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Cell phones off Open laptops in last row only. Chapter 5 Newton ’ s Laws of Motion. (sections 5.1-5.4 ). Reading and Review. Dropping a Package. a) quickly lag behind the plane while falling b) remain vertically under the plane while falling c) move ahead of the plane while falling

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Cell phones offOpen laptops in last row onlyChapter 5Newton’s Laws of Motion(sections 5.1-5.4)Reading and ReviewDropping a Packagea) quickly lag behind the plane while fallingb) remain vertically under the plane while fallingc) move ahead of the plane while fallingd) not fall at allYou drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will:Follow-up: what would happen if air resistance is present?Dropping a Packagea) quickly lag behind the plane while fallingb) remain vertically under the plane while fallingc) move ahead of the plane while fallingd)not fall at allYou drop a package from a plane flying at constant speed in a straight line. Without air resistance, the package will: Both the plane and the package have the samehorizontalvelocity at the moment of release. They will maintain this velocity in the x-direction, so they stay aligned.abA battleship simultaneously fires two shells at two enemy submarines. The shells are launched with the same magnitude of initialvelocity. If the shells follow the trajectories shown, which submarine gets hit first?c) both at the same timeFollow-up: Did you need to know that they had the same initial speed?abA battleship simultaneously fires two shells at two enemy submarines. The shells are launched with the same magnitude of initialvelocity. If the shells follow the trajectories shown, which submarine gets hit first? The flight time is fixed by the motion in the y-direction. The higher an object goes, the longer it stays in flight. The shell hitting submarine #2 goes less high, therefore it stays in flight for less time than the other shell. Thus, submarine#2 is hit first.c) both at the same timeKinematics: Assumptions, Definitions and Logical ConclusionsWhat have we done so far?Defined displacement, velocity, acceleration (also position, distance, speed)... Defined scalers (like speed) and vectors (like velocity) Laid out assumptions about free-fall noticed that 2-dimensional motion is really just two, simultaneous, 1-dimensional motions. Used this to shoot a monkey, range out a small cannon, etc.This wasn’t physics. This was preparing the language needed to talk about physics.Newton’s LawsHow can we consistently and generally describe the way objects move and interact? Newton in a 1702 portrait by Godfrey KnellerNewton in a 1689 portrait by Godfrey KnellerIsaac Newton1643-1727Nature and nature's laws lay hid in night;God said "Let Newton be" and all was light.I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.Newton’s epitaph, Alexander Popefrom a memoir by NewtonForceForce: push or pullForce is a vector – it has magnitude and directionMassMass is the measure of how hard it is to change an object’s velocity.Mass can also be thought of as a measure of the quantity of matter in an object. Newton’s First Law of MotionIf you stop pushing an object, does it stop moving?Only if there is friction!In the absence of any net external force, an object at rest will remain at rest.In the absence of any net external force a moving object will keep moving at a constant speed in a straight line.This is also known as the Law of Inertia.InertiaNewton’s First Law a) more than its weightb) equal to its weightc) less than its weight but more than zerod) depends on the speed of the pucke) zeroA hockey puck slides on ice at constant velocity. What is the net force acting on the puck?Newton’s First Law a) more than its weightb) equal to its weightc) less than its weight but more than zerod) depends on the speed of the pucke) zeroA hockey puck slides on ice at constant velocity. What is the net force acting on the puck? The puck is moving at a constant velocity, and therefore it is not accelerating. Thus, there must be no net force acting on the puck.Follow-up: Are there any forces acting on the puck? What are they?Newton’s First Lawa) a net force acted on itb) no, or insufficient, net force acted on itc) it remained at restd) it did not move, but only seemed toe) gravity briefly stopped acting on itYou put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why?Newton’s First Lawa) a net force acted on itb) no, or insufficient, net force acted on itc) it remained at restd) it did not move, but only seemed toe) gravity briefly stopped acting on itYou put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why? The book was initially moving forward (because it was on a moving bus). When the bus stopped, the book continued moving forward, which was its initial state ofmotion, and therefore it slid forward off the seat.Calibrating forceTwo equal weights exert twice the force of one; this can be used for calibration of a spring:Experiment: Acceleration vs ForceNow that we have a calibrated spring, we can do more experiments.Acceleration is proportional to force:Experiment: Acceleration vs MassAcceleration is inversely proportional to mass:Newton’s Second Law of MotionAcceleration is proportional to force:Acceleration is inversely proportional to mass:Combining these two observations givesOr, more familiarly, Newton’s Second Law of MotionAn object may have several forces acting on it; the acceleration is due to the net force:SI unit for force Newton is defined using this equation as: 1 N is the force required to give a mass of 1 kg an acceleration of 1 m/s2Units of force: NewtonsThe weight of an object is the force acting on it due to gravityWeight: W = Fg = ma = mg vertically downwardsSince , the weight of an object in Newtons is approximately 10 x its mass in kgadult human70 kg700 N ~ 160 lbs. Force of GravityWHERE?There is no “conversion” from kg to pounds!(Unless you specify what planet you are assuming)In order to change the velocity of an object – magnitude or direction – a net force is required.(I)(II)Newton’s First and Second LawsWhat about the bus... From the perspective of someone who didn’t know they were on the bus?In order to change the velocity of an object – magnitude or direction – a net force is required.(I)(II)Inertial Reference FramesNewton’s First and Second Laws do not work in an accelerating frame of referenceAn inertial reference frame is one in which the first and second laws are true. Accelerating reference frames are not inertial.Was the bus an inertial reference frame?Is the earth an inertial reference frame?No, but acceleration due to earth’s rotation around Its axis (0.034 m/s2), and due to earth’s rotation around sun (smaller) are negligible compared to g; so approximately yes.Analyzing the forces in a systemFree-body diagrams: A free-body diagram shows every force acting on an object. Sketch the forces Isolate the object of interest Choose a convenient coordinate system Resolve the forces into components Apply Newton’s second law to each coordinate direction Free-body DiagramExample of a free-body diagram:Newton’s First Law a) there is a net force but the book has too much inertiab) there are no forces acting on it at allc) it does move, but too slowly to be seend) there is no net force on the booke) there is a net force, but the book is too heavy to moveA book is lying at rest on a table. The book will remain there at rest because:Newton’s First Law a) there is a net force but the book has too much inertiab) there are no forces acting on it at allc) it does move, but too slowly to be seend) there is no net force on the booke) there is a net force, but the book is too heavy to moveA book is lying at rest on a table. The book will remain there at rest because:There are forces acting on the book, but the only forces acting are in the y-direction. Gravity acts downward, but the table exerts an upward force that is equally strong, so the two forces cancel, leaving no net force.Newton’s Third Law of MotionForces always come in pairs, acting on different objects:If object 1 exerts a force on object 2, then object 2 exerts a force – on object 1.These forces are called action-reaction pairs.Some action-reaction pairsNewton’s 3rd: F12 = - F21action-reaction pairs are equal and opposite, but they act on different bodiesAction-reaction pair?a) Yesb) NoNewton’s Third Law of MotionAlthough the forces are the same, the accelerations will not be unless the objects have the same mass.Q: When skydiving, do you exert a force on the earth? Does the earth accelerate towards you?Is the magnitude of the acceleration of the earth the same as the magnitude of your acceleration?Newton’s Third Law of MotionContact forces:The force exerted by one box on the other is different depending on which one you push.Assume the mass of the two objects scales with size, and the forces pictured are the same. In which case is the magnitude of the force of box 1 on box 2 larger?Truck on Frozen Lakea) it is too heavy, so it just sits thereb) it moves backward at constant speedc) it accelerates backwardd) it moves forward at constant speede) it accelerates forwardA very large truck sits on a frozen lake. Assume there is no friction between the tires and the ice. A fly suddenly smashes against the front window. What will happen to the truck?Truck on Frozen Lakea) it is too heavy, so it just sits thereb) it moves backward at constant speedc) it accelerates backwardd) it moves forward at constant speede) it accelerates forwardA very large truck sits on a frozen lake. Assume there is no friction between the tires and the ice. A fly suddenly smashes against the front window. What will happen to the truck? When the fly hit the truck, it exerted a force on the truck (only for a fraction of a second). So, in this time period, the truck accelerated (backward) up to some speed. After the fly was squashed, it no longer exerted a force, and the truck simply continued moving at constant speed.Follow-up: What if the fly takes off, with the same speed in the direction from whence it came?Fm2mContact Forcea) 2Fb) Fc) ½Fd) 1/3Fe) ¼FTwo blocks of masses 2mand mare in contact on a horizontal frictionless surface. If a force F0 is applied to mass 2m, what is the force on mass m?Fm2mContact Forcea) 2Fb) Fc) ½ Fd) 1/3 Fe) ¼ FTwo blocks of masses 2mand mare in contact on a horizontal frictionless surface. If a force F0 is applied to mass 2m, what is the force on mass m? The force F0 leads to a specific acceleration of the entire system. In order for mass mto accelerate at the same rate, the force on it must be smaller! For the two blocks together, F0 = (3m)a. Since a is the same for both blocks, Fm = maA 71-kg parent and a 19-kg child meet at the center of an ice rink. They place their hands together and push. (a) Is the force experienced by the child more than, less than, or the same as the force experienced by the parent? (b) Is the acceleration of the child more than, less than, or the same as the acceleration of the parent? Explain. (c) If the acceleration of the child is 2.6 m/s2 in magnitude, what is the magnitude of the parent’s acceleration?On vacation, your 1300-kg car pulls a 540-kg trailer away from a stoplight with an acceleration of 1.9 m/s2(a) What is the net force exerted by the car on the trailer? (b) What force does the trailer exert on the car? (c) What is the net force acting on the car?An archer shoots a 0.022-kg arrow at a target with a speed of 57 m/s. When it hits the target, it penetrates to a depth of 0.085 m. (a) What was the average force exerted by the target on the arrow? (b) If the mass of the arrow is doubled, and the force exerted by the target on the arrow remains the same, by what multiplicative factor does the penetration depth change? Explain.

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