Chap13

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Chap13
Kinetics of a particle Force and Acceleration.
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13.1 Newtons law of motion
1.Newtons 2nd law of motion
(1) A particle subjected to an unbalanced force
experiences an acceleration
having the same
and a magnitude that is directly
direction as
proportional to the force.
m
m mass of a particle
a quantitative measure of the resistance of the
particle to a change in its velocity.
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acting on the particle is
(2) The unbalanced force
proportional to the time rate of change of the
particles linear momentum.
(if mconstant)
2. Newtons Law of Gravitational Attraction
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G universal constant of gravitation
r distance between centers of two particles
Weight of a particle with mass m1 m
mg
m2 mass of the earth
r distance between the earth center and the
particle
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g
acceleration due to gravity
measured at a point on the surface of the
9.81
earth at sea level and at a latitude of
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13-2 The equations of motion

1. Equations of motion of a particle subjected to
   more than one force.

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Free body diagram of particle p.
p
...equation of motion
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DA lembert principle
inertia force vector
Dynamic equilibrium diagram
p
(???)
? ????????

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2. Inertial frame of reference (newtonian)
A coordinate system is either fixed or translates
in a given direction with a constant velocity.
(2) Noninertial frame
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13-3 Equation of motion for a system of particle
z
i
y
xyz Inertial Coordinate System
x
Equation of motion of particle i. Dynamic
equilibrium diagram of particle i.
i
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resultant external force
resultant internal force
Equation of motion of a system of particles.
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By definition of the center of mass for a
system of particles.
Position vector of the center of mass G.
Total mass of all particles.
Assume that no mass is entering or leaving the
system.
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Hence
This equation justifies the application of the
equation of motion to a body that is
represented as a single particle.
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13-4 Equations of motionRectangular
Coordinate
x
Equation of motion of particle P.
In rectangular components
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scalar eqns.
Analysis procedure

• Free Body Diagram.
• (1) Select the proper inertial coordinate
  system.
• (2) Draw the particles F.B.D.
• 2. Equation of motion
• (1) Apply the equations of motion in scalar
  form
• or vector form.

or
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(2) Friction force
(3) Spring force
3. Equations of kinematics Apply
for the solutions
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13.5 Equation of MotionNormal and Tangential
Coordinates
Curve path of motion of a particle is known.
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Equation of motion
Or scalar form
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Analysis procedure

• 1. Free body diagram
• Identify the unknowns in the problem.
• 2. Equation of motion
• Apply the equations of motion using normal
  and tangential coordinates.
• 3. Kinematics
• Formulate the tangential and normal
  components of acceleration.

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13.6 Equation of Motion Cylindrical coordinate
Equation of motion in cylindrical coordinates
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and
Cylindrical or polar coordinates are suitable for
a problem for which Data regarding the angular
motion of the radial line r are given, or in
Cases where the path can be conveniently
expressed in terms of these coordinates.
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• Normal and Tangential force
• If the particles accelerated motion is not
  completely specified, then information regarding
  the directions or magnitudes of the forces acting
  on the particle must be known or computed.
• Now, consider the case in which the force P
  causes the particle to move along the path rf(q)
  as shown in the following figure.

rf(q) path of motion of particle PExternal
force on the particle FFriction force along the
tangent NNormal force perpendicular to tangent
of path
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Direction of F N
The directions of F and N can be specified
relative to the radial coordinate r by computing
the angle y. Angle y is defined between the
extended radial line and the tangent to the path.
dr radial component rdq transverse
component dsdistance