Newton’s 2 nd Law Force and Acceleration

Galileo Conceptualized Acceleration G – Money defined the rate of change of velocity as acceleration Acceleration = change of velocity divided by time Any change! Slowing down Speeding up Changing direction

Galileo Conceptualized Acceleration Acceleration is a vector quantity It is a change in: Speed, Direction or Both So, a change in velocity is a change in acceleration

Galileo Conceptualized Acceleration Unless I miss my guess, this skier is accelerating all over the place…

Galileo Conceptualized Acceleration Suppose you are flying In 1 second your speed steadily increases from 30 km/hr to 35 km/hr The next second you speed increases from 35 km/hr to 40 km/hr and so on Your velocity changes by 5 km/hr each second Acceleration = Change of velocity/time 5km/hr ÷ 1s = 5km/hr per s

Galileo Conceptualized Acceleration Free Fall When air resistance does not affect the falling motion of an object Free fall acceleration is nearly identical for everything Acceleration = Change of velocity/time For free fall: 10m/s 2 …And I’m free. Free fallin’ ~T. Petty

Galileo Conceptualized Acceleration How much speed does an object thrown straight up lose per second? Since it fights against gravity, 10m/s Once it starts down it moves just as if it were dropped from rest at that height Thus, accelerates back down at 10m/s 2

Force Causes Acceleration Since acceleration is a change in velocity: Newton’s first law applies An object stays in constant velocity unless a net force acts upon it This net force (push or pull) causes the change in acceleration

Force Causes Acceleration Acceleration is directly proportional to the net force on an object Twice the net force = twice the acceleration 10 times the net force = 10 times the acceleration

Force Causes Acceleration Acceleration is directly proportional to the net force on an object The same net force on twice the mass = half the acceleration The twice the net force on twice the mass = the same acceleration as before

Mass Is a Measure of Inertia The more massive a thing is, the more inertia it has The more it wants to stay at rest The more it wants to stay in motion If a bear is chasing you, run zigzag “Get in my belly!” Tastes like chicken…

Mass Is a Measure of Inertia Mass is NOT Weight! Mass is the measure of how much stuff is in an object More massive objects have more stuff packed in them Less massive objects have less stuff packed in them Ping pong ball vs. bowling ball

Mass Is a Measure of Inertia Mass is NOT Weight Mass depends on how much stuff is packed in an object Weight depends on gravity One changes and the other doesn’t Which does what?

Mass Is a Measure of Inertia Mass is NOT Weight You can be weight-less not mass-less The amount of stuff packed into you does not change

Mass Is a Measure of Inertia Mass and weight are not the same but they are proportional to each other An object with a large mass has a large weight In the same location, twice as much mass weighs twice as much

Mass Is a Measure of Inertia Mass is NOT Volume Mass is a measure of how much stuff is packed into an object Volume is a measure of how much space that object take up

Mass Is a Measure of Inertia Mass is NOT Volume If an object has a large mass, it might have a large volume Not always: Ping pong ball vs. golf ball Bag of rice vs. bag of feathers Bag of rocks vs. bag of cotton balls Mass is measured in kilograms

Mass Is a Measure of Inertia What does mass weigh? One kilogram weighs 9.81 Newtons One kg = 2.2 lbs So 1 pound must =4.45 Newtons

Mass (Inertia) Resists Acceleration More massive objects resist a change in their “natural” state Natural state = equilibrium Massive, heavier objects require more force to move/slow or change direction

Mass (Inertia) Resists Acceleration For the same force, twice as much mass gives ½ as much acceleration Three times as much mass = 1/3 Four times as much mass = 1/4

Mass (Inertia) Resists Acceleration Acceleration ~ 1/mass Inversely proportional One goes up, the other goes down The bigger the mass (the denominator) the smaller the acceleration

Linking Force, Acceleration and Mass Isaac Newton was the first to connect force and mass with acceleration Newton’s 2 nd Law of Motion The acceleration is proportional to the net force applied The acceleration goes in the same direction as the net force Acceleration is inversely proportional to the mass

Linking Force, Acceleration and Mass Newton built on G-Money’s ideas and unified the three variables: Force Mass Acceleration Acceleration = net force/mass A = F/M F = M x A M = A/F

Friction Affects Motion Friction occurs when objects come into contact Solids, liquids and gases Always acts to oppose motion

Objects in Free Fall Have Equal Acceleration G-Money Proved: Free-fall Acceleration does not depend on mass Different Mass objects accelerate equally Different mass objects will fall at the same rate and hit the ground at practically the same time BUT, smart as he was, G-Money could not explain why

Newton’s 2 nd Law Explains Why N-Dawg put it all together and came up with; f/m = F/M Big, bold F = large force, big, bold M = large mass Small m = small mass, small f = small force It is an equal ratio! All free fall objects have the SAME force to mass ratio!

Newton’s 2 nd Law Explains Why In free fall, there is no air drag The ONLY force acting on the elephant and feather is gravity Gravity pulls the same on everything

Newton’s 2 nd Law Explains Why Try the ratio with: A 1kg rock A 10kg boulder Run the numbers and see for yourself I am not making this stuff up Even Buckaroo Banzai agrees…

Newton’s 2 nd Law Explains Why A 10kg bag of sheep eyes has a weight of 100N. When dropped, what is its acceleration? Tastes like chicken…

Newton’s 2 nd Law Explains Why A 5kg bag of calf brains has a weight of 50N. When dropped, what is its acceleration? Calf brains in black bean sauce Panko breaded calf brain with oil, lemon and garlic dressing

Newton’s 2 nd Law Explains Why Calculate the free fall acceleration of a 20kg bag of giraffe tongues. Giraffe tongue sautéed in olive oil, lemon and garlic dressing Giraffe tongue braised in garlic beef stock with lemon dressing

Acceleration is Less With Air Drag This is NOT free fall situation Net force = weight Falling through air Net force = weight – air drag Air Drag depends on two things: Speed Surface area

Acceleration is Less With Air Drag Air Drag: Speed As an object falls, acceleration occurs and air resistance is built up The greater the speed, the greater the air drag

Acceleration is Less With Air Drag

The greater the speed, the greater the air drag You know this! Even your dog know this… Stick you head out the window of a car moving 10 mph and one moving 55 mph!

Acceleration is Less With Air Drag Air Drag: Speed (cont) As the object accelerates, air drag builds (directly proportional)

Acceleration is Less With Air Drag Soon enough air drag is built up (support force) to cancel the acceleration due to gravity Support force = Gravity (∑F = 0, yes, again…) No acceleration = constant speed = terminal speed Dynamic equilibrium Gravity force (weight) Support force (air drag)

Acceleration is Less With Air Drag Air Drag: Surface Area The greater the surface area the greater the air drag The greater the surface area of the “down” facing part, the greater the air drag

Acceleration is Less With Air Drag Weight and air drag A heavier object falls faster through air The heavier weight “plows” through the air more effectively Encounters more air resistance but simply pushes through it

Acceleration is Less With Air Drag A feather falls slower (reaches terminal speed faster) than an elephant for this reason

Remember Your Targets!  Learning Target 1: Use Newton’s 2 nd Law to describe and predict motion  Explain, draw and interpret free body / force vector diagrams  Create “rate vs. time” graphs  Interpret motion graphs to determine the motion of the object that produced the graph  Predict the direction and magnitude of motion using a free body/force vector diagram  Explain how friction affects motion

Remember Your Targets!  Learning Target 2: Use Newton’s 2 nd Law to describe and predict motion  Predict the direction and magnitude of motion using a free body/force vector diagram  Calculate acceleration of an object (A = F/M, ∆v/∆t)

Remember Your Targets!  Learning Target 3: The Only Reason to Learn Algebra is to do Physics  Calculate distance, speed and time (D = RT)  Calculate the net force acting on an object  Calculate acceleration of an object (A = F/M, ∆v/∆t)  Interpret motion graphs