Newton's laws of motion

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Chapter 3
Newton's laws of motion
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Forces
3 .1 Force,weight,and gravitational mass
Kinematics describes motion, but does not
explain why motion occurs. In order to explain
the cause of motion, we must learn about
Statics and Dynamics and FORCES.
What is a Force?

• a push or pull that one body exerts on another
• Vector

• the force causes a change in velocity, or an
  acceleration

• There are two types of forces that we can see
• Contact Forces
• At a distance forces

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Contact Force Forces in which the two
interacting objects are physically in contact
with each other. EXAMPLES Hitting - Pulling
with a rope - Lifting weights - Pushing a couch
Frictional Force - Tensional Force - Normal
Force- Air Resistance Force Applied Force- Spring
Force
At A Distance Force (field force)

• Forces in which the two interacting objects are
  not in physical contact with each other, but are
  able to exert a push or pull despite the physical
  separation.

Example Gravitational Force - Electrical Force -
Magnetic Force- Nuclear Forces
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What is meant by unbalanced force?

• If the forces on an object are equal and
  opposite, they are said to be balanced, and the
  object experiences no change in motion. If they
  are not equal and opposite, then the forces are
  unbalanced and the motion of the object changes.

• Are forces that results in an objects motion
  being changed.

velocity changes (object accelerates)
Fnet
Fpull
Ffriction
W
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Balanced Force

• A force that produces no change in an objects
  motion because it is balanced by an equal,
  opposite force.

• no change in velocity

The object shown in the diagram must be at rest
since ther is no net force acting on it.
FALSE! A net force does not cause motion. A net
force causes a change in motion, or acceleration.
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Example On a horizontal, frictionless surface,
the blocks above are being acted upon by two
opposing horizontal forces, as shown. What is
the magnitude of the net force acting on the 3kg
block?
A. zero B. 2N C. 1.5 N D. 1N E. More
information is needed.
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Example
Example
0
a3.02 m / s
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Weight
Weight Mass x Gravity
The weight of an object is the gravitational
force that the planet exerts on the object. The
weight always acts downward, toward the center of
the planet. SI Unit of Weight Newton (N)

• m mass of the body (units kg)
• g gravitational acceleration (9.8m/s2,
• As the mass of a body increases, its weight
  increases proportionally

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• Weight
• the force of gravity on an object

W mg
W weight (N) m mass (kg) g acceleration due to
gravity (m/s2)
MASS always the same (kg)
WEIGHT depends on gravity (N)
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Mass

• is a measure of how much matter there is in
  something -- usually measured in kilograms in
  science
• causes an object to have weight in a
  gravitational field
• A measure of the resistance of an object to
  changes in its motion due to a force (describes
  how difficult it is to get an object moving)
• Scalar

Note that mass is involved in the force of
gravity! This is a separate property from that
of inertia, so we give this property the name
gravitational mass.
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Mass Inertia an objects resistance to motion
Would it be more difficult to pull an elephant or
a mouse?
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• what is the weight of a 2 kg mass?
• W Fg mxg 2 kg x 9.8 m/s2
• 19.6 N
• What is the mass of a 1000 N person?
• W Fg mxg
• m Fg/g 1000 N / 9.8 m/s2
• 102 kg

• A girl weighs 745 N. What is his mass

m F g m (745 N) (9.8 m/s2) m 76.0 kg
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3.3 Newton's first law
Every object continues in a state of rest , or of
uniform motion in a straight line , unless it is
compelled to change that state by forces acting
upon it. An equivalent statement of the first
law is that An object at rest will stay at
rest, and an object in motion will stay in motion
at constant velocity, unless acted upon by an
unbalanced force.
This, at first, does not seem obvious. Most
things on earth tend to slow down and stop.
However, when we consider the situation, we see
that there are lots of forces tending to slow the
objects down such as friction and air resistance.
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Inertia

• Inertia is a term used to measure the ability of
  an object to resist a change in its state of
  motion.
• An object with a lot of inertia takes a lot of
  force to start or stop an object with a small
  amount of inertia requires a small amount of
  force to start or stop.
• The word inertia comes from the Latin word
  inertus, which can be translated to mean lazy.

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example

• A railway engine pulls a wagon of mass 10 000 kg
  along a straight track at a steady speed. The
  pull force in the couplings between the engine
  and wagon is 1000 N.
• A. What is the force opposing the motion of the
  wagon?
• B .If the pull force is increased to 1200 N and
  the resistance to movement of the wagon remains
  constant, what would be
• The acceleration of the wagon?
• Solution
• a) When the speed is steady, by Newtons first
  law, the resultant force must be zero.
• The pull on the wagon must equal the resistance
  to motion. So the force resisting motion is 1000
  N.
• b) The resultant force on the wagon is 1200
  1000 200 N
• By Equation

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3.5Newtons Third Law of Motion

• When one object exerts a force on a second
  object, the second object exerts an equal but
  opposite force on the first.

• Identifying Newtons third law pairs
• Each force has the same magnitude
• Each force acts along the same line
• but in opposite directions
• Each force acts at the same time
• Each force acts on a different object
• Each force is of the same type

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3rd Law
According to Newton, whenever objects A and B
interact with each other, they exert forces upon
each other. When you sit in your chair, your body
exerts a downward force on the chair and the
chair exerts an upward force on your body.
All forces come in action-reaction pairs Ex
feet push backward on floor, the floor pushes
forward on feet
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• Problem

• How can a horse pull a cart if the cart is
  pulling back on the horse with an equal but
  opposite force?

• Arent these balanced forces resulting in no
  acceleration?

• Explanation

• forces are equal and opposite but act on
  different objects
• they are not balanced forces
• the movement of the horse depends on the forces
  acting on the horse

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example
a) Find the acceleration of a 20 kg crate along a
horizontal floor when it is pushed with a
resultant force of 10 N parallel to the floor.
b) How far will the crate move in 5s (starting
from rest)? Solution
b) Distance travelled
? X
? X
? X
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example
A 1kg stone fall freely from rest from a bridge.
a -What is the force causing it to accelerate? b
-What is its speed 4s later? c -How far has it
fallen in this time?
Solution
The force causing it to fall is its weight. As it
is falling with acceleration due to gravity
b)
c)
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• Action-Reaction Pairs

• The hammer exerts a force on the nail to the
  right.
• The nail exerts an equal but opposite force on
  the hammer to the left.

• Single isolated force cannot exist
• For every action there is an equal and opposite
  reaction

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• Action-Reaction Pairs

• The rocket exerts a downward force on the exhaust
  gases.
• The gases exert an equal but opposite upward
  force on the rocket.

Flying gracefully through the air, birds depend
on Newtons third law of motion. As the birds
push down on the air with their wings, the air
pushes their wings up and gives them lift.
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Other examples of Newtons Third Law

• The baseball forces the bat to the left (an
  action) the bat forces the ball to the right
  (the reaction).

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Normal Force Is Not Always Equal to the Weight
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3.6 Newtons Second Law

• Newtons Second Law of Motion
• The force F needed to produce an acceleration a
  is
• The acceleration of an object is directly
  proportional to the net force acting on it and
  inversely proportional to its mass.

F ma
F
F force (N) m mass (kg) aacceleration
(m/s2) 1 N 1 kg m/s2
m
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Newtons Third Law

• Action-Reaction Pairs

• Both objects accelerate.
• The amount of acceleration depends on the mass of
  the object.

• Small mass ? more acceleration
• Large mass ? less acceleration

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Newtons Second Law
F
m
F ma
F force (N) m mass (kg) aacceleration
(m/s2) 1 N 1 kg m/s2
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More about F ma
If you double the mass, you double the force. If
you double the acceleration, you double the
force. What if you double the mass and the
acceleration? (2m)(2a) 4F Doubling the mass
and the acceleration quadruples the force. So .
. . what if you decrease the mass by half? How
much force would the object have now?
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Equilibrium

• The condition of zero acceleration is called
  equilibrium.
• In equilibrium, all forces cancel out leaving
  zero net force.
• Objects that are standing still are in
  equilibrium because their acceleration is zero.
• Objects that are moving at constant speed and
  direction are also in equilibrium.
• A static problem usually means there is no motion.

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a2
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example

• 8 How much force is needed to accelerate a 1,300
  kg car at a rate of 1.5 m/s2?
• A- 867 N
• b 1,950 N
• c 8,493 N
• d 16,562 N

F m a or 1300Kg x
1.5m/s2 F 1950 N
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• Balancing Forces (Statics)
• There are often situations where a number of
  forces are acting on something, and the object
  has no motion it is STATIC or in EQUILIBRIUM or
  at rest.
• This means the NET FORCE on the object is zero,
  or in other words the forces balance each other
  out.

• SF m a
• a 0
• SF 0

Objects in equilibrium (no net external force)
also move at constant velocity
In a two-dimensional problem, we can separate
this equation into its two component, in the x
and y directions S Fx 0 S Fy 0
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• unbalanced Forces (Dynamics)
• There are other situations where all the forces
  acting on something do not cancel each other out
  completely.
• This means the NET FORCE on the object is not
  zero, the object will change its motion and
  accelerate proportional to the objects mass.
• SF m a

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• The acceleration of an object is equal to the
  force you apply divided by the mass of the
  object.

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• If you apply more force to an object, it
  accelerates at a higher rate.

• If an object has more mass it accelerates at a
  lower rate because mass has inertia.

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• What force would be required to accelerate
• a 40 kg mass by 4 m/s2?

F ma F (40 kg)(4 m/s2) F 160 N

• A 4.0 kg shot-put is thrown with 30 N of force.
  What is its acceleration?

a F m a (30 N) (4.0 kg) a 7.5 m/s2
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Newtons Second Law of Motion
Note that this is a vector equation, and should
really be worked in component form S Fx
max S Fy may . We can now see that Newtons
First Law of Motion is really just a special case
of his Second Law of Motion.
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• Example
• A railway engine pulls a wagon of mass 10 000 kg
  along a straight track at a steady speed. The
  pull force in the couplings between the engine
  and wagon is 1000 N.
• ) What is the force opposing the motion of the
  wagon?
• ) If the pull force is increased to 1200 N and
  the resistance to movement
• of the wagon remains constant, what would be the
  acceleration of the wagon?
• Solution
• a) When the speed is steady, by Newtons first
  law, the resultant force must be zero.
• The pull on the wagon must equal the resistance
  to motion. So the force resisting motion is 1000
  N.
• b) The resultant force on the wagon is 1200
  1000 200 N
• By Equation

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Example
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Example a) Find the acceleration of a 20 kg crate
along a horizontal floor when it is pushed with a
resultant force of 10 N parallel to the floor.
b) How far will the crate move in 5s (starting
from rest)? Solution
Distance travelled
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A 1kg stone fall freely from rest from a bridge.
a -What is the force causing it to accelerate? b
-What is its speed 4s later? c -How far has it
fallen in this time?
Solution
The force causing it to fall is its weight. As it
is falling with acceleration due to gravity
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Example
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3 . 7 the significance of Newton's laws of
motion 3 .7 some examples of Newton's laws Make
a diagram (conceptualize) Categorize no
acceleration (at rest )
accelerating object Isolate each object and
draw a free body diagram for each object. Draw
in all forces that act on the object. Establish a
convenient coordinate system. Write Newtons law
for each body and each coordinate component. ?
set of equations. Finalize by checking answers.
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Free body diagram
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Example
A lift with its load has a mass of 2000 kg. It is
supported by a steel cable. Find the tension in
the cable when it a -is at rest b - accelerates
upwards uniformly at 1m/s2 C - move upwards at a
steady speed of 1 m/s d - moves downwards at a
steady speed of 1 m/s e - accelerates downwards
with uniform acceleration of 1 m/s2
a) When at rest we can use Newtons first law
which says that the resultant force on the lift
is zero. Force acting down is the lifts
weight, the force acting up is the tension in the
cable. These two must be equal and opposite to
give a resultant force of zero.
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b) As the lift is accelerating upwards so T must
exceed the weight mg. So the resultant
acceleration force
by Newton second law, F ma, so
c) As in (a), by Newtons first law, the
resultant force on the lift must be zero, so
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d) As in (c) the tension in the cable will still
equal mg since the change in direction of motion
does not alter the fact that there is no
acceleration.
e ) If the lift accelerates downwards, then mg
must exceed the tension T. So the resultant
accelerating force is
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Example
Two hanging objects connected by a light string
passing over a frictionless pulley
What are the acceleration of the objects and the
tension on the string?
( m1 4 kg m2 7 kg )
m1 a1 T - m1 g - m2 a2 T m2 g
- m2 a T m2 g ? m2 a -T m2 g
a g (m2 m1) / (m1 m2) ( 7-4 ) x9.8
/ ( 74 ) 3x 9.8 / 11 29.4 /11 a 2 .
6 5 m/s2
m1 a T - m1 g T m1a m1g T m1 ( a g) T
4( 2.65 9.8 ) N
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Example
A body of mass 5kg lies on a smooth horizontal
table. It is connected by a light in extensible
string, which passes over a smooth pulley at the
edge of the table, to another body of mass 3kg
which is hanging freely. The system is released
from rest. Find the tension in the string and the
acceleration.
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Example
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Example
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3-12 Friction
Friction results from relative motion between
objects. Frictional forces are forces that resist
or oppose motion.

• Sliding Friction
• When two solid surfaces slide over each other.
• The amount of friction between two surfaces
  depends on two factors.
• The kinds of surfaces.
• The force pressing the surfaces together
  (weight).
• Static friction is the frictional force that
  prevents two surfaces from sliding past each
  other.

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Friction force To first order, we consider two
effects on friction 1. Normal force of contact
between the surfaces 2. Types of surfaces in
contact (texture of surfaces
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• The following empirical laws hold true about
  friction
• Friction force, f, is proportional to normal
  force, n.
• ?s and ?k coefficients of static and kinetic
  friction, respectively
• Direction of frictional force is opposite to
  direction of relative motion
• Values of ?s and ?k depend on nature of
  surface.
• ?s and ?k dont depend on the area of contact.
• ?s and ?k dont depend on speed.
• ?s, max is usually a bit larger than ?k.
• Range from about 0.003 (?k for synovial joints
  in humans) to 1 (?s for rubber on concrete). See
  table 5.2 in book.

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Table of friction coefficients
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Example A 10 N force pushes down on a box that
weighs 100 N. As the box is pushed horizontally,
the coefficient of sliding friction is
0.25. Determine the force of friction resisting
the motion.
Fs µ s x N (10100)x0.25 27.5
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The sled comes to a halt because the kinetic
frictional force opposes its motion and causes
the sled to slow down.
Suppose the coefficient of kinetic friction is
0.05 and the total mass is 40kg. What is the
kinetic frictional force?
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Calculate acceleration

• Three people are pulling on a wagon applying
  forces of 100 N,150 N, and 200 N.
• The wagon has a mass of 25 kilograms.
• Determine the acceleration and the direction the
  wagon moves. (2m/s2 ) to the left

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Calculate force

• An airplane needs to accelerate at 5 m/sec2 to
  reach take-off speed before reaching the end of
  the runway.
• The mass of the airplane is 5,000 kilograms.
• How much force is needed from the engine?
  (F25000N)

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A 1200 kg car moving at 100 km/h coasts to a stop
in 25 seconds. What is the value of the static
coefficient of friction?

• example

• m 1200 kg
• vo 100km/h 27.8 m/s
• t 25 s
• µF/N
• where F ma Nmg
• ma/mg
• (m(v vo)/t)/mg
• (27.8m/s/25 s )/ 9.8 m/s2)
• µ 0.113

vo
f
From v vo at, a (v-vo)/t
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Example

• A 10-kg box is being pulled across the table to
  the right at a constant speed with a force of
  50N.
• Calculate the Force of Friction
• Calculate the Force Normal

FN
Fa
Ff
mg
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Example

• Suppose the same box is now pulled at an angle of
  30 degrees above the horizontal.
• Calculate the Force of Friction
• Calculate the Force Normal

FN
Fa
Fay
Ff
30
Fax
mg
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Example
What is the weight of an object that is being
pulled at a constant velocity by a force of 25 N
if the coefficient of sliding friction between
the object and the surface is 0.75? ? Fy 0 N
- W 0 N
W ? Fx ma ( a 0 constant
velocity ) ? Fx 0 Fk F 25 N Fk µk N N Fk
/ µk W N 25 / 0.75 33.3 N W 33.3 N
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example

• Suppose 35 kg crate was not moving at a constant
  speed, but rather accelerating at 0.70 m/s2.
  Calculate the applied force. The coefficient of
  kinetic friction is still 0.30.

N
Fa
Ff
mg
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Summary of Chapter 3

• Newtons first law If the net force on an
  object is zero, it will remain either at rest or
  moving in a straight line at constant speed.
• Newtons second law
• Newtons third law
• Weight is the gravitational force on an object
  W m g.
• Free-body diagrams are essential for
  problem-solving. Do one object at a time, make
  sure you have all the forces, pick a coordinate
  system and find the force components, and apply
  Newtons second law along each axis.
• Kinetic friction Fk µkN
• Static friction Fs µsN .
• Fk lt Fs µk
  lt µs

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