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Do Now: What is a force?

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Newtons Laws of Motion

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General Overview Three physical laws that describe relationships between forces acting on a body and that bodys motion. Formulated by Sir Isaac Newton, English scientist and mathematician, in Have stood the test of time Only two exceptions: –Very fast objects: explained by Einsteins Special Theory of Relativity –Very small objects: explained by Theory of Quantum Mechanics

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The Three Laws First Law of Motion –An object will maintain its current state of rest or uniform velocity unless acted upon by an unbalanced force Second Law of Motion –The acceleration of an object is directly proportional to the net force exerted upon it and inversely proportional to its mass Third Law of Motion –For every action there is an equal and opposite reaction WAY TOO MANY UNFAMILIAR TERMS!!!

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Press the Easy Button! First Law of Motion: inertia Second Law of Motion: F net = m a Third Law of Motion: action-reaction YOU MIGHT STILL NEED A VOCAB LIST!!!

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The Vocab Breakdown Force: a push or pull on an object Rest: not moving Velocity: speed in a given direction Acceleration: change in velocity Uniform: constant, not changing

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The Vocab Breakdown Net: overall sum, considering different directions Mass: amount of matter in an object Directly Proportional: as the independent variable increases, the dependent variable increases Inversely Proportional: as the independent variable increases, the dependent variable decreases

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So… Newton used the force too?!? NO!!! NOT THAT KIND OF FORCE!

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Types of Forces Applied Force (F app ): force which is applied to an object by another object or by a person Tension (F tens ): force which is transmitted through a string, rope, or wire when it is pulled tight by forces acting at each end. Normal Force (F norm ): support force exerted upon an object which is in contact with another stable object. Exerted perpendicular to the surface.

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Types of Forces Friction (F fric ): force exerted by a surface as an object moves across it or makes an effort to move across it. Opposes the motion of the object. Air Resistance (F air ): special type of frictional force which acts upon objects as they travel through the air. Opposes the motion of the object. Gravitational Force (F grav ): force with which the earth, moon, or other massive body attracts an object towards itself. By definition, this is the weight of the object.

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Newtons First Law of Motion An object will maintain its current state of rest or uniform velocity unless acted upon by an unbalanced force. What it means: In the absence of an unbalanced force… –an object at rest will remain at rest –an object in motion will remain in motion at the same speed and in the same direction

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1 st Law Examples: Auto Collisions

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What is the occupants state of motion before the collision? –Constant forward velocity What is the occupants state of motion after the collision without a seatbelt? –Constant forward velocity What does a seatbelt provide? –An unbalanced force on the occupant –It decelerates the driver to rest

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1 st Law Examples: Whiplash Suppose you are sitting at a stoplight when you are rear-ended by another car. To an onlooker on the sidewalk, what initially happens to your head? –It stays at rest as the car and your body move forward. –It was at rest and will remain at rest. –An unbalanced force does not act on it until… –the headrest pushes your head forward.

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1 st Law Examples: The Tablecloth Parlor Trick TRY THIS AT HOME... with PAPER plates!!! Why does it work? If the tablecloth is pulled quickly enough, the frictional force is minimal, so the table setting remains practically at rest as the tablecloth is pulled out from underneath.

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Inertia The First Law is often called the Law of Inertia Inertia is the tendency of an object to maintain its state of rest or constant velocity Inertia is really a measure of MASS –More mass Greater tendency to stay at rest or in motion –Less mass Less tendency to stay at rest or in motion Which is easier to move from rest: a pebble or a boulder? Which is easier to stop when moving?

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So inertia is just weight?!? Not quite, young grasshopper! Mass and weight are not the same thing! Mass: amount of matter in an object –Measured in kilograms (kg) in metric system –Measured in slugs in English system –Never changes! Weight: force of gravity on an object –Measured in Newtons (N) in metric system –Measured in pounds (lbs) in English system –Changes based on location (altitude & planet)

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Calculating Weight Weight can be calculated very easily from the mass of the object. weight = mass x acceleration due to gravity On Earth, acceleration due to gravity is 9.8 m/s 2 weight = mass x 9.8 m/s 2

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Calculating Weight Solved Example: What is the weight of a 50 kg high school student? weight = mass x 9.8 m/s 2 equation weight = 50 kg x 9.8 m/s 2 plug & chug weight = 490 kg m/s 2 weight = 490 N answer Note: 1 N = 1 kg m/s 2

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Calculating Weight Try this one on your own! Show all work! What is the weight of 4 kg sack of potatoes? Solution: weight = mass x 9.8 m/s 2 equation weight = 4 kg x 9.8 m/s 2 plug & chug weight = 39.2 kg m/s 2 weight = 39.2 N answer

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Newtons Second Law of Motion The acceleration of an object is directly proportional to the net force exerted upon it and inversely proportional to its mass. as net force increases, acceleration increases (as long as mass is constant) Example: –Just you pushes a heavy piano. Piano doesnt speed up quickly. –Both you and a partner push the piano. Piano speeds up quicker.

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Newtons Second Law of Motion The acceleration of an object is directly proportional to the net force exerted upon it and inversely proportional to its mass. as mass increases, acceleration decreases (as long as force is constant) Example: –You pull an empty wagon with all your force. Wagon speeds up quickly. –You pull a wagon loaded with bricks with all your force. Wagon speeds up slowly.

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Newtons Second Law of Motion The 2 nd Law is expressed as an equation: F net = m·a where: F net is the net force acting on the object is measured in newtons (N) mis the mass of the object is measured in kilograms (kg) ais the acceleration of the object is measured in meters per second squared (m/s 2 )

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Whats a Net Force? Sum of forces acting in different directions Lefts vs. Rights Ups vs. Downs How do we know if theres a net force? The objects MOTION will tell us!!! –At rest: No net force –Moving at constant velocity: No net force –Accelerating: Net force acts The easiest way to analyze forces and determine the net force is by drawing!!!

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Drawing Forces We need to diagram both the magnitude and direction of these forces –Magnitude: size, amount, how much –Direction: which way is the push or pull A force ALWAYS needs both magnitude and direction –INCORRECT: a force of 5 N –CORRECT: a force of 5 N to the right

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Drawing Forces To draw forces, we use arrows These arrows are called force vectors Length of vector: magnitude of force Direction of vector: direction of force F 5 N right 3 N down 10 N left

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Free Body Diagrams To diagram ALL the forces acting on an object, we use a FREE BODY DIAGRAM Box represents the object Arrows represent forces Arrows drawn outward from box in direction of force Arrows are labeled with name of force F app

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Free Body Diagrams To draw correct FBDs, you need to think about the forces acting on the object. –This is difficult at first. –Practice makes perfect! Key to success: determine if theres a net force Remember: –At rest: No net force –Moving at constant velocity: No net force –Accelerating: Net force acts Net force is always in the direction of the acceleration!

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Free Body Diagrams Example: What does the FBD for a physics book resting on the desk look like? Solution: Is there a net force? No, the book is at rest. Consider all forces and decide which ones act. –Gravity? YES! Gravity always acts & pulls down. –Applied? NO! Nobody is pushing the book. –Tension? NO! Theres no string, rope, etc. –Friction? NO! It isnt sliding or trying to slide. –Normal? YES! The desk pushes up on the book. So… GRAVITY pulls down & NORMAL FORCE pushes up. Together it looks like…

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F grav F nor m BUT, PRACTICE MAKES PERFECT…

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Determining Net Force from FBDs Add forces in same direction Subtract forces in opposite directions The VECTOR SUM is the NET FORCE 5 N 6 N 2 N 1 N (Net Force)(All Forces)

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Determining Net Force from FBDs Treat horizontal and vertical forces separately. 5 N 4 N 3 N 1 N (Net Force)(All Forces) 2 N 1 N Trigonometry is needed to determine a single net force from these two!!!

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So, what about F net = m·a? Working with this equation is a synthesis of 2 nd Law knowledge: –First, identify forces acting and draw FBD If forces are balanced, F net = 0 If forces are unbalanced, express F net as either: –A single force –Vector sum (combination) of of two or more forces –Second, identify given info from problem –Third, Plug & Chug (you may need to rearrange!) –Finally, express your answer in the correct units!!!

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2 nd Law Example Problem #1 Using a rope, you pull your kid brother on a sled across the ice with a force of 75 N. If your brother and the sled have a combined mass of 30 kg, what is the resulting acceleration of the sled? (Ignore friction)

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2 nd Law Example Problem #1 Identify forces: –Vertically: Gravity & Normal balance out –Horizontally: Tension only!!! –Net Force? Yes!!! F net = F ten Identify info: –F ten = 75 Nm = 30 kga = ? Plug & Chug: F net = m·a 75 N = (30 kg)·a(need to rearrange!) a = 75 N / 30 kg Answer: a = 2.5 m/s 2 F norm F ten F grav

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2 nd Law Example Problem #2 You pull your kid brother in wagon with a force of 90 N. The resulting acceleration is only 2 m/s 2. If your brother and the wagon have a combined mass of 30 kg, what is the force of friction acting on the wagon?

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2 nd Law Example Problem #2 Identify forces: –Vertically: Gravity & Normal balance out –Horizontally: Applied & Friction –Net Force? F net = F app - F fric Identify info: –F app = 90 Nm = 30 kga = 2 m/s 2 F fric = ? Plug & Chug: F net = m·a 90 N – F fric = (30 kg)·(2 m/s 2 ) 90 N – F fric = 60 N F fric = 90 N – 60 N F fric = 30 N Answer: F fric = 30 N F norm F ten F grav

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