3Aristotle’s Motion Natural Motion is up or down Down for falling objectsUp for smokeCircular for heavenly bodies since without endViolent MotionDue to imposed forces such as wind pushing a ship or someone pulling a cartNatural state of motion is restA force is needed to keep something moving
4Aristotle’s Basic Error Friction not understood as a force
5Galileo’s Motion Force is a push or a pull Friction is a force that occurs when objects move past each otherFriction due to tiny irregularitiesOnly when friction is present is a force required to keep something moving
6Galileo’s Inclined Planes Ball rolling downhill speeds upBall rolling uphill slows downHe asked about ball on smooth level surfaceConcluded it would roll forever in absence of friction
7Inertia Resistance to change in state of motion Galileo concluded all objects have inertiaContradicted Aristotle’s theory of motionNo force required to keep Earth in motion around sun because no friction
8Newton Born 1665 Built on Galileo’s ideas Proposed three laws of motion at age of 23
9Newton’s First LawOurtesy hockey.gifEvery object continues in its state of rest, or of motion in a straight line at constant speed, unless compelled to change that state by forces exerted on it.Also called Law of Inertia: things move according to their own inertiaThings keep on doing what they are doingExamples: Hockey puck on ice, rolling ball, ball in space, person sitting on couch
10MassAmount of inertia depends on amount of mass…or amount of material (number and kind of atoms)Measured in kilogramsQuestion: Which has more mass, a kilogram of lead or a kilogram of feathers?Mass vs. Volume: volume is how much space something occupies
11Experiencing Inertia Inertia is resistance to shaking Which is easier to shake, a pen or a person?Why is it so hard to stop a heavy boat?
12Inertia in a Car Discuss three examples of inertia in a car Car hitting a wallCar hit from behind by a truckCar going around a corner
13Newton’s Second Law Law of Acceleration The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, and is inversely proportional to the mass of the body.Acceleration = net force ÷massF =maAcceleration is in direction of net force
14UnitsF = maUnit of force is the Newton (N)1 N = 1 kg m/s2
15Net Force Net Force means sum of all forces acting Sum is Vector sum Resultant force
16Understanding the Second Law The cause of acceleration is…_________ resists accelerationThe greater the force, the ________ the______________The greater the mass, the _________ the acceleration.ForceMass or inertiagreateraccelerationless
17F = ma is Three Equations F and a are vectorsSo F = ma equation is really threeSFx = max SFy = may SFz = maz
18ExamplesWhat force is required to accelerate a 1000 kg car at 2.0 m/s2 ?Answer: F = ma = 1000 kg x 2.0 m/s2 = 2000 N.What is the acceleration of a 145 g baseball thrown with a force of 20.0 N?a = F/m = 20.0 N/0.145kg = 138 m/s2
19F = ma Example; m unknown An astronaut puts a N force on an object of unknown mass producing an accelerations of m/s2 . What was the mass?M = F/a = 500.0N/0.462 m/s2 = 1082 Kg = 1.08 x 103 Kg
20Net force exampleIf four teams are playing tug of war (imagine a rope that looks like a cross, with the flag tied in the middle). Each team is 90⁰ from each other. Team A pulls with an overall force of 350 N to the North, Team B pulls with an overall force of 270 N to the South, Team C pulls with an overall force of 150 N to the East and Team D pulls with an overall force of 250 N to the West. If the flag in the middle has a mass of .25 kg, what is the magnitude and direction of its acceleration?
21Putting it all together……. Calculate the change in force of a car that has a mass of 2500 kg if it goes from 45 m/s to rest in 7 seconds at a stop sign, then accelerates up to 65 m/s in 5 seconds.
22a= vf-vi/t or a = F/ma1 = 0-45/7 = m/s2 a2 = 65-0/5 = 13 m/s2 The difference between them is m/s2. F = m x a = 2500 kg x m/s2 = N difference between the two accelerations
23Newton’s Third Law Forces always come in pairs Two forces on different objectsEvery action has an equal and opposite reactionWhenever one object exerts a force on a second object, the second exerts an equal and opposite force on the firstExample: hammer hits nail
24Example: pushing on wall What are the forces when you push on a wall?You exert force on wallYou accelerate in the opposite directionWall must have exerted a force on you in the direction you accelerated (by 2nd Law)
25Example: person walking Foot exerts force backward on groundGround exerts force forward on foot
26Example: Throwing ball Pitcher exerts force on ballBall exerts equal and opposite force on pitcherWhy doesn’t pitcher move?
27Example: Rocket Rocket engine exerts rearward force on gas molecules Molecules exert forward force on rocket.
28Book on TableThe mass of the book is one kg. What is the force (magnitude and direction) on the book?9.8 N upward
29Really putting it all together…… Calculate the Force necessary to launch a cannonball with a mass of 15 kg if it is fired at an angle of 43⁰ if it hits a target 210 m away in 6.3 seconds? What can we solve in this problem? What equations do we need to solve this problem?
30What we need to solve the force Vx = dx/t = 210/6.3 = 33.3 m/s Vf2 = Vi2 + 2 a(d) Vi = 0 for this problem a = Vf2/2d = / 2(210) = 2.64 m/s2 Force of the cannon: F = m(a) F = 15 kg (2.64 m/s2) = 39.6 N
31The Horse and the Cart Problem If there is always an equal an opposite reaction, how does anything move? For example, if you have a horse and a cart, how does the horse pull the cart?
32The Horse and Cart Problem. These appear to be the equalizing forces.A= - B B= - C C= -D A=B=C=D no acc!
33The Horse and Cart Problem. Because it is accelerating, the force the horse exerts on the cart has increased. By Newton's third law, the force of the cart on the horse has increased by the same amount. But the horse is also accelerating, so the friction of the ground on its hooves must be larger than the force the cart exerts on the horse. The friction between hooves and ground is static (not sliding or rolling) friction, and can increase as necessary (up to a limit, when slipping might occur, as on a slippery mud surface or loose gravel).So, when accelerating, we still have B = -C, by Newton's third law, but D>C and B>A, so D>A.
34More ExamplesCan you think of some more examples of Newton’s Third Law in Action?Imagine an astronaut floating in deep space, with only his spacesuit. Is there any way for him to move himself back to earth?
35Mass vs. Weight Mass is intrinsic property of any object Weight measures gravitational force on an object, usually due to a planetWeight depends on location of objectQuestion 1: How does mass of a rock compare when on Earth and on moon?Question 2: How does its weight compare?
36Review Mass vs. Weight What is mass? Answer: quantity of matter in something or a measure of its inertiaWhat is weight?Answer: Force on a body due to gravity
37Weight of 1 Kilogram 9.8 Newtons About 2.2 pounds Compare the weight of 1 kg nails with 1 kg styrofoamAnswer: Same
38Weight Examples What does a 70 kg person weigh? Weight = mass x g(acceleration due to gravity)W = mg = 70 kg x 9.80 N/m2 = 686 NAn object weighs 9800 N on Earth. What is its mass?m = W/g = 9800 / 9.8 m/s2 = 1000 kg
39Atwoods LabYou have 25 washers on your lab setup, if you have a unbalanced force, you will have acceleration. You will be using the stopwatch function of your data collector.Make a chart to record mass, time, acceleration and force.Put all washers on one side, raise that side to the top, then release it timing how long it takes to reach the bottom. Record this time.The mass of one washer is 16 g. It is the difference in mass that causes the acceleration. Calculate the difference in mass and record in table. 1st mass is 25 x 16, 2nd mass is 23 x 16, 3rd mass is 21 x 16 etc.Calculate the Acceleration = 2d/t2 (d = 1 m for the fall) so a = 2/ t2Calculate the Net force of the fall and record. (F= ma)Move one washer at a time over to the other side and repeat.Continue until the machine no longer turns (12 or 13 trials)
41Sliding Friction Often called kinetic friction A force opposite to direction of motionDue to bumps in surfaces and electric forcesSurface under microscopeFf
42Kinetic Friction is… Dependent on nature of the two surfaces Directly proportional to the normal force between the surfacesNormal Force is perpendicular to the surface. If it is on a flat surface, it is equal to the weight of the object.Independent of velocity
43Reducing Friction In order to reduce friction we can: A. Reduce surface areaB. Reduce weight of objectC. Change type of friction- sliding(the greatest amount)- rolling (use wheels to ease friction)- fluid ( Eliminate contact by using liquids or gases)
44Coefficient of friction mk Generally between zero and oneBased on comparing Friction Force to Normal ForceNormal Force is always perpendicular to surfaceCalculate from Ff / FN = µkCan be more than one for special rubberVery low for ice, Teflon, lubricated surfaces, ball bearings
45Friction: Good or BadMostly undesirable since reduces useful force and wastes energyFriction produces heatNecessary for walking!Necessary for braking
46Static Friction Force to start something moving Usually larger than kinetic friction for same surfacesRequires force to be exertedBefore sliding begins, is equal and opposite to applied force
47Where are all the forces? Block on an inclined plane
48Free Body Diagram Example 1 If the box below accelerates to the right at1 m/s2 Solve all of the following:
49Solution 1 Fgrav = m x g = 5 x 9.8 = 49 N Using the angle and the F applied, we can calculate the X and Y component of that force.Fx= 15 sin Fy = 15 cos 45Fx = 10.6 N Fy = 10.6 NIf the force of gravity is 49 N down and the applied force is 10.6 N up, then the normal force applied is the difference between the two. F norm= = N
50Solution 1 cont.If the object has an a of 1 m/s2 and a mass of 5 kg, then it has a net force of 5 N in the X direction.If the applied force in the X is 10.6 and the net is 5, then the force of friction is the difference between the two.Ffric= = 5.6 NTo solve the coefficient of friction we use this equation: Ff = mkFNmk= Ff/FN = 5.6/ 38.4 = .145
51Flat pullIf you pull a 2505 g box with a force of 15 N at an angle of 53⁰ to the horizon and the box accelerates at 2.0 m/s2 to the right, calculate the following:Fn, Fg, Ff, Fnet, Fapp, Fx, Fy and µ
52Friction LabPut a ramp flat in your lab space. Place two photogates relatively close together.If the mass of the sled is .040 kg calculate the Fnormal (Fn=Fg if on flat surface)Now, using your sled car (no wheels) launch the car with your rubber band. Make sure that it goes through both photo gates (you may have to adjust photo gates). Use our acceleration procedure from lab and calculate the rate of deceleration.Calculate Ffric= mass of sled x decelerationCalculate µ = Ff/Fn
53Free body diagram example 2 Say a box is sitting on 30⁰ slope and is frictionless, so the only forces are the normal force and gravity. What is the block's acceleration down the slope if the mass is 3.0 kg? What is the normal force?
54Free Body Diagram example 3 A box is sitting on a 35⁰ inclined plane. It is being pulled up the ramp by you with an acceleration of 2.5 m/s2. If the box has a mass of 25 kg and the force of friction is 3.5 N, solve all of the following: Fnet, Fnormal, Fgravity, Fapplied, and µ.
55A 50-N applied force (30 degrees to the horizontal) accelerates a box across a horizontal sheet of ice (see diagram). Glen Brook, Olive N. Glenveau, and Warren Peace are discussing the problem. Glen suggests that the normal force is 50 N; Olive suggests that the normal force in the diagram is 75 N; and Warren suggests that the normal force is 100 N. While all three answers may seem reasonable, only one is correct. Indicate which two answers are wrong and explain why they are wrong.
56Review: Newton’s Laws of Motion Newton’s First Law:Every object continues in its state of rest, or of motion in a straight line at constant speed, unless compelled to change that state by forces exerted on it.Newton’s Second Law:The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, and is inversely proportional to the mass of the body.Newton’s Third Law:Whenever one object exerts a force on a second object, the second exerts an equal & opposite force on the first
57Action- Reaction LabAdjust the smart track (or lab table) to be as level as possible(may have to put lab book under) put rubber band around one car.Squeeze two cars together and attach with the car link.Position car in middle of track, making sure all wheels are on track.With a quick upward motion, pull the link straight up and out from the cars.Describe how the cars move in a data table.Start adding marbles to cars and repeat procedures aboveMake all these combinations of marbles in cars0,0 0,1 0,2 0,3 1,1 1,2 1,3 2,2 2,3 3,3Sum up the action reaction effect on cars and marbles.
59Draw the free body diagram, if a = Draw the free body diagram, if a = .1 m/s2 and the force you push on the lawnmower is 25 N, solve for every force you know.
60Say a box is sitting on 40⁰ slope ramp. If the mass is 3. 0 kg Say a box is sitting on 40⁰ slope ramp. If the mass is 3.0 kg? What are all the forces acting on the box and what is µ?
61Renee is on Spring Break and pulling her 21-kg suitcase through the airport at a constant speed of 0.47 m/s. She pulls on the strap with 120 N of force at an angle of 38° above the horizontal. Determine the normal force and the total resistance force (friction and air resistance) experienced by the suitcase.
64For each collection of listed forces, determine the vector sum or the net force. Set A 58 N, right 42 N, left 98 N, up 98 N, down
65Hector is walking his dog (Fido) around the neighborhood Hector is walking his dog (Fido) around the neighborhood. Upon arriving at Fidella's house (a friend of Fido's), Fido turns part mule and refuses to continue on the walk. Hector yanks on the chain with a 67.0 N force at an angle of 30.0° above the horizontal. Determine the horizontal and vertical components of the tension force.
66Helen is parasailing. She sits in a seat harness which is attached by a tow rope to a speedboat. The rope makes an angle of 51° with the horizontal and has a tension of 350 N. Determine the horizontal and vertical components of the tension force.
67Jerome and Michael, linebackers for South’s varsity football team, delivered a big hit to the halfback in last weekend’s game. Striking the halfback simultaneously from different directions with the following forces:FJerome = 1230 N at 53° FMichael = 1450 at 107°Determine the resultant force applied by Jerome and Michael to the halfback. (The directions of the two forces are stated as counter-clockwise angles of rotation with East.)
682. A box is pulled at a constant speed of 0 2. A box is pulled at a constant speed of 0.40 m/s across a frictional surface. Perform an extensive analysis of the diagram below to determine the values for the blanks.
69Use your understanding of force relationships and vector components to fill in the blanks in the following diagram and to determine the net force and acceleration of the object. (Fnet = m•a; Ffrict = μ•Fnorm; Fgrav = m•g)
70The 5-kg mass below is moving with a constant speed of 4 m/s to the right. Use your understanding of force relationships and vector components to fill in the blanks in the following diagram and to determine the net force and acceleration of the object. (Fnet = m•a; Ffrict = μ•Fnorm; Fgrav = m•g)Friday Problem 1A 5-kg mass below is moving with a an acceleration of 4 m/s2 to the right. The coefficient of friction for this surface is .2. Use your understanding of force relationships and vector components to determine all your forces.
71Friday Problem 2You are pushing a 200 kg block up a 20 ⁰ hill with a force of 200 N. If the box moves up the hill with a constant speed of 2 m/s, calculate all the forces involved and calculate µ.
72Tuesday Problem 15. The following object is being pulled at a constant speed of 2.5 m/s. Use your understanding of force relationships and vector components to fill in the blanks in the following diagram and to determine the net force and acceleration of the object. (Fnet = m•a; Ffrict = μ•Fnorm; Fgrav = m•g)
73At one moment during a walk around the block, there are four forces exerted upon Fido - a 10.0 kg dog. The forces are:Fapp = 67.0 N at 30.0° above the horizontal (rightward and upward) Fnorm = 64.5 N, up Ffrict = 27.6 N, left Fgrav = 98 N, downResolve the applied force (Fapp) into horizontal and vertical components, then add the forces up as vectors to determine the net force and calculate the acceleration.
74A box is sliding down a ramp at an angle of 47⁰ to the horizontal A box is sliding down a ramp at an angle of 47⁰ to the horizontal. If it is accelerating at 2.5 m/s2 and has a mass of 150 kg, what is the Fnormal, Fnet, Fgravity, Ffric and µ?
75Ramp Problem #1Say a box is sitting on 30⁰ slope and is frictionless, so the only forces are the normal force and gravity. What is the block's acceleration down the slope if the mass is 3.0 kg? What is the normal force?
76Rotation & Centripetal Force Coutesy Space.comRotation & Centripetal ForceHow to Keep it Straight Without Getting Dizzy
77RotationIn addition to side to side (linear) motion, rotation plays an important role in physics, engineering, and life.Name some common phenomena or devices that show rotationTops, planets, bicycle, car wheels, gears, pulleys, fans etc
78Speed on a WheelWhich horses on a carousel move the fastest, inner or outer?Outerv = radius x angular speedv = rw
79Mass at the End of a String What force must thestring exert on the mass?What is the direction ofthis force?A force toward the center of the circle
80Centripetal ForceAny force directed toward the center of a circle is called centripetal.Centripetal forces have clear causes such as tension in a string, gravity, friction etc.Some people call centripetal force a “pseudoforce.” (not real)They say “a real force such as friction provides centripetal force.”
81How Big is Centripetal Force? Fc = mv2/rThe faster the speed the more the forceThe tighter (smaller) the radius the more the forcev2/r is called centripetal acceleration
82Is a mass moving at steady speed in a circle accelerating? Yes. The direction is changingWhat is the direction of this acceleration?Toward the center of the circle
83Car on a CurveWhen auto rounds corner, sideways acting friction between tires and road provides centripetal force that holds car on road
84Don’t Confuse Inertia With Force Tub’s inner wall exerts centripetal force on clothes, forcing them into circular pathWater escapes throughholes because it tends to move by inertia in a straight line pathClothes WasherPhoto courtesy HowStuffWorks.com
85How Can Water Stay In The Bucket? Bucket swung in avertical circleWhat force pushes on thewater?Weight and normal force downYou have to swing the bucket fast enough for the bucket to fall as fast as the waterThere must be a “normal” force exerted by the bottom of the bucket on the water, in addition to gravity
86Centrifugal Force The force ON THE PAIL is inward (centripetal) The force ON THE STRING is outward (centrifugal)If the string broke, which way would the can go?Tangent to the circle
87Change Your Point of View In rest frame of the can there appears to be a centrifugal force. This pseudoforce(or fictitious force) is a result of rotationUnlike real forces, centrifugal force is not part of an interaction
88Book on a Car SeatWhen a car goes around a curve to the left, a book slidesWhich way does it slide?Why doesn’t it keep moving with the car?There is not enough static friction force to keep it going in a circle. This friction must provide the necessary centripetal force.The explanation in the rotating rest frame is different. How?
89Roller Coaster Lab- Centripetal Force You are dropping the ball from 45⁰, practice dropping the steel ball and the plastic ball to observe when it gets around the track.Attach the photogate and calculate the speed and centripetal force of the marble at the top of the loop from various distances for both marbles. Width of ball= .019 mComplete the table for both marbles. (as many trials as necessary)steel = .028 kg plastic = .004 kg Fc= mv2/r radius of loop = .05 mDraw a free body force diagram when the ball is at the top of the loop, label all forces. Do the following lab to solve for the minimum force needed to keep the ball (steel and plastic) on the loop.Mass(kg)Weight(N)Photogate Time (sec)Speed (m/s)Centripetal Force (N)Did the marble stay on track?