Kinetics of a particle

Objectives To analyze the accelerated motion of a particle using the equation of motion with different coordinate systems. 08/12/61 MEE214 – Dynamics

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

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. 08/12/61 MEE214 – Dynamics

Newton’s Laws of Motions (1687) Third Law The mutual forces of action and reaction between two particles are equal, opposite, and collinear. 08/12/61 MEE214 – Dynamics

Equation of Motion Rectangular Coordinates 08/12/61 MEE214 – Dynamics

Procedure for Analysis Select the inertial coordinate system Draw FBD Establish direction and sense of acceleration Solve for unknowns 08/12/61 MEE214 – Dynamics

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 ME212 ดร. พิภัทร

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 ME212 ดร. พิภัทร

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 ME212 ดร. พิภัทร

Equation of Motion Normal and Tangential Coordinates 08/12/61 MEE214 – Dynamics

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? 08/12/61 MEE214 – Dynamics

Equation of Motion Cylindrical Coordinates 08/12/61 MEE214 – Dynamics

Useful Formulas 08/12/61 ME212 ดร. พิภัทร

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 ME212 ดร. พิภัทร