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 22
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Principle of Linear Impulse and Momentum
Initial momentum Sum of all Impulse
Final momentum
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Conservation of Linear Momentum for a system of
Particles
Conservation of linear momentum equation
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Impulse Average Force
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Impact

• Impact occurs when two bodies collide with each
  other during a very short period of time.
• Types of impact
• Central impact
• Oblique impact
• Line of impact
• Plane of impact

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Coefficient of restitution e
Coefficient of restitution e is defined as the
ratio of the restitution impulse to the
deformation impulse. Coefficient of
restitution e is defined as the ratio of relative
velocity after impact to the relative velocity
before impact Coefficient of restitution e is
according to the impact velocity, material, size
and shape of the colliding body, Coefficient of
restitution e range between 0-1 Coefficient of
restitution e is defined along the line of
impact only Elastic impact e 1 (re-bounce
with same velocity) Plastic impact e 0 (couple
or stick together and move with common velocity)
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Procedure for Analysis

• Identify the intial velocity you may use
• T1 V1 T2 V2
• Apply the conservation of momentum along the line
  of impact, you will get one equation with two
  unknown velocity
• Use the coefficient of restitution to obtain a
  second equation
• Solve both equation for final velocities after
  the impact

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Oblique Impact
Central Impact one Dimension Oblique Impact
Two Dimension
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Procedure for Analysis

• Establish x-axis as line of impact
• Establish y-axis as plane of impact
• Resolve the velocity components
• along x, and y as
• Apply the conservation of momentum along the
  line of impact
• Use the coefficient of restitution to obtain a
  second equation
• Solve both equation for final velocities along
  x-axis after the impact
• The momentum is conserved along the plane of
  impact so

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Procedure for Analysis
Along the line of the impact only
Along the Plane of the impact only
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ANGULAR MOMENTUM

• For a point object the angular momentum is

v
m
Units - kg.m2/s or sl.ft2/s It is a vector. Here
the vector is pointing toward you. Using
right-hand rule
r
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Angular Impulse and Momentum Principles
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Conservation of Angular Momentum
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Block A
Block B
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Example 15-9
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• Momentum of particle A,B is conserved along the y
  axis, since no impulse acts on particle A,B

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Thank you