King Fahd University of Petroleum

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King Fahd University of Petroleum Minerals

• Mechanical Engineering
• Dynamics ME 201
• BY
• Dr. Meyassar N. Al-Haddad
• Lecture 11

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Sir Isaac Newton 1642-1727
Proposed fundamental laws that are the basis of
modern mechanics 3 laws of motion law of
gravitation
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Newtons laws

• Law of inertia a body in motion will stay in
  motion and a body at rest will stay at rest
  unless acted upon by a net external force.
• Law of force-acceleration A particle acted upon
  by an unbalanced force F experiences an
  acceleration a that has the same direction as the
  force and a magnitude that is directly
  proportional to the force
• Law of action-reaction for every action, there is
  an equal and opposite reaction
  mg FN
• Law of gravitation - all bodies are attracted to
  one another with a force proportional to the
  product of their masses and inversely
  proportional to the square of the distance
  between them.

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13.2 The Equation of Motion

• Free-Body diagram (Force Diagram)
• Kinetic diagram (acceleration Diagram)

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13.3 Equation of Motion for a System of Particles
Internal forces cancel each other
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13.4 Equations of Motion Rectangular Coordinates

• When the net force is projected to separate
  coordinate axes the Newtons second law still
  holds

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Free Body Diagram Method

• Draw each object separately
• Draw all the forces acting on that object
• Get x and y components of all the forces to
  calculate the net force
• Apply Newtons second law to get acceleration
• Use the acceleration in any motion analysis and
  establish a Kinetic Diagram

ma
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Normal Frictional Force
Action-Reaction forces - mg FN

F
mg
Ff
FN
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Static Friction ( ms )

• Static friction parallel force on the surface
  when there is no relative motion between the 2
  objects
• Static friction force can vary from zero to
  Maximum
• The coefficient of static friction
• is material dependent.

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Kinetic Friction ( mk )

• Kinetic friction parallel force on the surface
  when there is relative motion between the 2
  objects
• Kinetic friction force is always the same
• The coefficient of Kinetic friction
• is material dependent.

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Friction (con.)

• When to use static friction or kinetic friction ?
• If the 2 objects have relative motion always
  use kinetic friction
• If the calculated friction force to keep the 2
  objects to stay together is greater than the
  maximum static friction use kinetic friction
• Otherwise no relative motion, friction force is
  smaller than Fmax use static friction

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Spring Force

• Spring force
• k spring stiffness (N/m)
• s stretched or compressed length

s
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Example 13-4

• m 2 kg
• y 1m
• smooth
• a ?

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Problem
a ?
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Example 13-5
m A 3 kg m B 5 kg From rest vB ? In 2 second
Block B
Same?should be
Block A
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Problem

• 
  VA ?
• 2Sc SA L
• 0 2ac aA aA -2ac

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Review

• Example 13.1
• Example 13.2
• Example 13.3
• Example 13.4

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Thank You