Lesson 6 Newton s First Law of Motion Inertia

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1 0 Introduction In daily life, motion is everywhere, but we would believe that something was causing it to move. Aristotle on Motion a. In fourth century B.C., Aristotle divided motion into natural motion and violent motion. b. Four elements: Aristotle believed the world was composed of four elements: earth, water, air, and fire. They were the building blocks of the material world. Each element had its own natural place in the hierarchy of the universe. Earth belonged to the lowest position. Water was next, then air, and fire. If any of these were out of its hierarchical position, its natural motion would be to return. c. Natural motion: Straight up or down motion. Heavy things fall (such as rocks) and light things rise (such as smoke). Circular motion was natural for the heavens (such as stars). Since these motions were considered natural, they were not thought to be caused by forces. d. Violent motion: Imposed motion with external cause. It was the result of forces that pushed or pulled. e. It is a commonly thought for nearly 2000 years that if an object was moving against its nature, then a force of some kind was responsible. If there were no force, there would be no motion. So the proper state of objects was one of rest (except in the vertical direction). f. Most thinkers before 6 th century considered that Earth must be in its natural rest place. 2 Copernicus and the Moving Earth a. Astronomer Nicolaus Copernicus formulated his theory of moving Earth. He dissatisfied with the old Ptolemaic system and developed a new theory. The seven propositions of Copernicus' theory are: i) There is no one center in the universe. ii) The Earth's center is not the center of the universe. iii) The center of the universe is near the sun. iv) The distance from the Earth to the sun is imperceptible compared with the distance to the stars. v) The rotation of the Earth accounts for the apparent daily rotation of the stars. vi) The apparent annual cycle of movements of the sun is caused by the Earth revolving around the sun. vii) The apparent retrograde motion of the planets is caused by the motion of the Earth, from which one observes. b. Copernicus worked on his ideas secretly to escape persecution, since his idea was extremely controversial at the time. His main theory is published in his book De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) in the year of his death, 543, though he had arrived at his theory several decades earlier. 3 Galileo on Motion a. Galileo publicly supported Copernicus s theory and suffered a trial and house arrest. b. The work of Galileo is considered to be a significant break from that of Aristotle. He demolished the notion that a force is necessary to keep an object moving. Mr. Lin

2 c. Friction is the force acting between materials that touch as they move past each other. Galileo argued that only when friction is present is a force needed to keep an object moving. d. He noted that a ball rolling down an inclined plane (partly in the direction of gravity) picked up speed. A ball rolling up an inclined plane (a direction opposed by gravity) slowed down. A ball rolling on a level surface (not with or against gravity) has almost constant speed. He claimed that if there is no friction, the ball moved horizontally would move forever. Slope Downward Speed Increases Slope Upward Speed Decreases No Slope Constant Speed e. Galileo described two inclined planes facing each other. A ball released to roll down on one plane would roll up to the other to reach nearly the same height. The smoother the planes were, the closer the heights would be. If the angle of the second plane was smaller, the ball would roll farther. Always, the ball went farther to reach the same height. If the angle of the second inclined plane reduced to zero, only the friction would keep the ball from rolling forever. f. Galileo was concerned with how things move rather than why they move. He stated that this tendency of a moving body to keep moving is natural and that every material object resists change to its state of motion. We call this property of a body to resist change inertia. 4 Newton s Law of Inertia a. Newton s first law: Usually called the law of inertia. Every object continues in a state of rest, or of motion in a straight line at constant speed, unless it is compelled to change that state by an unbalanced force exerted upon it. b. Snapping tablecloth from benesth dishes, sliding a hockey puck along ice, and tightening the head of a hammer by banging the handle are all examples of using Newton w first law. 5 Mass a. Measure of the inertia: The amount of inertia an object has depends on its mass the amount of material present in the object. The more mass an object has, the greater its inertia and the more force it takes to change its state of motion. b. Mass is not volume: Volume is a measure of space and is measured in units such as cubic centimeters (cm 3 or c.c.), cubic meters (m 3 ) and liters. Mass is measured in kilograms. c. Mass is not weight: We often determine the amount of matter in an object by measuring its gravitational attraction to Earth. However, mass is more fundamental than weight. Mass is the quantity of matter in an object and only depends on the number of and the kind of atoms that compose it. Weight is the force of gravity on an object. Weight depends on an object s location. Though they are not the same, they are proportional to each other in a given place. d. The weight unit in U.S. is pound. The SI unit of mass is the kilogram (kg). At Earth s surface, an -kg object has a weight of 2.2 pounds. The SI unit of force is the newton (N), an -kg object has a weight of 9.8 N. e. Weight = mass x acceleration due to gravity or = mg = 9.8 m Mr. Lin 2

3 6 Net Force a. Net force: The combination of all forces acting on an object is called the net force. In the absence of a net force, objects do not change their state of motion. b. Calculate net force: Vector addition can be used to calculate the net force. B A A + B B A A + B B A A - B B A A - B A A 0 A A 0 7 Equilibrium When Net Force Equals Zero a. Statics: Statics is the branch of mechanics concerned with the analysis of force on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity. b. Normal force: When an object rests on a surface, there are two forces involved. One is the force of gravity (weight) which acts on the object, and another force is the support force (or called normal force) of the surface. The normal force actually push up on the object as a compressed spring is pushing up. F N 2 F N 2 F N F N = c. Equilibrium: When an object is at rest, or at constant velocity, with the net force on it being zero, the object is in a state of equilibrium. d. Tension force: When an object hangs from a rope (or scale) and is in equilibrium, the tension in the rope equals to the weight of the object. F T 2 F T 2 F T F T = Mr. Lin 3

4 8 Vector Addition of Forces a. Force addition: An object of hangs from two spring scales. When the spring scales hang at 60 o from the vertical, their readings are each. When the angle has increased to 75.5 o, the readings are 20 N each. As the angle between the scales increases, the tension in the scales must increase for the resultant to remain. b. Vector resolution: The results can be calculated by vector resolution first and then adding the vertical components together. 60 o 60 o 20 N 75.5 o 75.5 o 20 N 2 F T cos = 2 x x cos 60 o = 2 x x /2 = 2 F T cos = 2 x 20 N x cos 75.5 o = 2 x 20 N x /4 = c. For any pair of scales, ropes, or wires supporting a load, the greater their angles from the vertical, the larger the tension force in them. The resultant of the tension forces, or the diagonal of the parallelogram they describe, must be equal and opposite to the load being supported. 9 Free-Body Diagram a. A diagram showing all the forces acting on an object is called a free-body diagram. b. We isolate, or free the object of concern from everything else, and represent that object by a dot. We then draw all the forces vectors acting on the object with its tail starting on the dot. We label each vector to indicate what type of force it represents W (or ) for a gravitational force, N (F N ) for a normal force, f (or F f ) for a friction force, and T (or F T ) for a tension force. c. Drawing a free-body diagram should always the first step in solving physics problems involving forces. 0 Equilibrium Example Problems For all the following problems, assume the air resistance can be neglected. The acceleration due to gravity is g. a. An m-kg block is connecting to a ball through a pulley and is resting on a frictionless inclined plane. The angle of the inclines plane is. What is the mass of the ball? Mr. Lin 4

5 b. An m-kg block is placed on a frictionless inclined plane. The angle of the inclines plane is. (a) How much force exerted at α is required to prevent the block from sliding down the inclined plane? (b) What s the normal force F N? α F N c. An m-kg block is hanging from the ceiling through two ropes and spring scales. The angle between the two ropes and the ceiling are α and β degree respectively. If the spring scales measure the weight in units of newtons (N), what are the readings on the spring scales? α T β T 2 d. An m-kg block is hanging from the ceiling and wall through two ropes and spring scales. The angle between one rope and the ceiling is and another rope is horizontal. If the spring scales measure the weight in units of newtons (N), what are the readings on the spring scales? T T 2 e. An m-kg ball is hanging from the ceiling through a rope and a spring scale. The ball is pulling horizontally by a force F. The angle between the rope and the perpendicular line is. If the spring scales measure the weight in units of newtons (N), (a) what is the reading on the spring scales? (b) What is the force F? T F Mr. Lin 5

6 f. A uniform ball with weight W is placed between two frictionless planes. The angles of the plane A and B are α and β respectively. What is the normal forces exerted from plane A and B to the ball. A B α β g. Two uniform balls with the same weight W and radius r are placed between two frictionless planes with distance D. The centers of both balls are on the same vertical plane. The normal forces at P, Q, R and S are N, N 2, F N and F respectively. Find N, N 2, F N and F in terms of W, D and r. P A N B F F S F N r N 2 Q R D Mr. Lin 6