Chapter 13: Kinetics of a Particle: Force and Acceleration

Sir Isaac Newton  Formulated basic concepts and laws of mechanics  Universal Gravitation  Calculus  Light and optics

First Law Law of inertia - a body in motion will stay in motion and a body at rest will stay at rest unless acted upon by a net external force.Law of inertia 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. Static law

Second Law A particle acted upon by an unbalanced force F experiences an acceleration that has the same direction as the force and a magnitude that is directly proportional to the force F3 F1 a1 F2 a2

Third Law Law of Action-Reaction - For every action, there is an equal and opposite reaction. The mutual forces of action and reaction between two particles are equal, opposite, and collinear.

Newton's Law of Universal Gravitation Law of gravitation - All bodies are attracted to one another with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. –F = forces of attraction –G = universal constant of gravitation = 66.73( )m 3 /(kg.s 2 ) –m 1,m 2 = mass of each of the two particle –r = distance between the centers of the two particles

Gravity on earth? Newton's Law of Universal Gravitation Compare with F = mg so g = GM/r 2 g depends inversely on the square of the distance g depends on the mass of the planet Nominally, g = 9.81 m/s 2 or 32.2 ft/s 2 –At the equator g = 9.78 m/s 2 –At the North pole g = 9.83 m/s 2 –g on the Moon is 1/6 of g on Earth.

Mass and Weight Weight –the amount of gravitational force exerted on a body F = m g W = m g –W: weight (units: N or lbs) –m: mass of the body (units: kg) –g: gravitational acceleration (9.81 m/s 2, 32.2 ft/s 2 ) As the mass of a body increases, its ’ weight increases proportionally Weight is not an inherent property of an object: –mass is an inherent property Weight depends upon location.

13.2 The Equation of Motion Free Body and Kinetic Diagram Free-Body diagram Kinetic diagram

13.3 Equation of Motion for a System of Particles