1. Kinetics of a particle

2. Objectives
To analyze the accelerated motion of a particle using the equation of motion with different coordinate systems.
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MEE214 – Dynamics

3. Newton’s Laws of Motions (1687)
First Law 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 unbalanced force.
08/12/61
MEE214 – Dynamics

4. Newton’s Laws of Motions (1687)
Second Law The unbalanced force acting on the particle is proportional to the time rate of change of the particle’s linear momentum.
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MEE214 – Dynamics

5. Newton’s Laws of Motions (1687)
Third Law The mutual forces of action and reaction between two particles are equal, opposite, and collinear.
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MEE214 – Dynamics

6. Equation of Motion Rectangular Coordinates
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MEE214 – Dynamics

7. Procedure for Analysis
Select the inertial coordinate system
Draw FBD
Establish direction and sense of acceleration
Solve for unknowns
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MEE214 – Dynamics

8. Problem 13-23
The winding drum D is drawing in the cable at an accelerated rate of 5 m/s2. Determine the cable tension if suspended crate has a mass of 800 kg.
08/12/61
ME ดร. พิภัทร

9. Problem 13-24
If the motor draws in the cable at a rate of, v=0.05s3/2 m/s where s is in meters, determine the tension developed in the cable when s=10 m. The crate has a mass of 20 kg, and the coefficient of kinetic friction between the crate and the ground is μk = 0.2.
08/12/61
ME ดร. พิภัทร

10. Problem 13-28
The driver attempts to tow the crate using a rope that has a tensile strength of 200 lb. If the crate is originally at rest and has a weight of 500 lb, determine the greatest acceleration it can have if the coefficient of static friction between the crate and the road is μk = 0.4 and the coefficient of kinetic friction is μk = 0.3.
08/12/61
ME ดร. พิภัทร

11. Equation of Motion Normal and Tangential Coordinates
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MEE214 – Dynamics

12. Problem 13-65
Determine the constant speed of the passengers on the amusement-park ride if it is observed that the supporting cables are directed at θ=30⁰ from the vertical. Each chair including its passenger has a mass of 80 kg. Also, what are the components of force in the n, t and b directions which the chair exerts on a 50-kg passenger during the motion?
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MEE214 – Dynamics

13. Equation of Motion Cylindrical Coordinates
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MEE214 – Dynamics

14. Useful Formulas
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ME ดร. พิภัทร

15. Problem 13-88
The boy of mass 40-kg is sliding down the spiral slide at a constant speed such that his position, measured from the top of the chute, has components r=1.5 m, θ=0.7t rad, and z=-0.5t m, where t is in seconds. Determine the components of force Fr, Fθ and Fz which the slide exerts on him at the instant t=2 s. Neglect the size of the boy.
08/12/61
ME ดร. พิภัทร