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Mechanics
Mechanics is a branch of physics
concerned with the behavior of physical
bodies when subjected to forces or
displacements also it deals with matter
and investigates energy.
Mechanics is divided into three branches:
1- Statics
2- Kinematics
3- Dynamics
In this slide we will discuss
1/21/2014

Dynamics.
IB Physics (IC NL)

1
Dynamics


The branch of mechanics that is
concerned with the effects of forces on
the motion of a body or system of
bodies, especially of forces that do not
originate within the system itself. That
is the external forces and not the
internal ones.

1/21/2014

IB Physics (IC NL)

2
Internal forces






These forces generate inside the body due
to the interaction between the particles,
atoms, molecules or even inside the
nucleus.
Forces that originate within the object
itself
They cannot change the object’s velocity

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IB Physics (IC NL)

3
Types of forces


In nature we have four fundamental
forces and all the other forces that
you know undergo these four which
are in order of strength:

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IB Physics (IC NL)

4
Strong force


The Strong Force - This force binds
neutrons and protons together in the
cores of atoms and is a short range
force.

1/21/2014

IB Physics (IC NL)

5
Electromagnetic force


Electromagnetic - This acts
between electrically charged
particles. Electricity, magnetism, and
light are all produced by this force
and it has an infinite range.

1/21/2014

IB Physics (IC NL)

6
Weak forces
Weak Force - This causes Beta decay (the
conversion of a neutron to a proton, an
electron and an antineutrino) and various
particles (the "strange" ones) are formed by
strong interactions but decay via weak
interactions. Like the strong force, the weak
force is also short range.
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7
Gravitational force


Gravitational - This force acts
between all masses in the universe
and it has infinite range.

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8
Table of strength
Interaction

Relative
strength

Range

Strong

1038

10-15

electromagnetic

1036

∞

Weak

1025

10-18

gravitational

1

∞

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9
Unit two: forces
In our IB, forces are to be studied from
a basic part of view and concerned with
external forces; later we might go to
forces related to the four preceding
forces.
 External force


Any force that results from the
interaction between the object and its
environment

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10
External Forces






Def: force is a mechanical action capable of:
i. moving a body initially at rest.
ii. Changing the motion of a body.
iii. Deforming a body.
Usually think of a force as a push or pull
Vector quantity
May be a contact force or a field force




Contact forces result from physical contact between two
objects
Field forces act between disconnected objects


Also called “action at a distance”

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IB Physics (IC NL)

11
Contact and Field Forces

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12
Newton’s First Law


If a body is at rest it remains at
rest, if it is moving with uniform
motion it keeps its uniform motion
unless acted upon by an external
force.


1/21/2014

The net force is defined as the vector
sum of all the external forces exerted
on the object
IB Physics (IC NL)

13
Equilibrium




An object either at rest or moving
with a constant velocity is said to
be in equilibrium
The net force acting on the object
is zero (since the acceleration is
zero)

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14
Condition of equilibrium


Fext

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IB Physics (IC NL)


0

15
Inertia




Is the tendency of an object to
resist any attempt to change its
state of motion.
An object's inertia is directly
proportional to its mass; the
heavier an object is, the more
inertia it has. Hence, a body's mass
measures its inertia.

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16
Mass





Is the quantity of matter found in a
body.
Scalar quantity
SI unit is kg

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IB Physics (IC NL)

17
Seat Belt Device




Illustration of how one
type of seat belt
operates involving the
inertia of a block
It protects you when
inertia keeps you
moving if the driver
suddenly applies the
brakes.
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18
Newton’s Second Law




If a body is subjected to a force this body
accelerates. The force and the acceleration
are directly proportional and in the same
direction.

F and a are both vectors

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19
Units of Force


SI unit of force is the Newton (N)
1 N = 1 kg.m.s-2

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20
Sir Isaac Newton









1642 – 1727
Formulated basic
concepts and laws
of mechanics
Universal
Gravitation
Calculus
Light and optics

1/21/2014

IB Physics (IC NL)

21
Horse and Barge








The barge mass is
2.00X103 kg
o
1 = 30.0
o
2 = 45.0
Values of the forces F1
and F2 are each 600 N
Find the x and y
resultant forces and
associated
accelerations
1/21/2014

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22
Gravitational Force




Mutual force of
attraction between
any two objects
Expressed by
Newton’s Law of
Universal Gravitation:

Fg
1/21/2014

m1 m2
G 2
r

G = 6.67 x 10-11 SI
IB Physics (IC NL)

23
Weight


The magnitude of the gravitational
force acting on an object of mass m
near the Earth’s surface is called the
weight w of the object


w = m g is a special case of Newton’s
Second Law




g is the acceleration due to gravity or
gravitational field strength.

g can also be found from the Law of
Universal Gravitation
1/21/2014

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24
More about weight


Weight is not an inherent property of
an object






mass is an inherent property or mass is
invariant.

Weight depends upon location.
Weight changes with g
g= 9.81ms-2 in Paris, 9.83ms-2 at the
pole and 9.78ms-2 at the equator.
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25
Newton’s Third Law
If object 1 and object 2 interact, the
force exerted by object 1 on object 2 is
equal in magnitude but opposite in
direction to the force exerted by object
2 on object 1.



Another version: for every action there is
an equal and opposite reaction.





Equivalent to saying a single isolated
force cannot exist

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26
Newton’s Third Law cont.


F12 may be called the
action force and F21
the reaction force






Actually, either force
can be the action or
the reaction force

The action and
reaction forces act
on different objects
Point of application
is always the center
of mass.
1/21/2014

IB Physics (IC NL)

27
Some Action-Reaction
Pairs







is the normal force,
the force the table
exerts on the TV
is always
perpendicular to the
surface
is the reaction – the
TV on the table



1/21/2014

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28
More Action-Reaction pairs





is the force the
Earth exerts on
the object
is the force the
object exerts on
the earth



1/21/2014

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29
Forces Acting on an Object






Newton’s Law
uses the forces
acting on an
object
are
acting on the
object
are
acting on other
objects

1/21/2014

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30
Applications of Newton’s
Laws


Assumptions


Objects behave as particles






Masses of strings or ropes are
negligible
Interested only in the forces acting
on the object


1/21/2014

can ignore rotational motion (for now)

can neglect reaction forces
IB Physics (IC NL)

31
Free Body Diagram






Must identify all the forces acting
on the object of interest
Choose an appropriate coordinate
system
If the free body diagram is
incorrect, the solution will likely be
incorrect

1/21/2014

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32
Free Body Diagram,
Example


The force is the
tension acting on
the box




The tension is the
same at all points
along the rope

are the
forces exerted by
the earth and the
ground
1/21/2014

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33
Free Body Diagram, final






Only forces acting directly on the object are
included in the free body diagram
Reaction forces act on other objects and so
are not included
The reaction forces do not directly influence
the object’s motion


In free body diagrams you can select one
point to be the point of application of all the
forces acting on the object.

1/21/2014

IB Physics (IC NL)

34
Solving Newton’s Second
Law Problems




Read the problem at least once
Draw a picture of the system





Identify the object of primary interest
Indicate forces with arrows

Label each force


1/21/2014

Use labels that bring to mind the
physical quantity involved
IB Physics (IC NL)

35
Solving Newton’s Second
Law Problems


Draw a free body diagram






Apply Newton’s Second Law




If additional objects are involved, draw
separate free body diagrams for each object
Choose a convenient coordinate system for
each object
The x- and y-components should be taken
from the vector equation and written
separately

Solve for the unknown(s)

1/21/2014

IB Physics (IC NL)

36
Equilibrium revisited.




Easier to work with the equation in
terms of its components:

This could be extended to three
dimensions

1/21/2014

IB Physics (IC NL)

37
Equilibrium Example –
Free Body Diagrams

1/21/2014

IB Physics (IC NL)

38
Inclined Planes




Choose the
coordinate
system with x
along the incline
and y
perpendicular to
the incline
Replace the force
of gravity with its
components
1/21/2014

IB Physics (IC NL)

39
Multiple Objects –
Example








When you have more than one
object, the problem-solving
strategy is applied to each object
Draw free body diagrams for each
object
Apply Newton’s Laws to each
object
Solve the equations

1/21/2014

IB Physics (IC NL)

40
Multiple Objects –
Example, cont.


A fish weights 40.0 N
when at rest.






Determine the weight
when a=2.00 m.s-2 up
When a=2.00 m.s-2
down
What is the weight if
the cable were to
break?

1/21/2014

IB Physics (IC NL)

41
Multiple Objects –
Example, cont.

1/21/2014

IB Physics (IC NL)

42
Forces of Friction(not in IB)


When an object is in motion on a
surface or through a viscous
medium, there will be a resistance
to the motion




This is due to the interactions
between the object and its
environment

This is resistance is called friction

1/21/2014

IB Physics (IC NL)

43
More About Friction










Friction is proportional to the normal
force
The force of static friction is generally
greater than the force of kinetic friction
The coefficient of friction (µ) depends
on the surfaces in contact
The direction of the frictional force is
opposite to the direction of motion
The coefficients of friction are nearly
independent of the area of contact

1/21/2014

IB Physics (IC NL)

44
Static Friction, ƒs








Static friction acts
to keep the object
from moving
If F increases, so
does ƒs
If F decreases, so
does ƒs
ƒs µ n

1/21/2014

IB Physics (IC NL)

45
Kinetic Friction, ƒk




The force of
kinetic friction
acts when the
object is in
motion
ƒk = µ n


1/21/2014

Variations of the
coefficient with
speed will be
ignored
IB Physics (IC NL)

46
Block on a Ramp, Example






Axes are rotated as
usual on an incline
The direction of
impending motion
would be down the
plane
Friction acts up the
plane




Opposes the motion

Apply Newton’s Laws
and solve equations
1/21/2014

IB Physics (IC NL)

47
Connected
Objects








Apply Newton’s Laws
separately to each
object
The magnitude of the
acceleration of both
objects will be the
same
The tension is the
same in each diagram
Solve the simultaneous
equations
1/21/2014

IB Physics (IC NL)

48
More About Connected
Objects


Treating the system as one object
allows an alternative method or a
check


Use only external forces


1/21/2014

If treating the system as one object then
tension is no more considered and it will
be an internal force. The mass is the
mass of the system

IB Physics (IC NL)

49

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Dynamics

  • 1. Mechanics Mechanics is a branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements also it deals with matter and investigates energy. Mechanics is divided into three branches: 1- Statics 2- Kinematics 3- Dynamics In this slide we will discuss 1/21/2014 Dynamics. IB Physics (IC NL) 1
  • 2. Dynamics  The branch of mechanics that is concerned with the effects of forces on the motion of a body or system of bodies, especially of forces that do not originate within the system itself. That is the external forces and not the internal ones. 1/21/2014 IB Physics (IC NL) 2
  • 3. Internal forces    These forces generate inside the body due to the interaction between the particles, atoms, molecules or even inside the nucleus. Forces that originate within the object itself They cannot change the object’s velocity 1/21/2014 IB Physics (IC NL) 3
  • 4. Types of forces  In nature we have four fundamental forces and all the other forces that you know undergo these four which are in order of strength: 1/21/2014 IB Physics (IC NL) 4
  • 5. Strong force  The Strong Force - This force binds neutrons and protons together in the cores of atoms and is a short range force. 1/21/2014 IB Physics (IC NL) 5
  • 6. Electromagnetic force  Electromagnetic - This acts between electrically charged particles. Electricity, magnetism, and light are all produced by this force and it has an infinite range. 1/21/2014 IB Physics (IC NL) 6
  • 7. Weak forces Weak Force - This causes Beta decay (the conversion of a neutron to a proton, an electron and an antineutrino) and various particles (the "strange" ones) are formed by strong interactions but decay via weak interactions. Like the strong force, the weak force is also short range. 1/21/2014 IB Physics (IC NL) 7
  • 8. Gravitational force  Gravitational - This force acts between all masses in the universe and it has infinite range. 1/21/2014 IB Physics (IC NL) 8
  • 10. Unit two: forces In our IB, forces are to be studied from a basic part of view and concerned with external forces; later we might go to forces related to the four preceding forces.  External force  Any force that results from the interaction between the object and its environment 1/21/2014 IB Physics (IC NL) 10
  • 11. External Forces     Def: force is a mechanical action capable of: i. moving a body initially at rest. ii. Changing the motion of a body. iii. Deforming a body. Usually think of a force as a push or pull Vector quantity May be a contact force or a field force   Contact forces result from physical contact between two objects Field forces act between disconnected objects  Also called “action at a distance” 1/21/2014 IB Physics (IC NL) 11
  • 12. Contact and Field Forces 1/21/2014 IB Physics (IC NL) 12
  • 13. Newton’s First Law  If a body is at rest it remains at rest, if it is moving with uniform motion it keeps its uniform motion unless acted upon by an external force.  1/21/2014 The net force is defined as the vector sum of all the external forces exerted on the object IB Physics (IC NL) 13
  • 14. Equilibrium   An object either at rest or moving with a constant velocity is said to be in equilibrium The net force acting on the object is zero (since the acceleration is zero) 1/21/2014 IB Physics (IC NL) 14
  • 16. Inertia   Is the tendency of an object to resist any attempt to change its state of motion. An object's inertia is directly proportional to its mass; the heavier an object is, the more inertia it has. Hence, a body's mass measures its inertia. 1/21/2014 IB Physics (IC NL) 16
  • 17. Mass    Is the quantity of matter found in a body. Scalar quantity SI unit is kg 1/21/2014 IB Physics (IC NL) 17
  • 18. Seat Belt Device   Illustration of how one type of seat belt operates involving the inertia of a block It protects you when inertia keeps you moving if the driver suddenly applies the brakes. 1/21/2014 IB Physics (IC NL) 18
  • 19. Newton’s Second Law   If a body is subjected to a force this body accelerates. The force and the acceleration are directly proportional and in the same direction. F and a are both vectors 1/21/2014 IB Physics (IC NL) 19
  • 20. Units of Force  SI unit of force is the Newton (N) 1 N = 1 kg.m.s-2 1/21/2014 IB Physics (IC NL) 20
  • 21. Sir Isaac Newton      1642 – 1727 Formulated basic concepts and laws of mechanics Universal Gravitation Calculus Light and optics 1/21/2014 IB Physics (IC NL) 21
  • 22. Horse and Barge      The barge mass is 2.00X103 kg o 1 = 30.0 o 2 = 45.0 Values of the forces F1 and F2 are each 600 N Find the x and y resultant forces and associated accelerations 1/21/2014 IB Physics (IC NL) 22
  • 23. Gravitational Force   Mutual force of attraction between any two objects Expressed by Newton’s Law of Universal Gravitation: Fg 1/21/2014 m1 m2 G 2 r G = 6.67 x 10-11 SI IB Physics (IC NL) 23
  • 24. Weight  The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object  w = m g is a special case of Newton’s Second Law   g is the acceleration due to gravity or gravitational field strength. g can also be found from the Law of Universal Gravitation 1/21/2014 IB Physics (IC NL) 24
  • 25. More about weight  Weight is not an inherent property of an object     mass is an inherent property or mass is invariant. Weight depends upon location. Weight changes with g g= 9.81ms-2 in Paris, 9.83ms-2 at the pole and 9.78ms-2 at the equator. 1/21/2014 IB Physics (IC NL) 25
  • 26. Newton’s Third Law If object 1 and object 2 interact, the force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1.  Another version: for every action there is an equal and opposite reaction.   Equivalent to saying a single isolated force cannot exist 1/21/2014 IB Physics (IC NL) 26
  • 27. Newton’s Third Law cont.  F12 may be called the action force and F21 the reaction force    Actually, either force can be the action or the reaction force The action and reaction forces act on different objects Point of application is always the center of mass. 1/21/2014 IB Physics (IC NL) 27
  • 28. Some Action-Reaction Pairs     is the normal force, the force the table exerts on the TV is always perpendicular to the surface is the reaction – the TV on the table  1/21/2014 IB Physics (IC NL) 28
  • 29. More Action-Reaction pairs    is the force the Earth exerts on the object is the force the object exerts on the earth  1/21/2014 IB Physics (IC NL) 29
  • 30. Forces Acting on an Object    Newton’s Law uses the forces acting on an object are acting on the object are acting on other objects 1/21/2014 IB Physics (IC NL) 30
  • 31. Applications of Newton’s Laws  Assumptions  Objects behave as particles    Masses of strings or ropes are negligible Interested only in the forces acting on the object  1/21/2014 can ignore rotational motion (for now) can neglect reaction forces IB Physics (IC NL) 31
  • 32. Free Body Diagram    Must identify all the forces acting on the object of interest Choose an appropriate coordinate system If the free body diagram is incorrect, the solution will likely be incorrect 1/21/2014 IB Physics (IC NL) 32
  • 33. Free Body Diagram, Example  The force is the tension acting on the box   The tension is the same at all points along the rope are the forces exerted by the earth and the ground 1/21/2014 IB Physics (IC NL) 33
  • 34. Free Body Diagram, final    Only forces acting directly on the object are included in the free body diagram Reaction forces act on other objects and so are not included The reaction forces do not directly influence the object’s motion  In free body diagrams you can select one point to be the point of application of all the forces acting on the object. 1/21/2014 IB Physics (IC NL) 34
  • 35. Solving Newton’s Second Law Problems   Read the problem at least once Draw a picture of the system    Identify the object of primary interest Indicate forces with arrows Label each force  1/21/2014 Use labels that bring to mind the physical quantity involved IB Physics (IC NL) 35
  • 36. Solving Newton’s Second Law Problems  Draw a free body diagram    Apply Newton’s Second Law   If additional objects are involved, draw separate free body diagrams for each object Choose a convenient coordinate system for each object The x- and y-components should be taken from the vector equation and written separately Solve for the unknown(s) 1/21/2014 IB Physics (IC NL) 36
  • 37. Equilibrium revisited.   Easier to work with the equation in terms of its components: This could be extended to three dimensions 1/21/2014 IB Physics (IC NL) 37
  • 38. Equilibrium Example – Free Body Diagrams 1/21/2014 IB Physics (IC NL) 38
  • 39. Inclined Planes   Choose the coordinate system with x along the incline and y perpendicular to the incline Replace the force of gravity with its components 1/21/2014 IB Physics (IC NL) 39
  • 40. Multiple Objects – Example     When you have more than one object, the problem-solving strategy is applied to each object Draw free body diagrams for each object Apply Newton’s Laws to each object Solve the equations 1/21/2014 IB Physics (IC NL) 40
  • 41. Multiple Objects – Example, cont.  A fish weights 40.0 N when at rest.    Determine the weight when a=2.00 m.s-2 up When a=2.00 m.s-2 down What is the weight if the cable were to break? 1/21/2014 IB Physics (IC NL) 41
  • 42. Multiple Objects – Example, cont. 1/21/2014 IB Physics (IC NL) 42
  • 43. Forces of Friction(not in IB)  When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion   This is due to the interactions between the object and its environment This is resistance is called friction 1/21/2014 IB Physics (IC NL) 43
  • 44. More About Friction      Friction is proportional to the normal force The force of static friction is generally greater than the force of kinetic friction The coefficient of friction (µ) depends on the surfaces in contact The direction of the frictional force is opposite to the direction of motion The coefficients of friction are nearly independent of the area of contact 1/21/2014 IB Physics (IC NL) 44
  • 45. Static Friction, ƒs     Static friction acts to keep the object from moving If F increases, so does ƒs If F decreases, so does ƒs ƒs µ n 1/21/2014 IB Physics (IC NL) 45
  • 46. Kinetic Friction, ƒk   The force of kinetic friction acts when the object is in motion ƒk = µ n  1/21/2014 Variations of the coefficient with speed will be ignored IB Physics (IC NL) 46
  • 47. Block on a Ramp, Example    Axes are rotated as usual on an incline The direction of impending motion would be down the plane Friction acts up the plane   Opposes the motion Apply Newton’s Laws and solve equations 1/21/2014 IB Physics (IC NL) 47
  • 48. Connected Objects     Apply Newton’s Laws separately to each object The magnitude of the acceleration of both objects will be the same The tension is the same in each diagram Solve the simultaneous equations 1/21/2014 IB Physics (IC NL) 48
  • 49. More About Connected Objects  Treating the system as one object allows an alternative method or a check  Use only external forces  1/21/2014 If treating the system as one object then tension is no more considered and it will be an internal force. The mass is the mass of the system IB Physics (IC NL) 49