the recoiling rifle is ...
a. greater than the acceleration of the bullet.
b. smaller than the acceleration of the bullet.
c. the same size as the acceleration of the bullet.
The force on the rifle equals the force on the bullet. Yet, acceleration depends
on both force and mass. The bullet has a greater acceleration due to the fact
that it has a smaller mass. Remember: acceleration and mass are inversely
proportional.
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