Chapter 1 Lecture - Patterns of Motion and Equilibrium PDF

Chapter 1 Lecture Chapter 1: Patterns of Motion and Equilibrium 1 This lecture will help you understand: Galileo's Concept of Inertia Mass—A Measure of Inertia Net Force The Equilibrium Rule Support Force Dynamic Equilibrium...

Chapter 1 Lecture Chapter 1: Patterns of Motion and Equilibrium 1 This lecture will help you understand: Galileo's Concept of Inertia Mass—A Measure of Inertia Net Force The Equilibrium Rule Support Force Dynamic Equilibrium The Force of Friction Speed and Velocity Acceleration 2 1  Galileo's Concept of Inertia Italian scientist Galileo demolished Aristotle's assertions in early 1500s. In the absence of a force, objects once set in motion tend to continue moving indefinitely. 3 Galileo's Concept of Inertia Legend of the Leaning Tower of Pisa: Galileo showed that dropped objects fall to the ground at the same time when air resistance is negligible. 4 2  Galileo's Concept of Inertia Discovery: In the absence of friction, no force is necessary to keep a horizontally moving object moving. 5 Galileo's Concept of Inertia Conclusion: The tendency of a moving body to keep moving is natural—every material object resists change in its state of motion. This property of things to resist change is called inertia. 6 3  Galileo's Concept of Inertia CHECK YOUR NEIGHBOR The use of inclined planes for Galileo's experiments helped him to A. eliminate the acceleration of free fall. B. discover the concept of energy. C. discover the property called inertia. D. discover the concept of momentum. 7 Galileo's Concept of Inertia CHECK YOUR ANSWER The use of inclined planes for Galileo's experiments helped him to A. eliminate the acceleration of free fall. B. discover the concept of energy. C. discover the property called inertia. D. discover the concept of momentum. Explanation: Note that inertia is a property of matter, not a reason for the behavior of matter. 8 4  Inertia: Additional Examples When we flip a coin in a high speed car, we catch the moving coin as we would if the car was at rest. This happens because of the coin’s inertia and its forward motion at the speed of the car. Birds move from the tree branch vertically below and catch the worm. If inertia is neglected this would be impossible and the worm would be swept far away with the moving earth. The actual situation is that when the bird drops from the branch its initial sideways motion remains unchanged. It catches the worm quite unaffected by the motion of its environment. 9 Inertia: Additional Examples Rapid deceleration is sensed by the driver who is pushed forward when the brakes are applied. The downward motion and sudden stop of the hammer hand tightens the hammer hand A tablecloth is whipped from beneath dishes sitting on a table, leaving the dishes in their initial state of rest. 10 5  Mass—A Measure of Inertia The amount of inertia possessed by an object depends on the amount of matter—the amount of material that composes it—its mass: greater mass greater inertia smaller mass smaller inertia 11 Mass—A Measure of Inertia Mass Quantity of matter in an object Measure of inertia or sluggishness that an object exhibits in response to any effort made to start it, stop it, or change its state of motion in any way 12 6  Mass—A Measure of Inertia Weight Amount of gravitational pull on an object Proportional to mass Twice the mass twice the weight Half the mass half the weight Weight = mass × acceleration of gravity 𝒘 = 𝒎𝒈 𝑚: mass in kg 𝑔: acceleration of gravity ≅ 10 m/s2 Weight is a force and has units of Newton (N). Direction of weight is downwards always. 13 A note on units Most physical quantities have units. It is necessary to indicate the units used. We use the international system of units (SI-units). There are three basic units in mechanics. In SI-units these are: Length in meters (m) Mass in kilograms (kg) Time in seconds (s) Other physical quantities have derived units, for example: Speed in m/s, Acceleration in m/s 2 Force in N (N ≡ kg. m/s 2 ) Volume in m3 One cannot mix different systems of units. It is recommended to use SI-units. Carry unit conversion when necessary 14 7  Example (including unit conversion) Calculate the weight of a 200 gram object. (Hint: check if the units are consistent and make proper unit conversion!) Calculate the mass of a man who weighs 600 N 15 Mass—A Measure of Inertia Mass versus volume: Mass involves how much matter an object contains Volume involves how much space an object occupies Density: Measure of compactness Density is the measure of how much mass occupies a given space 16 8  Mass—A Measure of Inertia CHECK YOUR NEIGHBOR The concept of inertia mostly involves A. mass. B. weight. C. volume. D. density. 17 Mass—A Measure of Inertia CHECK YOUR ANSWER The concept of inertia mostly involves A. mass. B. weight. C. volume. D. density. Explanation: Anybody get this wrong? Check the title of this slide! :-) 18 9  Mass—A Measure of Inertia Kilogram standard unit of measurement for mass on Earth's surface, 1 kg of material weighs 10 newtons away from Earth (on the Moon), 1 kg of material weighs less than 10 newtons 19 Mass—A Measure of Inertia Checkpoint 1. Does a 2 kg iron block have twice as much inertia as a 1 kg iron block? twice as much mass? Twice as much volume? Twice as much weight when weighed in the same location? 2. Does a 2 kg iron block have twice as much inertia as a 1 kg bunch of bananas? twice as much mass? Twice as much volume? Twice as much weight when weighed in the same location? 3. Does the mass of a bar of gold vary with location? 20 10  Mass—A Measure of Inertia CHECK YOUR NEIGHBOR The density of 1 kilogram of iron is A. less on the Moon. B. the same on the Moon. C. greater on the Moon. D. All of the above. 21 Mass—A Measure of Inertia CHECK YOUR ANSWER The density of 1 kilogram of iron is A. less on the Moon. B. the same on the Moon. C. greater on the Moon. D. All of the above. Explanation: Both mass and volume of 1 kilogram of iron is the same everywhere, so density is the same everywhere. 22 11  Force Force: simply a push or a pull Results from an interaction between two objects Units of force is Newton (N) Forces are vector quantities: They have direction Some common forces: 1. Weight 2. Support/Normal force 3. Friction force 23 A note on vector and scalar quantities Physical quantities are divided into two main types: 1) Vector Quantities: quantities that have magnitude and direction. (Velocity, acceleration, force, weight, …) 2) Scalar Quantities: quantities that have magnitudes only. (Time, temperature, mass, speed, work, energy, power…) 24 12  Net Force Net force combination of all forces that act on an object changes an object's motion 25 Net Force CHECK YOUR NEIGHBOR A cart is pushed to the right with a force of 15 N while being pulled to the left with a force of 20 N. The net force on the cart is A. 5 N to the left. B. 5 N to the right. C. 25 N to the left. D. 25 N to the right. 26 13  Net Force CHECK YOUR ANSWER A cart is pushed to the right with a force of 15 N while being pulled to the left with a force of 20 N. The net force on the cart is A. 5 N to the left. B. 5 N to the right. C. 25 N to the left. D. 25 N to the right. 27 Example Find the net force is the following cases: a) 12 N (right), b) 21 N (right), c) 14 N (left), d) 7 N (right) 28 14  The Equilibrium Rule The equilibrium rule: The vector sum of forces acting on a non- accelerating object or system of objects equals zero. Mathematical notation: ΣF = 0. 29 Types of Equilibrium 1. Static equilibrium: objects at rest (stationary objects) 2. Dynamic equilibrium: objects moving at a constant velocity (constant velocity = constant speed in a straight line). When two or more forces cancel to zero on a moving object, then the object is in equilibrium. Normal force Drag Thrust (air resistance) (engine) weight 30 15  The Equilibrium Rule CHECK YOUR NEIGHBOR The equilibrium rule, ΣF = 0, applies to A. vector quantities. B. scalar quantities. C. Both of the above. D. Neither of the above. 31 The Equilibrium Rule CHECK YOUR ANSWER The equilibrium rule, ΣF = 0, applies to A. vector quantities. B. scalar quantities. C. Both of the above. D. Neither of the above. Explanation: Vector addition takes into account + and – quantities that can cancel to zero. Two forces (vectors) can add to zero, but there is no way that two masses (scalars) can add to zero. 32 16  Dynamic Equilibrium CHECK YOUR NEIGHBOR A bowling ball is in equilibrium when it A. is at rest. B. moves steadily in a straight-line path. C. Both of the above. D. None of the above. 33 Dynamic Equilibrium CHECK YOUR ANSWER A bowling ball is in equilibrium when it A. is at rest. B. moves steadily in a straight-line path. C. Both of the above. D. None of the above. 34 17  Weight Weight is the force due to gravity. measured in Newton (SI-unit is N) always points downwards (towards the center of the Earth) Recall: 𝒘 = 𝒎𝒈 35 Support Force Support force is force that supports an object on the surface against gravity is also normal force (perpendicular to the surface) 36 18  Support Force CHECK YOUR NEIGHBOR When you stand on two bathroom scales, with one foot on each scale and weight evenly distributed, each scale will read A. your weight. B. half your weight. C. zero. D. actually more than your weight. 37 Support Force CHECK YOUR ANSWER When you stand on two bathroom scales, with one foot on each scale and weight evenly distributed, each scale will read A. your weight. B. half your weight. C. zero. D. actually more than your weight. Explanation: You are at rest on the scales, so ΣF = 0. The sum of the two upward support forces is equal to your weight. 38 19  Support Force Note: the support (normal) force is NOT necessarily equal to the weight 39 The Force of Friction Friction the resistive force that opposes the motion or attempted motion of an object through a fluid or past another object with which it is in contact always acts in a direction to oppose motion 40 20  The Force of Friction Friction (continued) between two surfaces, the amount depends on the kinds of material and how much they are pressed together due to surface bumps and also to the stickiness of atoms on the surfaces of the two materials 41 The Force of Friction CHECK YOUR NEIGHBOR The force of friction can occur A. with sliding objects. B. in water. C. in air. D. All of the above. 42 21  The Force of Friction CHECK YOUR ANSWER The force of friction can occur A. with sliding objects. B. in water. C. in air. D. All of the above. Explanation: Friction can also occur for objects at rest. If you push horizontally on your book and it doesn't move, then friction between the book and the table is equal and opposite to your push. 43 Mass—A Measure of Inertia 44 22  Mass—A Measure of Inertia 45 The Force of Friction CHECK YOUR NEIGHBOR When Nellie pushes a crate across a factory floor at constant speed, the force of friction between the crate and the floor is A. less than Nellie's push. B. equal to Nellie's push. C. equal and opposite to Nellie's push. D. more than Nellie's push. 46 23  The Force of Friction CHECK YOUR ANSWER When Nellie pushes a crate across a factory floor at constant speed, the force of friction between the crate and the floor is A. less than Nellie's push. B. equal to Nellie's push. C. equal and opposite to Nellie's push. D. more than Nellie's push. 47 The Force of Friction CHECK YOUR NEIGHBOR When Nellie pushes a crate across a factory floor at an increasing speed, the amount of friction between the crate and the floor is A. less than Nellie's push. B. equal to Nellie's push. C. equal and opposite to Nellie's push. D. more than Nellie's push. 48 24  The Force of Friction CHECK YOUR ANSWER When Nellie pushes a crate across a factory floor at an increasing speed, the amount of friction between the crate and the floor is A. less than Nellie's push. B. equal to Nellie's push. C. equal and opposite to Nellie's push. D. more than Nellie's push. Explanation: The increasing speed indicates a net force greater than zero. Her push is greater than the friction force. The crate is not in equilibrium. 49 Speed and Velocity Speed is described as the distance covered per amount of travel time speed is measured in units of m/s or km/h Unit conversion: 1000 m 5 1 km/h = = m/s 60×60 s 18 18 1 m/s = km/h 5 50 25  Speed and Velocity Average speed is total distance traveled divided by travel time equation: total distance covered average speed = travel time Instantaneous speed is speed at any instant of time; the speedometer of your car shows the instantaneous speed not the average speed 51 Speed and Velocity CHECK YOUR NEIGHBOR The average speed in driving 30 km in 1 hour is the same average speed as driving A. 30 km in one-half hour. B. 30 km in two hours. C. 60 km in one-half hour. D. 60 km in two hours. 52 26  Speed and Velocity CHECK YOUR ANSWER The average speed in driving 30 km in 1 hour is the same average speed as driving A. 30 km in one-half hour. B. 30 km in two hours. C. 60 km in one-half hour. D. 60 km in two hours. 53 Exercises A car is moving with a speed of 90 km/h, what is its speed in m/s A horse is running with a speed of 15 m/s what is its speed in km/h 54 27  Exercises A man runs at 8 m/s; find the distance he travels in half an hour. A boy swims at 3 m/s, what time is needed for him to travel a distance of 105 m? 55 Velocity When we know both the speed and the direction of motion of an object, then we know its velocity. Velocity = speed and direction For example, if a car is moving at 80 km/h to the west, then its speed is 80 km/h and its direction is to the west. Constant velocity: means that the object is neither speeding up nor slowing down and at the same time is moving in the same direction (along a straight line). Question: Can you round a curve with your car at constant velocity? Explain. 56 28  Acceleration Galileo first formulated the concept of acceleration in his experiments with inclined planes. 57 Acceleration Acceleration is the rate at which velocity changes with time. The change in velocity may be in magnitude, in direction, or both. Equation for acceleration: Change in velocity Acceleration = time interval 𝛥𝑣 𝑣𝑓 − 𝑣𝑖 𝑎= = 𝑡 𝑡 58 29  Acceleration CHECK YOUR NEIGHBOR An automobile cannot maintain a constant velocity when A. accelerating. B. rounding a curve. C. Both of the above. D. None of the above. 59 Acceleration CHECK YOUR ANSWER An automobile cannot maintain a constant velocity when A. accelerating. B. rounding a curve. C. Both of the above. D. None of the above. Explanation: When rounding a curve, the automobile is accelerating, for it is changing direction. 60 30  Acceleration CHECK YOUR NEIGHBOR Acceleration and velocity are actually A. much the same as each other. B. rates, but for different quantities. C. the same when direction is not a factor. D. the same for free-fall situations. 61 Acceleration CHECK YOUR ANSWER Acceleration and velocity are actually A. much the same as each other. B. rates, but for different quantities. C. the same when direction is not a factor. D. the same for free-fall situations. Explanation: Velocity is the rate at which distance changes with time; acceleration is the rate at which velocity changes with time. 62 31  Notes on Acceleration Notes Constant velocity means no acceleration (= zero acceleration). Unit of acceleration is (units of velocity)/(units of time) = m/s2. Acceleration is the change in velocity not the change in speed, so even the change in direction only is considered to be acceleration. For example, when a car makes a turn at a constant speed it is still accelerating. Positive acceleration (with positive velocity) means increasing speed (speeding up) and negative acceleration (with positive velocity) means decreasing speed (slowing down). When something slows down, we often call this deceleration. Constant acceleration means that the same increase in velocity takes place in equal time intervals. 63 Constant acceleration Constant acceleration: constant change in velocity at similar time intervals 64 32  Exercises Exercise: If the speed of a certain car at a certain moment is 12 m/s and its acceleration is 3 m/s2, what will be the speed of the car 8 seconds later? (Ans. 36 m/s) Exercise: A train slows down from a speed of 126 km/h to a speed of 54 km/h in 8 seconds. a) What is the acceleration of the train? (note: mind the units!) (126 km/h = 35 m/s, 54 km/h = 15 m/s ). (Ans. −2.5 m/s2; what does the negative sign mean?) b) If it continues to decelerate at the same rate, how long will it take it to stop from its initial speed? 65 Acceleration Free fall: When the only force acting on a falling object is gravity (the weight), with negligible air resistance, the object is in a state of free fall. An upward moving object under these conditions is also in free-fall! 66 33  Free Fall Acceleration Acceleration of free fall does not depend on mass. It is constant. 67 Free Fall Acceleration Neglecting air resistance, all objects in free fall in the earth's gravitational field have a constant acceleration of magnitude: g ≅9.81 m/s 2 ≈10 m/s 2 Direction of g is always downwards (towards earth’s center). In other words, the speed of an object increases by 10 m/s each second while falling down and decreases by 10 m/s each second while moving up. Formula to use: Using 𝑎 = −𝑔 = −10 m/s 2 in the acceleration equation, we get: 𝒗𝒇 = 𝒗𝒊 − 𝒈𝒕 (keep in mind 𝑣 can be positive or negative) The distance travelled by a freely falling object released from rest is directly proportional to the square of the time of fall, In 𝟏 equation form:𝒅 = 𝒈𝒕𝟐 𝟐 68 34  Acceleration CHECK YOUR NEIGHBOR If a falling object gains 10 m/s each second it falls, its acceleration is A. 10 m/s. B. 10 m/s per second. C. Both of the above. D. Neither of the above. 69 Acceleration CHECK YOUR ANSWER If a falling object gains 10 m/s each second it falls, its acceleration is A. 10 m/s. B. 10 m/s per second. C. Both of the above. D. Neither of the above. Explanation: It is common to express 10 m/s per second as 10 m/s/s, or 10 m/s2. 70 35  Acceleration CHECK YOUR NEIGHBOR A free-falling object has a speed of 30 m/s at one instant. Exactly one second later its speed will be A. the same. B. 35 m/s. C. more than 35 m/s. D. 60 m/s. 71 Acceleration CHECK YOUR ANSWER A free-falling object has a speed of 30 m/s at one instant. Exactly one second later its speed will be A. the same. B. 35 m/s. C. more than 35 m/s. D. 60 m/s. Explanation: One second later its speed will be 40 m/s, which is more than 35 m/s. 72 36  Acceleration CHECK YOUR NEIGHBOR The distance fallen by a free-falling body A. remains constant each second of fall. B. increases each second when falling. C. decreases each second when falling. D. None of the above. 73 Acceleration CHECK YOUR ANSWER The distance fallen by a free-falling body A. remains constant each second of fall. B. increases each second when falling. C. decreases each second when falling. D. None of the above. Explanation: See Table 1.2 for verification of this. Falling distance ~ time squared. 74 37  Exercises Exercise: A 7-kg ball is thrown at 10 m/s straight upward. Neglecting air resistance, the net force that acts on the ball when it is half way to the top of its path is about a) 10 N b) 5 N c) 35 N d) 70 N e) None of the above. Exercise: An object is in a downward free-fall. At one instant, it travels at a speed of 37 m/s. Exactly 2 s later, its speed is about: a) 37 m/s b) 10 m/s c) 57 m/s d) 17 m/s e) 20 m/s Exercise: A rock is thrown vertically into the air. At the top of its path, its acceleration in m/s2 is about: a) 10 b) Zero c) Between 0 and 10 d) Greater than 10 e) None of the above 75 Exercises Exercise: A ball is thrown at a speed of 90 m/s directly upward from ground. a) What is the speed of the ball 7 seconds later? b) What is the time needed for the ball to reach the top point? c) What is the speed of the ball 4 seconds after reaching the top point? e) What is the ball’s flight time? 76 38  Exercises Exercise: A stone is dropped from rest from a large height. What is the distance traveled in the seventh second? Exercise: A ball thrown vertically upward from the ground is caught again by the thrower 12 seconds later. What is the maximum height reached by the ball? 77 39