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Kinematics of particles

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• 1. F E B R U A R Y 2 6 , 2 0 1 4 KINETICS AND PARTICLES: FORCE and ACCELERATION
• 2. 2 Main Factors that affect motion in an Object 1. The Forces acting on an object 2. The Mass of an object
• 3. Mass &#x2013; amount of matter in an object - property of an object that specifies how much resistance an object exhibits to change in velocity Acceleration &#x2013; is the rate of change of the velocity Force &#x2013; push or pull of an Object &#x2013; according to Isaac Newton, these are what causes any change in the velocity of an object at the same time, it causes acceleration.
• 4. Newton's Laws Newton described force as the ability to cause a mass to accelerate. First law: When the sum of the forces acting on a particle is zero, its velocity is constant. In particular, if the particle is initially stationary, it will remain stationary. Or if it moves with constant speed in a single direction. Second law: The rate of change of linear momentum of an object is directly proportional to the applied force F and the object moves in the direction in which force F is applied. If the mass is constant, the sum of the forces is equal to the product of the mass of the particle and its acceleration. F = ma
• 5. Newton's Laws Third law: The forces exerted by two particles on each other are equal in magnitude and opposite in direction. F2 = &#x2212;F1 4th Law : Newton&#x2019;s Gravitational Attraction This law governs the gravitational attraction between any two particles/bodies.
• 6. Newton's 2nd Law of Motion The force and acceleration are directly proportional, the constant of proportionality can be determined in the ratio m = F1 / a1, on the other hand if another force of different magnitude say, (F2) is acted on an object, it will create another acceleration say, a2 such that m = F2 / a2&#x2026; Thus, m serves as the constant of proportionality. Equation of Motion F = ma
• 7. In the case that 2 or more forces acting on a particle, the resultant force is determined by a vector summation of all the forces. FR = F Generally, the equation of motion is written as F = ma Static Equilibrium: F = 0 FR = F = 0 thus , a = 0 Dynamic Equilibrium: FR = F = ma F &#x2013; ma = 0
• 8. Equations of Motion: Rectangular Coordinates In a x,y &amp; z frame of reference, the forces acting on a particle can be expressed in terms of i, j, k components, so we have F = ma Fx i + Fy j + Fz k = m ( ax i + ay j + az k ) To satisfy the given condition with its respective i, j, k components: Fx = max Fy = may Fz = maz
• 9. F R I CT I O N : If the particle contacts on rough surface, it is necessary to use the frictional equation, which relates the coefficient of Kinetic Friction &#xB5;k to the magnitude of the Frictional Force (Ff) and Normal Force (N) acting on the surface of contact, Ff = &#xB5;k N Where: Ff - frictional force acting opposite the subjected Force &#xB5;k - coefficient of kinetic friction N - normal force - force acting perpendicular to the point of contact.
• 10. The 50 kg crate rests on a horizontal plane for which the coefficient of kinetic friction is &#xB5;k = 0.3 . If the crate is subjected to a 400-N towing force 30&#x2070; from the horizontal, determine the velocity of the crate in 5 sec starting from rest. EXAMPLE # 1
• 11. The 100 kg block A is released from rest. If the mass of the pulleys and the cord are neglected, determine the speed of the 20 kg block B in 2 seconds. EXAMPLE # 2
• 12. At a given instant the 10 kg block A is moving downward with a speed of 6 m/s. determine its speed 2 sec later. Block B has a weight of 4 kg, and the coefficient of kinetic friction between it and the horizontal plane is &#xB5;k = 0.2 . Neglect the mass of the pulleys and cord. EXAMPLE # 3
• 13. Determine the time needed to pull the cord at B down 4 m starting from rest when a force of 10 kg is applied to the cord. Block A weighs 20 kg. Neglect the mass of the pulleys and cords. EXAMPLE # 4