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Chapter 2, 4 &5 Newton’s Laws of Motion Aristotle (384-322)BC Aristotelian School of Thought Natural Motion Every Object in the universe has a proper place, determined by its nature. Heavier objects strive harder to be in their proper place. This implies that heavier objects fall faster than lighter objects. Violent Motion: All motion results from a push or pull. Except for celestial objects (the realm of the Gods), the normal “natural” state of an object was to be at rest. The Earth does not move. Aristotle’s school of thought dominated western culture for the next 2000 years, until the 16th century. Celestial Spheres Copernicus and the Moving Earth Ptolemaic Model • Copernican Model Copernicus asserts that the Sun is at the center of the solar system instead of the Earth. This runs contrary to the Aristotelian school of thought. 1543 – Copernicus publishes De Revolutionibus Galileo Galilei Galileo is considered to be the father of experimental science. Galileo demolished the Aristotelian model by doing experiments and proving it wrong. Inclined plane demo Galileo’s Inclined Planes Inertia The tendency of a body to resist changes in its motion. Mass is a measure of inertia – A more massive body has more inertia. Chapter 3 Linear Motion Description of Motion -Kinematics dis tan ce Speed time Average Speed = total distance/time Total distance = (Average speed) x (time) Velocity Speed in a particular direction Examples 70mi/h due north --- is a velocity 70mi/h ----- is a speed Approximate Speeds in Different Units 20km/h 12 mi/h 6 m/s 40 km/h 60 km/h 25 mi/h 37 mi/h 11 m/s 17 m/s 65 km/h 40 mi/h 18 m/s 80 km/h 50 mi/h 22 m/s 88 km/h 100 km/h 55 mi/h 24 m/s 62 mi/h 28 m/s 120 km/h 75 mi/h 33 m/s Velocity is proportional to the time velocity (m/s) 200 150 100 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 time(sec) Acceleration Acceleration = change in velocity/change in time V a t How quickly how fast changes Constant Acceleration – Free Fall Near the surface of the earth, all objects fall with the same acceleration baring effects from air friction. In this case, a = g = 9.8m/s/s or 32 ft/s/s or a = g = 9.8m/s2 or 32 ft/s2 Distance traveled Assume a= 2 m/s/s and is constant. 1 sec 2 sec 3 sec The distance traveled is proportional to the time squared. 1 2 d at 2 1 2 d at 2 2d t a Distance vs time d = ½ gt2 distance (m) 2000 1500 1000 500 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 time (sec) x d V t t V a t If a is constant V at V at V Vo a(t to ) V Vo a(t to ) If the particle starts with an initial velocity of Vo at zero seconds (to = 0 sec) then: V Vo at V Vo at Assume Vo = 1m/s and a = 10m/s2 t(sec) V(m/s) 0s 1 m/s 1s 11 m/s 2s 21 m/s 3s 31 m/s 4s 41 m/s 5s 51 m/s 6s 61 m/s 7s 71m/s 8s 81 m/s 9s 91m/s 10 s 101 m/s 1 11 21 31 41 51 61 71 81 91 101 V 51m / s 11 Vo V 1 101 V 51m / s 2 2 x d V t t V a t Vo V V 2 For free-fall a g y d V t t x y d Vo V V 2 V g t Newton’s Laws of Motion Newton’s First Law of Motion Every object continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it. Newton’s Second law of Motion The acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object. Fnet ma Newton’s Third Law of Motion For every action, there is always opposed an equal reaction. By “action”, we mean a force. Action/reaction forces do not act on the same object. Types of Forces Gravitational Friction Normal Electromagnetic Forces between masses Contact force Contact force Forces between charges. Nuclear Forces between nuclear particles (protons, neutron) Spring Restoring Forces When the acceleration is g we have Free Fall m 2m F 2F F g m 2F g 2m When acceleration is zero Equilibrium N Fnet N mg Fnet ma 0 N mg 0 mg N mg When acceleration is zero Equilibrium N mg N v = constant Fa f mg FH Fa f 0 Fa f Action/Reaction pairs Action: Reaction: Tire Pushes on Road Road pushes on Tire Action/Reaction Action: Rocket pushes on gas Reaction: Gas pushes on rocket Nonlinear Motion Velocity : A vector quantity A B A+B Vector quantities have magnitude and direction A R=A+B B R is called the resultant vector The Pythagorean Theorem R2 = A2 + B2 A B Projectile Motion Any object that is projected by some means and continues in motion under the influence of gravity and air resistance is called a projectile. The path of a projectile is called the trajectory Projectile Motion -g vector Projectile Range 14 At 30 degrees Vertical Distance (m ) 12 10 8 6 At 15 degrees 4 2 0 0 20 40 60 Horizontal distance (m) 80 100 120 Fast Moving Projectiles Satellites The Earth’s curvature drops a vertical distance of 5 meters every 8,000 meters horizontally Circular Motion V=r r