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 10

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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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First law

• 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.
• A particle originally at rest, or moving in a
  straight line with a constant velocity, will
  remain in this state provided the particle is not
  subjected to an unbalance force.
• Static law

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Second law

• A particle acted upon by an unbalanced force F
  experiences an acceleration that has the same
  direction as the force and a magnitude that is
  directly proportional to the force

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Third law

• Law of action-reaction - for every action, there
  is an equal and opposite reaction
• The mutual forces of action and reaction between
  two particles are equal, opposite, and collinear.
• Fb,a -Fa,b

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Newton's Law of Universal Gravitation

• 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.
• F forces of attraction
• G universal constant of gravitation
  66.73(10-12)m3/(kg.s2)
• m1,m2 mass of each of the two particle
• r distance between the centers of the two
  particles

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Gravity on earth?

• Newton's Law of Universal Gravitation
• Compare with F mg so g GM/r2
• g depends inversely on the square of the distance
• g depends on the mass of the planet
• Nominally, g 9.81 m/s2 or 32.2 ft/s2
• At the equator g 9.78 m/s2
• At the North pole g 9.83 m/s2
• g on the Moon is 1/6 of g on Earth.

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Mass and Weight

• Weight
• the amount of gravitational force exerted on a
  body
• F m g
• W m g
• W weight (units N or lbs)
• m mass of the body (units kg)
• g gravitational acceleration (9.81 m/s2, 32.2
  ft/s2)
• As the mass of a body increases, its weight
  increases proportionally

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13.2 The Equation of MotionFree Body and Kinetic
Diagram

• Free-Body diagram
• Kinetic diagram

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13.3 Equation of Motion for a System of Particles
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Thank You