1. MEE 214 (Dynamics) Tuesday 8.30-11.20
Dr. Soratos Tantideeravit (สรทศ ตันติธีรวิทย์)
Lecture Notes, Course updates, Extra problems, etc
No Homework
Final Exam (Date & Time – TBD)
29/11/61
MEE214 – Dynamics

2. Course Overview Kinematics of a Particle Kinetics of a Particle
Rectilinear and Curvilinear Motion
Kinetics of a Particle
Force and Acceleration
Work and Energy
Impulse and Momentum
Kinetics of a System of Particles
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3. Introduction to Dynamics
Statics
Engineering
Mechanics
Dynamics
Kinematics
Kinetics
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4. Kinematics of a particle

5. Objectives
Concepts of position, displacement, velocity, and acceleration.
Particle motion along a straight line
Particle motion along a curved path using different coordinate systems.
Analysis of dependent motion of two particles.
Principles of relative motion of two
particles using translating axes.
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6. Rectilinear Kinematics
Origin
Define a fixed point in space
Position
Defined by a position vector r
or an algebraic scalar s
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7. Rectilinear Kinematics
Displacement
Change in position
Velocity
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8. Rectilinear Kinematics
Acceleration
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9. Constant Acceleration
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10. Problem 12-31
The acceleration of a particle along a straight line is defined by a=(2t-9) m/s2, where t is in seconds. At t=0, s=1 m and v=10 m/s. When t=9 s, determine (a) the particle’s position, (b) the total distance traveled and (c) the velocity.
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11. General Curvilinear Motion
Curvilinear motion occurs when the particle moves along a curved path
Position. The position of the particle, measured from a fixed point O, is designated by the position vector r = r(t).
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MEE214 – Dynamics

12. General Curvilinear Motion
Displacement. Suppose during a small time interval Δt the particle moves a distance Δs along the curve to a new position P`, defined by r` = r + Δr. The displacement Δr represents the change in the particle’s position.
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13. General Curvilinear Motion
Velocity
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14. General Curvilinear Motion
Acceleration.
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15. Curvilinear Motion: Rectangular Components
Position. Position vector is defined by
The magnitude of is always positive and defined as
The direction of r is specified by the components of the unit vector
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16. Curvilinear Motion: Rectangular Components
Velocity.
The velocity has a magnitude defined as the positive value of
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17. Curvilinear Motion: Rectangular Components
Acceleration.
The acceleration has a magnitude defined as the positive value of
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18. Curvilinear Motion: Rectangular Components
The acceleration has a direction specified by the components of the unit vector
Since a represents the time rate of change in velocity, a will not be tangent to the path.
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19. Motion of Projectile Constant downward acceleration, no air resistance
Mathematical expressions, ↑ [=] +, → [=] +
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20. Example 12.12
The chipping machine is designed to eject wood chips at vO = 25 ft/s. If the tube is oriented at 30° from the horizontal, determine how high, h, the chips strike the pile if they land on the pile 20 ft from the tube.
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21. Curvilinear Motion: Normal and Tangential Components
When the path of motion of a particle is known, describe the path using n and t coordinates which act normal and tangent to the path
Consider origin located at the particle
Tangential direction
Normal direction
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22. Curvilinear Motion: Normal and Tangential Components
Velocity.
Since the particle is moving, s is a function of time
Particle’s velocity v has direction that is always tangent to the path and a magnitude that is determined by taking the time derivative of the path function s = s(t)
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23. Curvilinear Motion: Normal and Tangential Components
Acceleration
Acceleration of the particle is the time rate of change of velocity
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24. Curvilinear Motion: Normal and Tangential Components
Acceleration
Find
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25. Curvilinear Motion: Normal and Tangential Components
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26. Problem
The automobile is originally at rest at s=0. If it then starts to increase its speed at ft/s2 where t is in seconds, determine the magnitudes of its velocity and acceleration at s = 550 ft.
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27. Problem
At a given instant the train engine at E has a speed of 20 m/s and an acceleration of 14 m/s2 acting in the direction shown. Determine the rate of increase in the train’s speed and the radius of curvature of the path.
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28. Problem
If the speed of the box at point on the track is 30ft/s which is increasing at the rate of ft/s2 , determine the magnitude of the acceleration of the box at this instant.
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29. Curvilinear Motion: Cylindrical Components
Fixed origin
Radial direction
Transverse direction
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30. Curvilinear Motion: Cylindrical Components
Position
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31. Curvilinear Motion: Cylindrical Components or Polar
Velocity
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32. Curvilinear Motion: Cylindrical Components
Acceleration
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33. Example 12-19
The searchlight casts a spot of light along the face of a wall that is located 100m from the searchlight. Determine the magnitudes of the velocity and acceleration at which the spot appears to travel across the wall at the instant θ = 45°. The searchlight is rotating at a constant rate of 4 rad/s
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34. Problem
The slotted arm AB drives pin C through the spiral groove described by the equation r = (1.5Ө) ft, where Ө is in radians. If the arm starts from rest when Ө = 60˚ and is driven at an angular velocity of Ө̇ = (4t) rad/s, where t is in seconds, determine the radial and transverse components of velocity and acceleration of the pin C when t=1 s.
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35. Absolute Dependent Motion
Dependent motions of two particles are normally associated with systems of connected masses via inextensible cords and pulleys.
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36. Absolute Dependent Motion
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37. Problem
If the hydraulic cylinder at H draws in rod BC by 200 mm at 2ft/s, determine how far the slider A moves and the speed of the slider.
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38. Example 3
A man at A is hoisting a safe S by walking to the right with a constant velocity vA = 0.5m/s. Determine the velocity and acceleration of the safe when it reaches the elevation at E. The rope is 30m long and passes over a small pulley at D.
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39. Problem
If block A is moving downward with a speed of 6 ft/s while C is moving down at 18 m/s, determine the speed of block B.
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40. Relative Motion Analysis
The relative position of B with respect to A is given by
The relative velocity and acceleration of B with respect to A are given by
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41. Example 4
A train, traveling at a constant speed of 60 mi/h, crosses over a road. If automobile A is traveling t 45 mi/h along the road, determine the magnitude and direction of relative velocity of the train with respect to the automobile.
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42. Problem
The two particles A and B start at the origin O and travel in opposite directions along the circular path at constant speeds vA=0.7 m/s and vB=1.5 m/s respectively. Determine at t= 2s, (a) the displacement along the path of each particle, (b) the position vector to each particle, and (c) the magnitude of the acceleration of particle B.
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