Chapter 2 Motion 2-1. Speed 2-2. Vectors 2-3. Acceleration 2-4. Distance, Time, and Acceleration 2-5. Free Fall System 2-6. Air Resistance 2-7. First Law of Motion 2-8. Mass 2-9. Second Law of Motion 2-10. Mass and Weight 2-11. Third Law of Motion 2-12. Circular Motion 2-13. Newton's Law of Gravity 2-14. Artificial Satellites 2-1. Speed Definitions: Speed The rate at which something moves a given distance. Faster speeds = greater distances General formula for speed: Speed = distance / time Abbreviations commonly used: d = distance t = time v = speed v = d/t 2-1. Speed Velocity d 100miles miles v = = = 40 = 40mph t 2.5hours hour Distance miles ( ) 6hours miles d = v t = 30 = 180 hour Time d 100miles miles t = = = 2.5 = 2. 5hours v 40miles / hour miles / hour 1
2-1. Speed Average speed is the total distance traveled by an object divided by the time taken to travel that distance. Instantaneous speed is an object's speed at a given instant of time. 2-2. Vectors Magnitude of a quantity tells how large the quantity is. Scalar quantities have magnitude only. Vector quantities have both magnitude and direction. 2-2. Vectors Velocity is a vector quantity that includes both speed and direction. 2
2-3. Acceleration Acceleration of an object is the rate of change of its velocity and is a vector quantity. For straight-line motion, average acceleration is the rate of change of speed: change in speed Accelerati on = time interval vf vi a = t 2-3. Acceleration 3 Types of Acceleartion Speeding Up Slowing Down Turning 2-4. Distance, Time and Acceleration V avg = (V 1 + V 2 ) 2 (20 mph + 60 mph ) = 40mph 2 d = v avg t d = ½at 2 30 mph 2 hr = 60 miles ½ 10 m/s/s 5 2 = 125 m 3
2-5. Free Fall The acceleration of gravity (g) for objects in free fall at the earth's surface is 9.8 m/s 2. Galileo found that all things fall at the same rate. 2-5. Free Fall The rate of falling increases by 9.8 m/s every second. Height = ½ gt 2 For example: ½ (9.8 )1 2 = 4.9 m ½(9.8)2 2 = 19.6 m ½ (9.8)3 2 = 44.1 m ½ (9.8)4 2 = 78.4 m 2-5. Free Fall A ball thrown horizontally will fall at the same rate as a ball dropped directly. 4
2-5. Free Fall A ball thrown into the air will slow down, stop, and then begin to fall with the acceleration due to gravity. When it passes the thrower, it will be traveling at the same rate at which it was thrown. 2-5. Free Fall An object thrown upward at an angle to the ground follows a curved path called a parabola. 2-6. Air Resistance In air A stone falls faster than a feather Air resistance affects stone less In a vacuum A stone and a feather will fall at the same speed. 5
2-6. Air Resistance Free Fall A person in free fall reaches a terminal velocity of around 54 m/s With a parachute, terminal velocity is only 6.3 m/s Allows a safe landing 2-6. Air Resistance Ideal angle for a projectile In a vacuum, maximum distance is at an angle of 45 o With air resistance (real world), angle is less Baseball will go furthest hit at an angle of around 40 o 2-7. First Law of Motion The first law of motion states: If no net force acts on it, an object at rest remains at rest and an object in motion remains in motion at a constant velocity. 6
Foucault Pendulum Inertia keeps a pendulum swinging in the same direction regardless of the motion of the earth. This can be used to measure the motion of the earth. As the Foucault Pendulum swings it appears to be rotating, but it is the earth that is rotating under it. To the right is the Foucault Pendulum at the Pantheon in Paris, France. Foucault Pendulum Other Web sites that illustrate the Foucault Pendulum. http://www.physclips.unsw.edu.au/jw/foucault_ pendulum.html http://en.wikipedia.org/wiki/file:foucaultrotz.gif http://aspire.cosmicray.org/labs/scientific_method/pendulum.swf http://www.calacademy.org/products/pendulum/ page7.htm http://www.youtube.com/watch?v=nb2sxlyw KkM 2-8. Mass Inertia is the apparent resistance an object offers to any change in its state of rest or motion. 7
2-9. Second Law of Motion Newton's second law of motion states: The net force on an object equals the product of the mass and the acceleration of the object. The direction of the force is the same as that of the acceleration. F = Ma 2-9. Second Law of Motion A force is any influence that can cause an object to be accelerated. The pound (lb) is the unit of force in the British system of measurement: 1 lb = 4.45 N (1 N = 0.225 lb) 2 1newton = 1 N = 1(kg)(m/s ) 2-10. Mass and Weight Weight Definition: The force with which an object is attracted by the earth s gravitational pull Example: A person weighing 160 lbs is being pulled towards the earth with a force of 160 lbs (712 N). Near the earth s surface, weight and mass are essentially the same Weight = (mass)(acceleration of w = mg gravity) 8
2-11. Third Law of Motion The third law of motion states: When one object exerts a force on a second object, the second object exerts an equal force in the opposite direction on the first object. 2-11. Third Law of Motion Examples of the 3 rd Law 2-12. Circular Motion Centripetal force is the inward force exerted on an object to keep it moving in a curved path. Centrifugal force is the outward force exerted on the object that makes it want to fly off into space. 9
2-12. Circular Motion 2-12. Circular Motion 833 N is needed to make this turn. If he goes too fast, which wheels are likely to come off the ground first? 2-13. Newton's Law of Gravity Gravitational force Gm m = F = R 1 2 2 G = 6.67 x 10-11 N m/kg 2 10
2-13. Newton's Law of Gravity How can we determine the mass of the earth using an apple? This illustrates the way scientists can use indirect methods to perform seemingly impossible tasks 2-13. Newton's Law of Gravity How can we determine the mass of the earth using an apple? This illustrates the way scientists can use indirect methods to perform seemingly impossible tasks Gravitational force on apple GmM = mg R = F = 2 2 2 6 2 gr (9.8 m / s )(6.4 10 m) 24 M = = = 6 10 kg 11 2 2 G 6.67 10 N m / kg 2-15. Artificial Satellites The world's first artificial satellite was Sputnik I, launched in 1957 by the Soviet Union. GPS-Global Positioning Satellite 11
2-15. Artificial Satellites The escape speed is the speed required by an object to leave the gravitational influence of an astronomical body; for earth this speed is about 40,000 km/h. 2-15. Artificial Satellites The escape speed is the speed required by an object to leave the gravitational influence of an astronomical body; for earth this speed is about 40,000 km/h. Lecture Quiz 2 1. What are Newton s three laws of motion? 2. What is the acceleration due to gravity? 3. What is the difference between mass and weight? 4. What is the difference between centripetal and centrifugal forces? 5. What is the equation for Newton s law of gravity? 12
Lecture Quiz 2 1. What are Newton s three laws of motion? 1) Things have tendency to stay in constant motion. (Inertia) 2) F=ma 3) For every action, equal opposite reaction. 2. What is the acceleration due to gravity? 9.8 m/s 2 or 32 ft/s 2 3. What is the difference between mass and weight? Weight is due to the force of gravity and mass is the amount of matter and is the same everywhere regardless of the force of gravity. Lecture Quiz 2 4. What is the difference between centripetal and centrifugal forces? Centripital-inward force Centrifugal-outward force 5. What is the equation for Newton s law of gravity? G m 1 m 2 F= ----------- R 2 13
Lecture Quiz 2 1. How far can you go with a velocity of 20 miles/hour for 4 hours? 2. How far would you fall in 4 seconds? 3. What are the three types of acceleration? 4. What causes the Foucault Pendulum to swing in different directions? 5. What is Newton s second law of motion? Lecture Quiz 2 How far can you go with a velocity of 20 miles/hour for 4 hours? 20mi/hr x 4hr = 80 miles How far would you fall in 4 seconds? ½ (9.8)42 = 78.4 m What are the three types of acceleration? speed up, slow down, turn What causes the Foucault Pendulum to swing in different directions? rotation of earth What is Newton s second law of motion? F=ma Lecture Quiz 2 4. What is the difference between centripetal and centrifugal forces? Centripetal force is an attractive force between the center and the revolving body. Centrifugal force is the repulsive force between the center and the revolving body or the inertia to travel in a straight line. 5. What is the equation for Newton s law of gravity? Gravitational force = F = Gm m R 1 2 2 14