Motion & Forces Newton s Laws of Motion If I have seen far, it is because I have stood on the shoulders of giants. - Sir Isaac Newton (referring to Galileo)
A. Newton s First Law Newton s First Law of Motion An object at rest will remain at rest and an object in motion will continue moving at a constant velocity unless acted upon by a net force.
B. Newton s Second Law Newton s Second Law of Motion The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F = ma
C. Newton s Third Law Newton s Third Law of Motion When one object exerts a force on a second object, the second object exerts an equal but opposite force on the first.
Motion & Forces Describing Motion
Newton s First Law Newton s First Law of Motion An object at rest will remain at rest and an object in motion will continue moving at a constant velocity unless acted upon by a net force.
A. Motion Problem: Is your desk moving? We need a reference point... nonmoving point from which motion is measured
A. Motion Motion Change in position in relation to a reference point. Reference point Motion
A. Motion Problem: You are a passenger in a car stopped at a stop sign. Out of the corner of your eye, you notice a tree on the side of the road begin to move forward. You have mistakenly set yourself as the reference point.
B. Speed & Velocity Speed rate of motion d v t distance traveled per unit time speed distance time
B. Speed & Velocity Instantaneous Speed speed at a given instant Average Speed avg. speed total distance total time
B. Speed & Velocity Problem: A storm is 10 km away and is moving at a speed of 60 km/h. Should you be worried? It depends on the storm s direction!
B. Speed & Velocity Velocity speed in a given direction can change even when the speed is constant!
C. Acceleration v f - v i Acceleration a t the rate of change of velocity change in speed or direction a v f t v i a: acceleration v f : final velocity v i : initial velocity t: time
C. Acceleration Positive acceleration speeding up Negative acceleration slowing down
GIVEN: D. Calculations Your neighbor skates at a speed of 4 m/s. You can skate 100 m in 20 s. Who skates faster? WORK: d = 100 m v = d t t = 20 s v =? d v = (100 m) (20 s) v = 5 m/s v t You skate faster!
GIVEN: D. Calculations A roller coaster starts down a hill at 10 m/s. Three seconds later, its speed is 32 m/s. What is the roller coaster s acceleration? WORK: v i = 10 m/s t = 3 s v f = 32 m/s a =? v f - v i a = (v f - v i ) t a = (32m/s - 10m/s) (3s) a = 22 m/s 3 s a t a = 7.3 m/s 2
GIVEN: D. Calculations Sound travels 330 m/s. If a lightning bolt strikes the ground 1 km away from you, how long will it take for you to hear it? WORK: v = 330 m/s d = 1km = 1000m t =? d t = d v t = (1000 m) (330 m/s) t = 3.03 s v t
GIVEN: D. Calculations How long will it take a car traveling 30 m/s to come to a stop if its acceleration is -3 m/s 2? WORK: t =? v i = 30 m/s v f = 0 m/s a = -3 m/s 2 v f - v i t = (v f - v i ) a t = (0m/s-30m/s) (-3m/s 2 ) t = -30 m/s -3m/s 2 a t t = 10 s
E. Graphing Motion Distance-Time Graph A B slope = speed steeper slope = faster speed straight line = constant speed flat line = no motion
E. Graphing Motion Distance-Time Graph A B Who started out faster? A (steeper slope) Who had a constant speed? A Describe B from 10-20 min. B stopped moving Find their average speeds. A = (2400m) (30min) A = 80 m/min B = (1200m) (30min) B = 40 m/min
Distance (m) E. Graphing Motion Distance-Time Graph 400 300 200 Acceleration is indicated by a curve on a Distance-Time graph. 100 0 0 5 10 15 20 Time (s) Changing slope = changing velocity
Speed (m/s) E. Graphing Motion Speed-Time Graph 3 2 slope = acceleration +ve = speeds up -ve = slows down 1 0 0 2 4 6 8 10 Time (s) straight line = constant accel. flat line = no accel. (constant velocity)
Speed (m/s) E. Graphing Motion 3 2 Speed-Time Graph Specify the time period when the object was... slowing down 5 to 10 seconds speeding up 0 to 3 seconds 1 0 0 2 4 6 8 10 Time (s) moving at a constant speed 3 to 5 seconds not moving 0 & 10 seconds
Bell Ringer What is Speed? What is Acceleration?
Motion & Forces Defining Force
A. Force Force - a push or pull that one body exerts on another What forces are being exerted on the football? F kick F grav
A. Force Has the ability to change an object's motion : Starting Stopping Speeding up Slowing down Changing direction
A. Force May change an object's shape Forces give energy to an object All of the forces acting on an object together are known as net forces
A. Force Forces can be represented with arrows called vectors. Vectors show the direction and magnitude of a force. Forces are measured in Newtons ( N).
A. Force Balanced Forces forces acting on an object that are opposite in direction and equal in size no change in velocity Net force = 0
A. Force Unbalanced Forces unbalanced forces that are not opposite and equal velocity changes (object accelerates)- change in movement Net force is greater than zero F net F friction F pull N W N
Bell Ringer What is a Force? What unit is force measured in? What is a vector?
B. Newton s First Law Newton s First Law of Motion An object at rest will remain at rest and an object in motion will continue moving at a constant velocity unless acted upon by a net force.
B. Newton s First Law Newton s First Law of Motion Law of Inertia Inertia tendency of an object to resist any change in its motion increases as mass increases
B. Newton s First Law Objects do not change their motion unless a force acts on them An object will NOT start moving unless a force acts on it. An object will NOT stop moving unless a force acts on it. An object will NOT change speed unless a force acts on it An object will NOT change direction unless a force acts on it http://www.youtube.com/watch?v=8zse3mpz6 Hw The more mass an object has, the more inertia it has. This means that the more mass an object has, the harder it is to move, stop, or change the speed or direction of the object.
B. Newton s First Law Don t let this be you. Wear seat belts! Because of inertia, objects (including you) resist changes in their motion. When the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 m/hour.
C. Friction Friction - force that opposes motion between 2 surfaces depends on the: types of surfaces force between the surfaces
C. Friction Friction is greater... between rough surfaces when there s a greater force between the surfaces (e.g. more weight)
Rolling the friction between a rolling object and the surface it rolls on is rolling friction. C. Friction Three kinds of friction: Static frictions between two surfaces that are NOT moving past each other Sliding the force that opposes the motion of two surfaces sliding past each other.
Bell Ringer What is friction? What are the three types of friction? What two things affect friction?
Motion & Forces Force & Acceleration
A. Newton s Second Law Newton s Second Law of Motion The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F = ma
A. Newton s Second Law a F F m m a F = ma F: force (N) m: mass (kg) a: accel (m/s 2 ) 1 N = 1 kg m/s 2
Gravity B. Gravity force of attraction between any two objects in the universe increases as... mass increases distance decreases
B. Gravity Who experiences more gravity - the astronaut or the politician? Which exerts more gravity - the Earth or the moon? less distance more mass
Weight B. Gravity the force of gravity on an object W = mg W: weight (N) m: mass (kg) g: acceleration due to gravity (m/s 2 ) MASS always the same (kg) WEIGHT depends on gravity (N)
B. Gravity Would you weigh more on Earth or Jupiter? Jupiter because... greater mass greater gravity greater weight
Bell Ringer What is the formula for Weight? What is gravity? What is the formula for Newton s 2 nd Law of motion? What unit of measurement is force measured in? What are the units for: velocity, acceleration, distance, mass?
B. Gravity Accel. due to gravity (g) In the absence of air resistance, all falling objects have the same acceleration! On Earth: g = 9.8 m/s 2 g W m g W m elephant feather Animation from Multimedia Physics Studios.
C. Air Resistance Air Resistance a.k.a. fluid friction or drag force that air exerts on a moving object to oppose its motion depends on: speed surface area shape density of fluid
C. Air Resistance Terminal Velocity maximum velocity reached by a falling object reached when F air F grav = F air no net force no acceleration constant velocity F grav
C. Air Resistance Terminal Velocity increasing speed increasing air resistance until F air = F grav Animation from Multimedia Physics Studios.
C. Air Resistance Falling with air resistance heavier objects fall faster because they accelerate to higher speeds before reaching terminal velocity F grav = F air larger F grav need larger F air need higher speed Animation from Multimedia Physics Studios.
D. Calculations What force would be required to accelerate a 40 kg mass by 4 m/s 2? GIVEN: F =? m = 40 kg a = 4 m/s 2 F WORK: F = ma F = (40 kg)(4 m/s 2 ) F = 160 N m a
D. Calculations A 4.0 kg shotput is thrown with 30 N of force. What is its acceleration? GIVEN: m = 4.0 kg F = 30 N a =? F WORK: a = F m a = (30 N) (4.0 kg) a = 7.5 m/s 2 m a
D. Calculations Mrs. J. weighs 557 N. What is her mass? GIVEN: F(W) = 557 N m =? a(g) = 9.8 m/s 2 F m a WORK: m = F a m = (557 N) (9.8 m/s 2 ) m = 56.8 kg
Bell Ringer What force would be required to accelerate a 40 kg mass by 4 m/s 2? A 4.0 kg shot-put is thrown with 30 N of force. What is its acceleration? Sound travels 330 m/s. If a lightning bolt strikes the ground 1 km away from you, how long will it take for you to hear it?
Motion & Forces Nonlinear Motion
A. Projectile Motion Projectile any object thrown in the air acted upon only by gravity follows a parabolic path called a trajectory has horizontal and vertical velocities PROJECTILE MINI-LAB
A. Projectile Motion Projectile Velocities Horizontal and vertical velocities are independent of each other!
A. Projectile Motion Horizontal Velocity depends on inertia remains constant Vertical Velocity depends on gravity accelerates downward at 9.8 m/s 2
B. Circular Motion Centripetal Acceleration acceleration toward the center of a circular path caused by centripetal force The word centripetal means to move toward the center.
What would happen if the string broke?
B. Circular Motion On the ground... friction provides centripetal force
B. Circular Motion In orbit... gravity provides centripetal force ROUND LAB
B. Circular Motion In orbit... Which satellites travel faster? Near-Earth Satellites Geostationary Satellites
Free-Fall C. Free-Fall when an object is influenced only by the force of gravity Weightlessness sensation produced when an object and its surroundings are in free-fall object is not weightless!
C. Free-Fall Weightlessness surroundings are falling at the same rate so they don t exert a force on the object
Go to NASA. Go to CNN.com. Go to Space Settlement Video Library. C. Free-Fall Space Shuttle Missions NASA s KC-135 - The Vomit Comet
Motion & Forces Action and Reaction
A. Newton s Third Law Newton s Third Law of Motion When one object exerts a force on a second object, the second object exerts an equal but opposite force on the first.
A. Newton s Third Law Problem: How can a horse pull a cart if the cart is pulling back on the horse with an equal but opposite force? Aren t these balanced forces resulting in no acceleration? NO!!!
A. Newton s Third Law Explanation: forces are equal and opposite but act on different objects they are not balanced forces the movement of the horse depends on the forces acting on the horse
A. Newton s Third Law Action-Reaction Pairs The hammer exerts a force on the nail to the right. The nail exerts an equal but opposite force on the hammer to the left.
A. Newton s Third Law Action-Reaction Pairs F G The rocket exerts a downward force on the exhaust gases. The gases exert an equal but opposite upward force on the rocket. F R
A. Newton s Third Law Action-Reaction Pairs Both objects accelerate. The amount of acceleration depends on the mass of the object. a F m Small mass more acceleration Large mass less acceleration
Examples: As a man exits a canoe, the canoe moves in the opposite direction. The canoe has an equal and opposite reaction to the man s action. A gun exerts a force on a bullet and the bullet exerts the SAME force on the gun. As the paddle is pushed backward in the water the canoe moves forward. A swimmer pushes water back with his arms, but his body moves forward.
B. Momentum Momentum quantity of motion p = mv m p v p: momentum (kg m/s) m: mass (kg) v: velocity (m/s)
GIVEN: B. Momentum Find the momentum of a bumper car if it has a total mass of 280 kg and a velocity of 3.2 m/s. WORK: p =? m = 280 kg v = 3.2 m/s p p = mv p = (280 kg)(3.2 m/s) p = 896 kg m/s m v
GIVEN: B. Momentum The momentum of a second bumper car is 675 kg m/s. What is its velocity if its total mass is 300 kg? WORK: p = 675 kg m/s v = p m m = 300 kg v =? p v = (675 kg m/s) (300 kg) v = 2.25 m/s m v
C. Conservation of Momentum Law of Conservation of Momentum The total momentum in a group of objects doesn t change unless outside forces act on the objects. p before = p after
C. Conservation of Momentum Elastic Collision KE is conserved Inelastic Collision KE is not conserved
C. Conservation of Momentum A 5-kg cart traveling at 1.2 m/s strikes a stationary 2-kg cart and they connect. Find their speed after the collision. Cart 1: m = 5 kg v = 4.2 m/s Cart 2 : m = 2 kg v = 0 m/s BEFORE p = 21 kg m/s p = 0 p before = 21 kg m/s Cart 1 + 2: m = 7 kg v =? AFTER m p v v = p m v = (21 kg m/s) (7 kg) v = 3 m/s p after = 21 kg m/s
C. Conservation of Momentum A 50-kg clown is shot out of a 250-kg cannon at a speed of 20 m/s. What is the recoil speed of the cannon? Clown: m = 50 kg v = 0 m/s Cannon: m = 250 kg v = 0 m/s BEFORE p = 0 p = 0 p before = 0 AFTER Clown: p = 1000 kg m/s m = 50 kg v = 20 m/s Cannon: p = -1000 kg m/s m = 250 kg v =? m/s p after = 0
C. Conservation of Momentum So now we can solve for velocity. GIVEN: p = -1000 kg m/s m = 250 kg v =? p m v WORK: v = p m v = (-1000 kg m/s) (250 kg) v = - 4 m/s (4 m/s backwards)
Motion & Forces Forces in Fluids
A. Archimedes Principle Fluid matter that flows liquids and gases Buoyancy the ability of a fluid to exert an upward force on an object immersed in it
A. Archimedes Principle Bouyant Force upward force exerted by a fluid on an immersed object bouyant force > weight balloon rises bouyant force < weight balloon sinks bouyant force = weight balloon floats
A. Archimedes Principle Archimedes Principle the bouyant force on an object in a fluid is equal to the weight of fluid displaced by the object More Not Very enough little water water needs water needs is to displaced be to be displaced in order in order in to order cancel to to weight cancel weight ball sinks. ball floats lower on surface. in the water. View Buoyancy JAVA Applet. View animations produced by students at Poly Prep Country Day School in Brooklyn, New York.
B. Pascal s Principle Pascal s Principle pressure applied to a fluid is transmitted unchanged throughout the fluid View hydraulics explanation. F1 P A 1 F F A 2 A 2
GIVEN: B. Pascal s Principle A car weighing 1000 N sits on a 250 m 2 platform. What force is needed on the 10 m 2 plunger to keep the car from sinking? Platform: F = 1000 N A = 250 m 2 Plunger: F =? A = 10 m 2 WORK: 1000 N = F 2 250 m 2 10 m 2 (1000 N)(10 m 2 )=(250 m 2 )F 2 F 2 = 40 N F1 A 1 F A 2 2
C. Bernoulli s Principle Bernoulli s Principle as the velocity of a fluid increases, the pressure exerted by the fluid decreases EX:airplane lift, curve balls
C. Bernoulli s Principle Airplane lift Curve Ball View airplane wings explanation.
C. Bernoulli s Principle Funnel Demos View funnel explanation. View inverted funnel explanation.
C. Bernoulli s Principle Venturi Effect fluids flow faster through narrow spaces causing reduced pressure EX: garden sprayer, atomizer, carburetor
C. Bernoulli s Principle Venturi Effect - Atomizers