Properties of Motion It took about 2500 years to different generations of philosophers, mathematicians and astronomers to understand Aristotle's theory of Natural Motion and Violent Motion: Falling bodies fall at steady speed Heavier things fall faster, the speed being proportional to the weight. how to describe motion how a force can cause a motion how to predict the motion caused by a known force 1 Aristotle (384-322 B.C.) First one to think quantitatively about motion The speed of fall of a given object depends inversely on the density of the medium it is falling through, so, for example, the same body will fall twice as fast through a medium of half the density. 2 Galileo Galilei (1564-1642) Experiments to understand. motion: photo Ball rolling down the slope Ball rolling up a slope Ball rolling on a flat surface Objects in free fall Do heavy objects fall faster than the lighter ones? Galileo s Experiments 2. Falling bodies pick up speed at a steady rate New and correct understanding of forces and motion 3 1. Speed remains constant (the first correct law of motion)
Isaac Newton 1642-1727 Properties of Motion 1. Generalized and extended Galileo's discussion of motion 2. Formulated the Laws of Motion 3. Law of Universal Gravitation 4. Explanation of the observed motions of all planets Force: Inertia: Basics terms and concepts action that changes the state of motion of an object. the resistance of an object to the change of its state of motion. "mass" has two meanings: amount of matter measure of inertia (more massive bodies are more inert) 5 6 Force Push or pull, anything that can change the motion of an object Force is a vector quantity - has magnitude and direction To apply a force means to give a push or pull There is a close relationship between force and motion To describe a motion we need to know all forces acting on the object Net force - vector sum of all applied forces 7 Examples of Forces Force of gravity the most universal force known at the Earth surface the force of gravity is the pull of the Earth -- weight Normal Force force exerted by a surface and perpendicular to this surface Force of friction due to the microscopic roughness of surfaces in contact acts in direction opposite to the motion 8
Balanced and Unbalanced Forces Balanced and Unbalanced Forces Balanced forces do not cause motion Normal Force Weight 9 Balanced forces do not cause motion 10 Balanced and Unbalanced Forces Pull Unbalanced forces change the velocity of the object 12
Force, Velocity and Acceleration Motion without acceleration - Balanced forces The First Law of Newton: the Law of Inertia "Unless some net (unbalanced) force changes its state of motion, an object at rest remains at rest and a moving object continues to move forever in a straight line with constant speed. Motion with acceleration - Unbalanced force 13 14 Inertia The Second Law: a = F/m, or F = ma Force m a Acceleration: the rate of change of velocity - speeding up, slowing down, or changing direction of motion "The acceleration of an object is proportional to the net force on it and inversely proportional to its mass". 15 The bigger the force, the bigger the acceleration. The bigger the mass the smaller the acceleration. 16
3. The Third Law: action-reaction "Forces occur in pairs that are equal in magnitude and opposite in direction". Examples of the Third Law Box: weight is balanced by normal force Normal force and force exerted on table - action-reaction pair Consider these interactions: book-table, hammer-nail, rocket-fuel Normal force Box These action-reaction pairs are applied to the two different bodies Table 17 Force exerted on table Weight of box 18 Universal Gravitational Force Every two masses, M and m, attract each other with a force proportional to them, and inversely proportional to the square of the distance between them: M d m Mm F = G 2 d G is the gravitational constant, measured experimentally, G=6.67x10-11 Nm 2 /kg 2 How does gravity work? The Meaning of Force: two broad categories: contact forces: two interacting objects are physically in contact forces resulting from action-at-a-distance: no physical contact; push or pull despite the physical separation Gravitational Field Q: Is the force that Earth exerts on the Moon larger than the force 19 20 that the Moon exerts on the Earth?
Inverse square dependence F ~ 1/d 2 When d doubles, the force decreases 2 2 = 4 times. When d triples, F decreases 3 2 = 9 times. The force decreases rapidly, but never reaches zero! This dependence is frequently seen in nature (gravity, electrostatic forces, brightness) 21