PHY 110 Introduction to Physics Dr Henry SC

PHY 110, Introduction to Physics Dr. Henry SC 453, 572 -6164 (alt 572 -5309) E-Mail: henryh 1@nku. edu Web Site: www. nku. edu/~henryh 1/ © Hugh Henry, 2008

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Chapter 2 Newton’s Laws © Hugh Henry, 2008

Galileo Galilei, 1564 -1642 • Built on Work of Copernicus • Found Mathematics suggested the Sun is the Center of the Solar System The_First_Revolution_in_Physics 4

Sir Isaac Newton, 1642 -1727 • Inventor of Calculus • Father of Physics – Newton’s Laws govern “Classical Mechanics, ” and dominated physics until Einstein • Invented reflecting telescope • Newton’s Law of Universal Gravitation explained motion of Heavenly bodies 5

Sir Isaac Newton, 1642 -1727 Nature and Nature’s laws lay hid in night God said “Let Newton be” and all was light” – Alexander Pope 6

Force • The concept of Force is is the key new concept of Classical Mechanics (aka Newtonian Mechanics) • To understand Classical Mechanics, we must understand Force 7

Force n Force is a push or pull on a body. It usually causes: a distortion in the body, n a change in the body’s velocity, or n both. n n Force is a vector. n Force is the agent for a change in motion. Forces_and_Vectors 8

Force is a push or pull acting on a body 9

Force is a push or pull acting on a body 10

Force usually causes some distortion of the body, a change in its velocity, or both 11

Force usually causes some distortion of the body, a change in its velocity, or both 12

Force usually causes some distortion of the body, a change in its velocity, or both 13

Force is a vector 14

Force is a vector 15

Force n Force is a push or pull on a body. It usually causes: a distortion in the body, n a change in the body’s velocity, or n both. n n Force is a vector. n Force is the agent for a change in motion. 16

Force, cont’d n The units of force include: n SI: newton (N) n English: pound (lb), ounce (oz) or ton (2000 lb). n To convert between SI and English: 17

Weight: the Force of Gravity n Weight is the force of gravity acting on a body. n We typically use the symbol W. n Your weight depends on the force of gravity on the planet you are on. n A 200 lb person on Earth weighs about 33 lb on the Moon. 18

Weight: the Force of Gravity n Downward force of gravity is the same whether a body is stationery or moving – and how it is moving

The Force of Friction n Friction is a resistive force to relative motion between two bodies or substances in contact. Between the tires and the road; n Between the boy and the air. n 20

The Force of Friction n Friction is a resistive force to relative motion between two bodies or substances in contact. Between the tires and the road; n Between the boy and the air. n n Friction is proportional to the force it opposes 21

Friction Provides the Centripetal Force to Keep Your Car on the Road Going Around a Curve

Weight and Friction Weight is always a force toward the Earth’s center, but it might not always appear that way. n Consider a box on a ramp. n We can break the weight into “components” parallel and perpendicular to the ramp. The perpendicular component holds the box on the ramp. n Friction opposes the parallel component, which accelerates the box down the ramp. n

Two Types of Friction n Static Friction acts when there is no relative motion between two objects in contact. n Kinetic (or Dynamic) Friction acts when there is relative motion between two objects in contact. 24

Examples of Static Friction 25

Bicycle brakes are an example of Kinetic Friction 26

A box on a ramp demonstrates both static and kinetic friction 27

The Force of Friction, cont’d n Friction is proportional to the perpendicular weight component, which holds the box on the ramp. n As the ramp becomes steeper and steeper, this component goes lower and lower. 28

The Force of Friction, cont’d n Yet as the ramp becomes steeper, the parallel weight component, a force to accelerate the box down the ramp, gets bigger and bigger. n Friction must oppose this component. 29

The Force of Friction, cont’d n Hence as the ramp becomes steeper, the maximum force of friction goes down, while the force to move the box goes up. n For a time, the force of static friction is high enough to hold the box on the ramp (b), Ff = Fg 30

The Force of Friction, cont’d n Eventually, the maximum friction is equal to the accelerating force (c), Ff = Fg n For steeper ramps, the accelerating force is greater than friction (d), Ff < Fg – now dynamic friction (less than static friction). 31

The Force of Friction, cont’d n Static friction is the resistance you experience when you try to start sliding an object. n It is static because there is no relative motion between the surfaces. n Kinetic friction is the resistance you experience while sliding an object. n It is kinetic since there is relative motion. 32

Newton’s first law of motion n Newton’s First Law of Motion states: An object will remain at rest or in motion with constant velocity unless acted on by a net external force. n An external force is a force applied to the object from some other object. n force from an impact, gravity, air resistance, etc. Newton_s_First_Law_of_Motion 33

Section 2. 2: Newton's First Law of Motion At Rest Constant Velocity • An object will remain at rest or in motion with constant velocity unless acted on by a net external force. 34

Newton's First Law of Motion n An object will remain at rest or in motion with constant velocity unless acted on by a net external force. n An object at rest will remain at rest n An object that is already moving will not speed up, slow down, or change direction unless a force acts on it. Truck and Ladder 35

Newton’s first law of motion, cont’d n The force can be with, against, or oblique to the motion 36

Newton’s first law of motion, cont’d n The ball was at rest until kicked by the 1 st boy n The ball would have continued in the same direction – but was kicked by the 2 nd boy 37

Newton’s first law of motion, cont’d n The net force is the vector sum of all external forces. n n If you and a friend push on opposite ends of a truck with the same force, the net force is zero — the forces cancel. If you push in the same direction, there is a non-zero net force. 38

Newton’s first law of motion, cont’d n If the two forces are in different directions, the net force is an “in-between” direction. 39

Newton’s first law of motion, cont’d n Remember centripetal acceleration? n The acceleration experienced by an object moving in a circular path. n There must be a force pulling the object toward the center. n Otherwise the object would fly off. 40

When Centripetal Force is stopped. . . An object in motion will remain in motion with constant velocity unless acted on by a net external force, so the ball will fly off at a tangent to the circle

According to Newton’s First Law. . . n Where does little David release his slingshot to hit Goliath. . . ?

Newton’s first law of motion, cont’d n You can create an “artificial gravity” in a space station by rotating it. 43

Mass n Mass is a measure of an object’s resistance to acceleration, i. e. , changes in the object’s motion. n It also indicates the amount of matter in an object. 44

Mass is a measure of an object's resistance to acceleration 45

Mass, cont’d n An object of little mass requires little force to accelerate it. n A massive object requires a much larger force to give it the same acceleration. 46

Mass, cont’d n The mass of the object is independent of the force of gravity of the planet you are on. n The weight of an object depends on your planet. . . eg, for a 1 kg hammer. . . 47

Inertia n An object in motion will remain in motion with constant velocity unless acted on by a net external force (Newton’s First Law) n Mass is a measure of an object's resistance to acceleration. n Inertia reflects an object’s resistance to acceleration. . . the deceleration force necessary to slow it or stop it 48

The understanding that gravity is just another force comes from Einstein’s theory of General Relativity. . . which also assumes that all systems are Inertial systems in curved spacetime You don’t have to remember this!

Newton’s 2 nd law of motion n Newton’s 2 nd Law of Motion states that an object is accelerated when a net external force acts on it. n The net force equals the object’s mass times its acceleration: Newton_s_Second_Law_of_Motion 50

Newton’s 2 nd law of motion, cont’d n Think about why you might add more dogs to a sled: F = ma n Acceleration is proportional to Force: a = F/m 51

Newton’s 2 nd law of motion, cont’d n A force opposite to the velocity produces deceleration: F = ma n Acceleration is proportional to Force: a = F/m 52

F= ma a = F/m acceleration is inversely proportional to mass 53

Newton’s 2 nd law of motion, cont’d n The object will accelerate according to n If the object experiences a centripetal acceleration, the centripetal force is 54

For a body in circular motion at the end of a string. . . The Centripetal Force is the String Tension

Newton’s 2 nd law of motion, cont’d n The SI unit of force, the newton, is defined according to Newton’s 2 nd law: 56

Newton’s 2 nd law of motion, cont’d n A falling object accelerates due to the Earth’s gravity at n So the force the object feels from Earth, i. e. , its weight, is: 57

Example 2. 2 An automobile manufacturer decides to build a car that can accelerate uniformly from 0 to 60 mph (27 m/s) in 10 s. The car’s mass is to be about 1, 000 kilograms. What is the force required? 58

Example 2. 2 ANSWER: The problem gives us: The force is: 59

Example 2. 2 DISCUSSION: What produces this force? n n The engine provides the power to turn the wheels. . . but the force that moves the car is the friction between the car’s tires and the road. If the road is too slick, the tires cannot get enough “grip” and they spin. 60

Example 2. 3 In Example 1. 5, we computed the centripetal acceleration of a car going 10 m/s around a curve with a radius of 20 meters. If the car’s mass is 1, 000 kilograms, what is the centripetal force? 61

Example 2. 3 ANSWER: The problem gives us: The force is: 62

Example 2. 3 DISCUSSION: Where does this force come from? n It is the friction between the tires and the road. n If the road is too slick, the tires could not generate this force, and the car slides into the ditch. 63

International System of Units (SI) 64

International System of Units (SI) 65

Types of motion free-fall n Free-fall is a type of motion in which the only force acting on the object is the object’s weight. n There is no friction, no air resistance, etc. n Gravity always acts toward the Earth’s center. 66

Types of motion free-fall, cont’d n A ball thrown upward will slow-down because gravity is “pulling” down on the ball. 67

Types of motion free-fall, cont’d Eventually it will stop. n It will then fall back to the Earth due to gravity. n n The time it takes to go up is the same amount of time for it to fall. 68

Projectile Motion Projectile. Motion. Waterslide. mov 69

Types of motion Projectile Motion n Why does a football follow a curved trajectory? ANSWER: n Gravity acts in the vertical (Newton’s 2 nd Law). n So the vertical speed changes. n Ideally, there is no force in the horizontal direction (Newton’s 1 st Law). n The horizontal speed does not change. 70

Types of motion Projectile Motion n Why does a football follow a curved trajectory? ANSWER: n So the ball goes up and down just like if you had thrown it straight-up. n But the horizontal speed carries it downfield. Projectile Motion Truck & Ball 71

Projectile Motion Constant acceleration d = ½at 2 Constant velocity d = vt Non-Horiz Projectile 72

Projectile Motion follows shape of a Parabola d = at 2/2 d = vt 73

Droplets of water graphically show pattern of parabola 74

Plane & Package d = vt v = at d = at 2/2 Projectile Motion v = at d = at 2/2 An arrow shot from a bow and an arrow dropped from the same height hit the ground at the same time. They follow the same vertical equations. 75

A golf ball goes up to a maximum height (its apex), then falls to the ground. It takes the same time for a golf ball to hit the ground as it takes for a ball dropped from its apex. They follow the same equations. v = at d = at 2/2 76

Non-Constant Forces

Types of motion simple harmonic motion n Imagine a block attached to a spring. n If we stretch the spring and release it, the block moves in a regular, periodic fashion. 78

Types of motion simple harmonic motion n This type of motion is called simple harmonic motion. n Notice: The speed is a zero when the block is farthest from its rest position. n The speed is a maximum when the block passes through its rest position. n 79

A Pendulum Works the Same Way The speed is zero when the bob is farthest from its rest position, and a maximum when it goes through its rest position. 80

Harmonic Motion is Periodic 81

Spring Motion Equations F = kd F = Force k = spring constant d = distance from center Frequency of Oscillation

Pendulum Motion Equation Frequency of Oscillation

Definition of a Meter § A meter was first defined as the length of a pendulum with a half-period of 1 second. §T=2 s § f = 0. 5 Hz

Types of motion falling with air resistance n What really happens when you drop an ball? n Think about the forces acting on the ball. n Gravity is accelerating it downward. n The air offers resistance, trying to prevent the ball’s descent. 85

Types of motion falling with air resistance, cont’d n The ball’s weight pulls it down. n The air has to be forced out of the ball’s way — it exerts an upward force trying to slow the ball down. 86

Types of motion falling with air resistance, cont’d n As the ball’s speed increases, the force of air resistance increases. n Eventually the ball no longer accelerates. n At this point, the terminal velocity has been reached. n The ball continues to fall at a constant velocity. 87

Falling Body With Air Resistance Skydiving 88

Newton’s third law of motion n Newton’s 3 rd Law of Motion states that forces always occur in pairs: n When one object exerts a force on a second object, the second exerts an equal and opposite force on the first. Newton_s_Third_Law_of_Motion 89

Newton’s third law of motion, cont’d n If object A exerts a force on object B, then object B exerts an equal force in the opposite direction on A: n When you fall down, you feel the Earth exerting a force on you but you also exert that same force on the Earth. 90

Newton's Third Law of Motion n Forces always come in pairs n When one object exerts a force on a second object, the second exerts an equal and opposite force on the first. n Popularly stated: “For every Action there is an Equal and Opposite Reaction” n Be careful, this is a subtle point; examples follow 91

The key concept is: when there is no motion. . . the net force is zero

Man Sitting in a Chair n No Motion Takes Place n v = 0, a = 0 n Net Force = 0 93

Think about pushing a wall. n You push the wall n The wall pushes back n No Motion Takes Place n v = 0, a = 0 n Net Force = 0 94

Horse pulls cart with constant velocity • v = constant, a = 0 • Net Force = 0 Cart pulls backward on horse Horse pulls Forward on cart 95

Newton’s third law of motion, cont’d n Think about a man with roller skates pushing off against a wall. He pushes against the wall. n The wall pushes back. n The push of the wall causes him to move away. n The 3 rd Law Force is real! n 96

Rockets are propelled by “ 3 rd Law” reverse forces 97

Newton’s third law of motion, cont’d n Consider an airplane’s wing. n Due to the angle of attack, the air impacts the bottom of the wing. n The wing pushes the air out of the way. n The air pushes back and provides some lift. n More on this in Chapter 4 98

Pulling out a Dresser Drawer • Friction of Drawer Exerts Force of Resistance • With no motion, v = 0, a = 0, Net Force = 0 • There is motion until the Drawer Comes out, – then Pulling Force > Resistance Force • Net force = 0 again when drawer is pulled with constant velocity 99

Pulling force and “ 3 rd law force” (from friction) are the same, until movement just begins Then they may or may not be the same, depending on whethere is acceleration or constant velocity 100

rd “ 3 Law” forces on lady in elevator • Scale reflects force of elevator on passenger • When elevator is stopped v = 0, a = 0, Net Force = 0 – force of elevator on passenger is 3 rd law force = force of gravity • When elevator goes up, Net Force is not 0; force on elevator is added to the 3 rd law force (equal to gravity) • When elevator moves at constant velocity, v = constant, a = 0, Net Force = 0 – force of elevator on passenger is 3 rd law force = force of gravity • Similar situation when the elevator goes down 101

Summary of 3 rd Law Force Conditions in an Elevator Physics No acceleration v = constant Upward Acceleration Downward Acceleration (Downward Deceleration) (Upward Deceleration) Free Fall 102

Elevator Problem In other words, if the elevator is accelerating or decelerating as it moves up or down, the scale reading reflects the vector addition of the “ 3 rd law” reverse force of gravity (always up) and the elevator acceleration (up or down). If the elevator is not accelerating, the scale reading reflects the person’s weight. . ie, W = mg 103

Newton’s 3 rd Law Applied to Block and Tackle Force Addition Force exerted is always based on 3 rd Law 104

Newton’s Third Law 105

The law of universal gravitation Newton calculated the centripetal acceleration of the moon based on earlier astronomical measurements, and realized it was inversely proportional to the square of the distance • a=v 2/r • The Moon’s orbital radius is 60 times the earth’s radius • The Moon’s centripetal acceleration is g/3600 = g/602 • F ~ 1/d 2 Gravitation 106

107

The law of universal gravitation n Newton’s Law of Universal Gravitation states that every object exerts a gravitational force on every other object. The force increases as either object’s mass increases. n The force decreases as the objects move farther apart. n 108

The law of universal gravitation, cont’d n Mathematically, we can write n n n m 1 is the mass of one object m 2 is the mass of the other object d is the center-to-center distance separating the objects. 109

The law of universal gravitation, cont’d n Note that Newton’s 3 rd law means: n the Earth pulls down on you with a force equal to your weight, and n you pull “up” on the Earth with you’re a force equal to your weight. n You move more than the Earth because the Earth is much more massive than you. 110

Moon’s gravity exerts the same force on the Earth as the Earth’s gravity exerts on the Moon 111

Cavendish Experiment with Torsion Balance (1798) Determined Gravitational Constant G = 6. 67 x 10 -11 N-m 2/kg 2 112

The law of universal gravitation, cont’d n Using the gravitational constant, we can write the law of gravity as 113

Force of Gravity between a Large Body and Two Smaller Bodies 114

The law of universal gravitation, cont’d • If you could stand on a tower 4, 000 miles high, you would weigh one-fourth your usual weight. – You are 2×’s farther from the Earth’s center. 115

Example Problem 2. 25 A space probe is launched from the Earth, headed for deep space. At a distance of 10, 000 miles from the Earth’s center, the gravitational force on it is 600 lb. What is the size of the force when it is 20, 000 miles from the Earth’s center? 116

Example Problem 2. 25 ANSWER: The problem gives us: The force is: 117

Example Problem 2. 25 ANSWER: From the given info, we know: We can write these equations as 118

Example Problem 2. 25 ANSWER: So we have, 119

Example Problem 2. 25 ANSWER: The requested force is 120

Example Problem 2. 25 DISCUSSION: We could solve for the mass using Newton’s Law of Universal Gravitation. . . but it would require lots of calculation. This approach is less work and gives us some insight into the nature of the gravitational force. 121

The law of universal gravitation, cont’d n We can combine the law of gravity and Newton’s 2 nd law to calculate the gravitational acceleration. n Let’s take: M to be the Earth’s mass, n R to be the Earth’s radius n n distance from you to the Earth. 122

The law of universal gravitation, cont’d n Equating our usual formula for weight to the actual gravitational force: 123

The law of universal gravitation, cont’d n This gives us a method to calculate the gravitational acceleration: 124

Example Let’s calculate the acceleration due to gravity at the Earth’s surface: 125

Example ANSWER: 126

Example DISCUSSION: The Earth is not a perfect sphere. We used an average radius so we obtained an average acceleration (at sea level). Notice that we never had to worry about the mass of the accelerating object. 127

Example We can also calculate the acceleration due to gravity at the Moon’s surface: 128

Example ANSWER: 129

Example DISCUSSION: You would weigh one-sixth your usual weight on the Moon. Things fall at one-sixth the rate. You could jump about six times higher. 130

Gravitational “Field” • A “Field” is a Force Waiting to Happen • The closer the field lines are together, the stronger the force • The further the field lines are apart, the weaker the force • “Field Theory” is very important in physics (but not in this course) 131

The concept of a “field” is well illustrated by a “Magnetic Field” discussed in Chapter 8 Where the force is the stronger, the density of iron filings is greater 132

Orbital Motion Newton’s Cannon Ball Analogy n Shoot a Cannon Ball with Greater and Greater Velocity n Eventually it goes into Orbit 133

Orbits n Consider an object orbiting the Earth in a circular orbit. n Let’s say it is a distance r from the Earth’s center. n There is one force acting on it: Gravity. n It’s acceleration is centripetal. 134

Gravity is the Centripetal Force for Bodies in Orbit 135

Calculate Velocity of Satellite in Orbit at Earth’s Surface • Assume satellite is rotating just above the earth’s surface • F = mg = mv 2/R • v 2 = g. R • R = 6. 4 x 106 m • v 2 = (9. 8)(6. 4 x 106) • v = (6. 27 x 107)1/2 • v ~ 7900 m/s 136

Orbits, cont’d n Newton’s second law gives: n So therefore: 137

Orbits, cont’d n So we can determine what speed a satellite has if we know its distance from the Earth’s center. n The altitude (height above the surface) is just the distance less the Earth’s radius. 138

Example A communications satellite is at an altitude of 35, 900 kilometers. At what speed is the satellite orbiting the Earth? 139

Example ANSWER: The problem gives us: This is the distance above the Earth. We need the distance from the center: 140

Example ANSWER: This is almost 7000 mph. 141

Example DISCUSSION: This type of orbit is called “geosynchronous” because the satellite remains above the same location on the Earth’s surface. That’s where you want a communications satellite. 142

Orbits, cont’d n This graphic details the orbit of Halley’s comet. n It illustrates some general results from the law of gravity. 143

Orbits, cont’d n The orbits are ellipses. n Either circles or stretched-out circles. n The Sun is at a focus of the ellipse. n Or at the center if the orbit is a circle. 144

Orbits, cont’d n Halley’s comet moves faster when its nearer the Sun. n If the distance from the Sun is smaller, our orbital speed formula says the speed is higher: n More on this in chapter 3. 145

Tides A Constant Reminder of Newton’s Law of Gravity

Tides • Moon’s Gravity Exerts Different Force at Different Locations on Earth 147

Tides • Moon’s Gravity Exerts Different Force at Different Locations on Earth • Changes Occur as the Earth Rotates 148

Summary of Important Equations Frequency of Oscillation for a pendulum F = kd Force constant for a spring Frequency of Oscillation for a spring 149

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