the definition of dynamics in math

1. Dynamics
1. 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. 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. 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. 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. 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. 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. 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. 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
9. 9. Table of strength Interaction Relative strength Range Strong 1038 10-15
electromagnetic 1036 ∞ Weak 1025 10-18 gravitational 1 ∞ 1/21/2014 IB
Physics (IC NL) 9
10. 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. 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. 12. Contact and Field Forces 1/21/2014 IB Physics (IC NL) 12
13. 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

2. 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. 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
15. 15. Condition of equilibrium  Fext 1/21/2014 IB Physics (IC NL)  0 15
16. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

3. 28. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 38. Equilibrium Example – Free Body Diagrams 1/21/2014 IB Physics (IC
NL) 38
39. 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. 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

4. 41. 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. 42. Multiple Objects – Example, cont. 1/21/2014 IB Physics (IC NL) 42
43. 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. 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. 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. 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. 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. 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. 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
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