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Physics: Understanding Motion Year 10 Core Science 2012 What do we need to learn? How do we convert units? What do these terms mean? Distance, displacement, vector, scalar, speed, velocity, acceleration, force and momentum How can we describe and analyse motion? What do we need to learn? How are changes in movement caused by the actions of forces? What are Newton’s 3 laws of motion? How do we explain and apply them to the real world? What is momentum and how does it apply to real life situations? There’s lots to learn… What’s going to help us? Asking lots of Questions Conducting experiments Drawing graphs Applying the theory to real life situations 1.0 An Ideal World To make life easier for Physics students, situations or events which require mathematical analysis are often described as occuring in an ideal, frictionless world. In the ideal world an object under the influence of Earth’s gravity will accelerate at 9.8 ms-2 throughout its journey never reaching a terminal velocity. In the ideal world the laws of motion apply exactly, eg. objects which are moving will continue to move with the same speed unless or until something occurs to change this. In the ideal world energy transformations are always 100% efficient, so that the potential energy of a pendulum at the top of its swing is all converted to Kinetic Energy (motion energy) at the bottom. In the ideal world perpetual motion machines are common place. Physics language Some units we will be using. Quantity (Unit) Fundamental Units Force (Newton) Mass (kg), length (m), time (s) Acceleration (ms-2) Length (m), time (s) Momentum (kgms-1) Mass (kg), length (m), time (s) Velocity (ms-1) Mass (kg), length (m), time (s) Work (Joule) Note: W = F.d Length (m), time (s) Standard International units are: meter, kilogram, second, ampere Why do we need standard units? When things go wrong… Why do we need standard units? It is important that scientists can share their data and findings. To do this, they use a common set of units. The SI unit for both distance and displacement is the metre (m) and the SI unit for speed is metres per second (m/s). You may have seen ‘metres per second’ also written as ‘ms−1’. This expression is derived from the rule for calculating speed: Speed = distance = time taken metres seconds When shifting the ‘seconds’ from the denominator to the numerator of the fraction, the index (or power) becomes negative. Hence, the seconds are written with an index of −1 in ms−1 (we’ll learn more about this later…) What’s the difference? Scalars have magnitude (size) only Vectors have magnitude and direction. Eg distance traveled is 300meters Eg distance traveled is 300m north Other scalar quantities: Shown by a Speed, mass, time, temp, energy Line showing magnitude arrow showing direction Motion in motion What is the relationship between 100 and 27.78 To change units from m/s to km/h X 3.6 100km/h 27.78 ÷ 3.6 m/s Convert the following 1. 40km/h to m/s 2. 60km/h to m/s 3. 80km/h to m/s 4. 100km/h to m/s 5. 110km/h to m/s 6. 1m/s to km/h 7. 10m/s to km/h 8. 12m/s to km/h 9. 60m/s to km/h 10.15m/s to km/h Convert the following 1. 40km/h = 11.11m/s 2. 60km/h = 16.67m/s 3. 80km/h = 22.22m/s 4. 100km/h = 27.78m/s 5. 110km/h = 30.56m/s 6. 1m/s = 3.6km/h 7. 10m/s = 36km/h 8. 12m/s = 43.2km/h 9. 60m/s = 216km/h 10.15m/s = 54km/h Fundamental skills Show that 1 ms-1 = 3.6 kmh-1 Two relevant conversion factors are: 1 km = 1000 m, 1 h = 3600 s These can be written as: 1km or 1000m 1000m and 1km 1h or 3600 s 3600s 1h Which ones to use ? Easy, you want to end up with km on the top line and h on the bottom 1m x 1km x s 1000m 3.6 3600s 1h so 1 ms-1 = 3.6 kmh-1 Who are these men? Who are these men? Who are these men? So who is faster? Did Usain Bolt run the 100m faster than Michael Johnson ran the 400m? Calculate the speed of the two men. Speed (m/s)= distance (m) ÷ time taken (sec) World records 100m- Usain Bolt 400m Michael Johnson 9.58 seconds 43.18 seconds How many meters per second? 10.44 m/s How many meters per second? 9.26 m/s How many km per hour? 37.59 km/h So the faster runner was… How many km per hour? 33.34km/h Usain Bolt Motion Aim: To convert: meters per second (m/s or ms-1) to kilometers per hour (km/h or kmh-1) using a formula World records Distance Time 100m 9.58 400m 43.18 1km 2:12 2km 4:45 20km 55:48 Distance in meters Time in seconds m/s km/hr World records Distance Time 100m 9.58 Distance in meters 100 Time in seconds 9.58s m/s km/hr 10.44 37.58 400m 43.18 400 43.18s 9.26 33.34 1km 2:12 1000 132.96s 7.52 27.07 2km 4:45 2000 284.79s 7.02 25.28 20km 55:48 20000 3348s 5.97 21.51 Converting units Position & Displacement In order to specify the position of an object we first need to define an ORIGIN or starting point from which measurements can be taken. For example, on the number line, the point 0 is taken as the origin and all measurements are related to that point. -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 Numbers to the right of zero are labelled positive Numbers to the left of zero are labelled negative A number 40 is 40 units to the right of 0 A number -25 is 25 units to the left of 0 Position Questions 1. What needs to be defined before the position of any object can be specified ? A zero point needs to be defined before the position of an object can be defined 2. (a) What distance has been covered when an object moves from position +150 m to position + 275 m ? Change in position = final position – initial position = +275 – (+150) = + 125 m. Just writing 125 m is OK (b) What distance has been covered when an object moves from position + 10 m to position -133.5 m ? Change in position = final position – initial position = -133.5 – (+10) = - 143.5 m. Negative sign IS required Distance & Displacement Distance is a measure of length travelled by an object. It has a Unit (metres). Displacement is the shortest possible length between the start and finish of the travelling object. Distance is best defined as “How far you have travelled in your journey” Displacement is best defined as “How far from your starting point you are at the end of your journey” Distance & Displacement Distance is a scalar measurement. Remember: Scalar measurements are expressed only as a size, with no direction. Displacement is a vector measurement. Remember: Vector measurements are expressed as a size and a direction Distance & Displacement The difference between distance & displacement is easily illustrated with a simple example. You are sent on a message from home to tell the butcher his meat is off. Positive Direction 2 km At this point in the journey, Distance travelled = 2km and Displacement = + 2km At the end of the journey, Distance travelled = 2 + 2 = 4km while Displacement = +2 + (-2) = 0 km Let’s see if this makes sense… Lets read through pages 262-263 and attempt some questions Let’s recall distance and displacement… Distance Is how far on object has traveled, from point A to point B. Distance has only magnitude (scalar) Eg the distance traveled by the runner was 9km Displacement Is the change in position or the shortest distance between two points. Displacement has a magnitude and direction (vector) Eg the runner ran 6km to the right and 3km down, (displacement 6.7km south east) How far did the person travel? start 6km 3km Distance: 6 + 3 = 9km Displacement: 6.7km south east finish Let’s visualise the difference… Speed and Velocity So what’s the difference? Speed & Velocity These two terms are used interchangeably in the community but strictly speaking they are different: Speed is the time rate of change of distance, i.e., Speed = Distance Time Velocity is the time rate of change of displacement, i.e., Velocity = Displacement Time Speed & Velocity Speed is a SCALAR QUANTITY, having a unit (ms-1), but no direction. Thus a speed would be: 100 kmh-1 or, 27 ms-1 Velocity is a VECTOR QUANTITY, having a unit (ms-1) AND a direction. Thus a velocity would be: 100 kmh-1 South or - 27 ms-1 Instantaneous & Average Velocity The term velocity can be misleading, depending upon whether you are concerned with an Instantaneous or an Average value. The best way to illustrate the difference between the two is with an example. You take a car journey out of a city to your gran’s place in a country town 90 km away. The journey takes you a total of 2 hours. The average velocity for this journey, vAV = Total Displacement = 90 = 45 kmh-1 Total Time 2 Questions Instantaneous & Average Velocity Recall: The average velocity for this journey, vAV = Total Displacement = 90 = 45 kmh-1 Total Time 2 However, your instantaneous velocity measured at a particular time during the journey would have varied between 0 kmh-1 when stopped at traffic lights, to, say 120 kmh-1 when speeding along the freeway. Average and Instantaneous velocities are rarely the same. Unless otherwise stated, all the problems you do in this section of the course require you to use Instantaneous Velocities. Questions Speed and Velocity Average speed- total distance by the total time Average Speed = total distance traveled (m) Total time taken (s) Velocity- is the displacement by the time taken Velocity = displacement (m) time taken (s) Speed vs. Velocity Speed is simply how fast you are travelling… This car is travelling at a speed of 20m/s-1 Velocity is “speed in a given direction”… This car is travelling at a velocity of 20m/s-1 east Quick questions A female runner completes a 400 m race (once around the track) in 21 seconds what is: (a)Her distance travelled (in km), (b) her displacement (in km), (c) her speed (in ms-1) and (d) her velocity (in ms-1) ? (a) Distance = 0.4 km (b) Displacement = 0 km (c) Speed = distance/time = 400/21 = 19ms-1 (d) Velocity = displacement/time = 0/21 = 0 ms-1 6km The runner takes half and hour to finish start 3km Distance= 9km Displacement= 6km Speed= 18km/hr Velocity= 12km/hr finish Motion prac Let’s collect some data. . . . Motion by Graphs Distance (a) Describe how the object moving? Time Displacement (b) Time Graphical Relationships Graphs are used to help give us an image of movement of an object Graphs “tell you a story”. There are two basic types of graphs used in Physics: You need to develop the skills and abilities to “read (a)Sketch Graphs – give a “broad brush” picture or show the the story”. “trend”. (b) Numerical Graphs – give the exact relationship between the two variables graphed and may be used to calculate other values. Sketch Graphs Sketch graphs have labelled axes but no numerical values, they show a “trend” between the quantities. Velocity Distance Displacement Time The Story: The Story: The object begins its journey The The Story: Story: As time passes itsthe at the origin at t = 0.the As time As As time time passes passes, passes its displacement displacement gets larger velocity distance remains of the object increases at a constant rate atfrom an isincreasing rate. constant. its starting (slope constant). So point time This is the graph of rate ofischange of displacement This does anot graph change. of anan which equals velocity is object moving with object This travelling is the graph at of a constant. constant acceleration constant stationary velocity object This is a graph of an object travelling at constant velocity Sketch Graphs Distance (a) Time Displacement (b) Time Distance versus time graph. As time passes displacement remains the same. This is the graph of a stationary object Displacement versus time graph. As time passes its displacement is increasing in a uniform manner. This is a graph of an object travelling at constant velocity. Sketch Graphs (c) Velocity versus time graph. As time passes the velocity of the object remains the same. This is a graph of an object travelling at constant velocity. Velocity Time (d) Displacement Time Displacement versus time graph. As time passes its displacement gets larger at an increasing rate. This is a graph of an accelerating object. What a graph can tell you. The graphs you are required to interpret mathematically are those where distance or displacement, speed or velocity or acceleration are plotted against time. The information available from these graphs are summarised in the table given below. Graph Type Read directly from the graph Obtained from slope of graph Obtained from area under the graph Distance or Displacement Vs Time Distance or displacement Speed or velocity No useful information Acceleration Distance or displacement Speed or Velocity Speed or velocity Vs Time Displacement-time graphs 2) Horizontal line = 4) Diagonal line downwards = Remaining stationary Returning to the starting position 40 Distance 30 (metres) 20 10 Time/s 0 20 1) Diagonal line = Moving forwards 40 60 80 100 3) Steeper diagonal line = Moving forwards faster 40 Distance (metres) 30 20 10 0 20 40 60 80 100 Time/s 1) What is the speed during the first 20 seconds? Distance/time = 0.5 ms-1 2) How far is the object from the start after 60 seconds? Read from 40 m graph 3) What is the speed during the last 40 seconds? 4) When was the object travelling the fastest? Distance/time = 1 ms-1 Between 40 & 60 seconds at 1.5 ms-1 Acceleration Acceleration is defined as the time rate of change of velocity, i.e., Acceleration = Change in velocity Time a = ΔV t = Vf - Vi t Acceleration has units of (ms-2) Acceleration simply means how much an object is speeding up by every second Acceleration means an increase in velocity over time, while Deceleration means a decrease in velocity over time. v a When v and a are in the same direction, the car accelerates and its velocity will increase over time. a v When v and a are in the opposite direction, the car decelerates and its velocity will decrease over time. Acceleration For example If an object has an acceleration of 2ms-2, this means that an object will increase its speed by 2ms-1 every second v a If a= 2ms-2 and its initial speed is 10ms-1 then t=0 t=1 t=2 v = 10ms-1 v = 12ms-1 v = 14ms-1 v a If a = -2ms-2 and its initial speed is 20ms-1, then t=0 t=1 t=2 v = 20ms-1 v = 18ms-1 v = 16ms-1 Acceleration A roller coaster, at the end of its journey, changes it’s velocity from 36 ms-1 to 0 ms-1 in 2.5 sec. Calculate the roller coaster’s acceleration. a= = V t 0 36 2.5 = - 14.4 ms-2 Practice Acceleration questions Acceleration = change in velocity (in m/s) (in m/s2) time taken (in s) 1) A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration? 2 ms-2 2) A ball is dropped and accelerates downwards at a rate of 10m/s2 for 12 seconds. How much will the ball’s velocity increase by? 120 ms-1 3) A car accelerates from 10 to 20m/s with an acceleration 5s of 2m/s2. How long did this take? 4) A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration? 2000 ms-2 Velocity-time graphs 1) Upwards line = 4) Downward line = 6 0 Velocity 40 m/s 20 0 2) Horizontal line = 10 20 30 40 3) Upwards line = 50 T/s 80 Velocity m/s 60 40 20 0 10 20 30 40 1) How fast was the object going after 10 seconds? 2) What is the acceleration from 20 to 30 seconds? 3) What was the deceleration from 30 to 50s? 4) How far did the object travel altogether? 50 Time/s Graphical Interpretation 1) Given below is the Distance vs Time graph for a cyclist riding along a straight path. (a) In which section (A,B,C or D) is the Distance cyclist stationary ? A B C D (b) In which section is the cyclist travelling at her slowest (but not zero) 20 speed ? (c) What is her speed in part (b) above ? 10 (d) What distance did she cover in the first 40 seconds of her journey ? (e) In which section(s) of the graph is Time (s) her speed the greatest ? 0 (f) What is her displacement from her 20 30 40 50 60 10 starting point at t = 50 sec ? (a) Stationary in section C (b) Section B (c) Travels 10 m in 20 s speed = 10/20 = 0.5 ms-1 (d) 20 m (read directly from graph) (e) Section D (travels 20 m in 10 s) speed = 2 ms-1 (f) Displacement at t = 50 s is 0 m (i.e., back at starting point) Graphical Interpretation Velocity 2) Shown below is the Velocity vs Time graph for a motorist travelling along a straight section of road. (ms-1) 10 8 6 4 Time(s) 2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -2 -4 -6 -8 -10 (a) Displacement = area under velocity time graph. Between t = 0 and t = 4 s. Area = ½ (10 x 4) = 20 m (b) Acceleration = slope of velocity time graph = (10 – 0)/(4 – 0) = 2.5 ms-2 (c) Distance = area under graph (disregarding signs) Total area = ½(10 x 4) + (6 x 10) + ½(10 x 2) + ½(9 x 2) + (6 x 9) = 20 + 60 + 10 + 9 + 54 = 153 m (d) Displacement = area under graph (taking signs into account) = ½(10 x 4) + (6 x 10) + ½(10 x 2) - ½(9 x 2) - (6 x 9) = 20 + 60 + 10 - 9 – 54 = 27 m (a) What is the motorist's displacement after 4.0 sec ? (b) What is the motorists acceleration during this 4.0 sec period ? (c) What distance has the motorist covered in the 20.0 sec of his journey ? (d) What is the motorist's displacement at t = 20.0 sec (e) What happens to the motorists velocity at t = 20.0 sec? Is this realistic ? (f) Sketch an acceleration vs time graph for this journey. Graphical Interpretation 3) An object is fired vertically upward on a DISTANT PLANET. Shown below is the Velocity vs Time graph for the object. The time commences the instant the object leaves the launcher (a) What is the acceleration of Velocity (ms-1) the object ? 30 (b) What is the maximum height attained by the object ? (c) How long does the object take to stop ? Time (s) (d) How far above the ground is 0 2 4 6 8 10 12 the object at time t = 10.0 sec ? -30 (a) Acceleration = slope of velocity time graph. Slope = (30 – 0)/(0 – 6) = -5.0 ms-2 (b) Displacement = area under velocity time graph = ½ (6 x 30) = 90 m (c) Stops at t = 6.0 sec (d) The rocket has risen to a height of 90 m in 6 sec. It then falls a distance of ½ (4 x 20) = 40 m, so it will be 90 – 40 = 50 m above the ground at t = 10 s Measuring Acceleration with a ticker timer Forced Change What is a Force ? "A force is an interaction between two material objects involving a push or a pull." How is this different from the usual textbook definition of a Force simply being a “push or a pull” ? First, a force is an "interaction". You can compare a force to another common interaction - a conversation. How is Force like a Conversation? A conversation is an interaction between 2 people involving the exchange of words (and ideas). Some things to notice about a conversation (or any interaction) are: To have a conversation, you need two people. One person can't have a conversation A conversation is something that happens between two people. It is not an independently existing "thing" (object), in the sense that a chair is an independently existing "thing". How is Force like a Conversation? Forces are like conversations in that: To have a force, you have to have 2 objects - one object pushes, the other gets pushed. In the definition, "(material) objects" means that both objects have to be made out of matter - atoms and molecules. They both have to be "things", in the sense that a chair is a "thing". A force is something that happens between 2 objects. It is not an independently existing "thing" (object) in the sense that a chair is an independently existing "thing". Force Questions 1. A force is an interaction between 2 objects. Therefore a force can be likened to A: Loving chocolate B: Fear of flying C: Hatred of cigarettes D: Having an argument with your partner 2. Between which pair can a force NOT exist ? A: A book and a table B: A person and a ghost C: A bicycle and a footpath D: A bug and a windscreen What Kinds of Forces Exist ? For simplicity sake, all forces (interactions) between objects can be placed into two broad categories: 1. Contact forces are types of forces in which the two interacting objects are physically contacting each other. Examples of contact forces include frictional forces, tensional forces, normal forces, air resistance forces, and applied forces. 2. Field Forces are forces in which the two interacting objects are not in contact with each other, yet are able to exert a push or pull despite a physical separation. Examples of field forces include Gravitational Forces, Electrostatic Forces and Magnetic Forces What Kinds of Forces Exist ? Force is a quantity which is measured using the derived metric unit known as the Newton. One Newton (N) is the amount of force required to give a 1 kg mass an acceleration of 1 ms-2. So 1N = 1 kgms-2 Force is a vector quantity, you must describe both the magnitude (size) and the direction. Contact or Field Forces 1. Classify the following as examples of either Contact or Field forces in action (or maybe both acting at the same time). EXAMPLE (a) A punch in the nose (b) A parachutist free falling (c) Bouncing a ball on the ground CONTACT FORCE FIELD FORCE √ √ √ √ (d) A magnet attracting a nail √ (e) Two positive charges repelling each other √ (f) Friction when dragging a refrigerator across the floor (g) A shotput after leaving the thrower’s hand √ √ √ What Do Forces Do ? BEGINNING MOTION: A constant force (in the same direction as the motion) produces an ever increasing velocity. Forces affect motion. They can: • Begin motion • Change motion • Stop motion • Have no effect FR NO EFFECT: A total applied force smaller than friction will not move the mass CHANGING MOTION: A constant force (at right angles to the motion) produces an ever changing direction of velocity. STOPPING MOTION: A constant force (in the opposite direction to the motion) produces an ever decreasing velocity. Net Force 1. A body is at rest. Does this necessarily mean that it has no force acting on it ? Justify your answer. NO – A body will remain at rest if the NET FORCE acting is zero – it could have any number of forces acting on it. So long as these forces add to zero it will remain at rest. 2. Calculate the net force acting on the object in each of the situations shown. (a) (b) 900 N 1200 N N 300 N Left 75 N 95 N 20 N Left (c) 250 N 0N 250 N (d) 300 N Down 150 N 450 N Mass V’s Weight What’s the difference? Mass Mass is the matter that makes up an object Weight Weight is the outcome of a gravitational field acting on a mass Weight is a FORCE and is measured in Newtons. Its direction is along the line joining the centres of the two bodies which, between them, generate the Gravitational Field. 1 kg 9.8 N Near the surface of the Earth, each kilogram of mass is attracted toward the centre of the earth by a force of 9.8 N. (Of course each kilogram of Earth is also attracted to the mass by the same force, Newton 3) So, the Gravitational Field Strength near the Earth’s surface = 9.8 Nkg-1 Weight and mass are NOT the same, but they are related through the formula: W = mg Where: W = Weight (N) m = mass (kg) g = Grav. Field Strength (Nkg-1) 1 kg Weight vs Mass Earth’s Gravitational Field Strength is 10N/kg. In other words, a 1kg mass is pulled downwards by a force of 10N. W Weight = Mass x Gravitational Field Strength (in N) (in kg) (in N/kg) M 1) g What is the weight on Earth of a book with mass 2kg? 2) What is the weight on Earth of an apple with mass 100g? 3) Dave weighs 700N. What is his mass? 4) On the moon the gravitational field strength is 1.6N/kg. What will Dave weigh if he stands on the moon? Mass & Weight Fill in the blank spaces in the table based on a persons mass of 56kg on earth. Planet Mass on planet (kg) Grav Field Strength (Nkg-1) Weight on planet (N) Earth 56 9.81 549.4 Mercury 56 0.36 20.2 Venus 56 0.88 20.2 Jupiter 56 26.04 1458.2 Saturn 56 11.19 626.6 Uranus 56 10.49 587.4 Your Mass & Weight Fill in the blank spaces in the table based on your mass on earth. Planet Mass on planet (kg) Grav Field Strength (Nkg-1) Earth 9.81 Mercury 0.36 Venus 0.88 Jupiter 26.04 Saturn 11.19 Uranus 10.49 Weight on planet (N) Newton’s Laws of Motion Newton’s Laws Newton developed 3 laws which cover all aspects of motion (provided objects travel at speeds are well below the speed of light). Law 1 (The Law of Inertia) A body will remain at rest, or in a state of uniform motion, unless acted upon by a net external force. Law 2 The acceleration of a body is directly proportional to net force applied and inversely proportional to its mass. Mathematically, a = F/m more commonly written as F = ma Law 3 (Action Reaction Law) For every action there is an equal and opposite reaction. Newton, at age 26 Motion at or near the speed of light is explained by Albert Einstein’s Theory of Special Relativity. Newton’s Objects want to keep on doing what they are doing st 1 Newton’s 1st Law states: A body will remain at rest, or in a state of uniform motion, unless acted upon by a net external force. Another way of saying this is: Law If NO net external force exists No Net Force means No Acceleration There is no experiment that can be performed in an isolated windowless room which can show whether the room is stationary or moving at constant velocity. Newton 1 deals with non accelerated motion. It does not distinguish between the states of “rest” and “uniform Most importantly: It requires an motion” (constant unbalanced force Force is NOT needed to velocity). to change the keep an object in motion velocity of an As far as the law is object concerned these are the same thing (state). Is this how you understand the world works ? Newton’s Newton’s 2nd Law states: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force FNET, in the same direction as the net force, and inversely proportional to the mass of the object. Mathematically, a = FNET/m more commonly written as FNET = ma nd 2 Law Using the formula FNET = ma is only valid for situations where the mass remains constant Newton actually expressed his 2nd law in terms of momentum. The Net Force on Newton 2 deals with accelerated an object equals motion. the rate of change of its momentum FNET is the VECTOR SUM of all the forces acting on an object. Momentum (p) = mass x velocity The acceleration and FNET are ALWAYS in the same So, FNET = change in momentum = Δp = mΔv = ma direction. change in time Δt Δt Force and acceleration If the forces acting on an object are unbalanced then the object will accelerate, like these wrestlers: Force (in N) = Mass (in kg) x Acceleration (in m/s2) F M A Force, mass and acceleration 1) A force of 1000N is applied to push a mass of 500kg. How quickly does it accelerate? F 2) A force of 3000N acts on a car to make it accelerate by 1.5m/s2. How heavy is the car? 3) A car accelerates at a rate of 5m/s2. If it weighs 500kg how much driving force is the engine applying? 4) A force of 10N is applied by a boy while lifting a 20kg mass. How much does it accelerate by? M A Newton’s nd 2 Law Unbalanced force or Net force causes Terminal Velocity Consider a skydiver: 1) At the start of his jump the air resistance is _______ so he _______ downwards. 2) As his speed increases his air resistance will _______ 3) Eventually the air resistance will be big enough to _______ the skydiver’s weight. At this point the forces are balanced so his speed becomes ________ - this is called TERMINAL VELOCITY Terminal Velocity Consider a skydiver: 4) When he opens his parachute the air resistance suddenly ________, causing him to start _____ ____. 5) Because he is slowing down his air resistance will _______ again until it balances his _________. The skydiver has now reached a new, lower ________ _______. Velocity-time graph for terminal velocity… Parachute opens – diver slows down Velocity Speed increases… Terminal velocity reached… Time New, lower terminal velocity reached Diver hits the ground Newton’s Newton's 1st and 2nd Laws tell you what forces do. Newton's 3rd Law tells you what forces are. For every action there is an equal and opposite reaction rd 3 Law 2. People associate action/reaction with "first an action, then a reaction” For example, first Suzie annoys Johnnie (action) then Johnny says "Mommy! Suzie’s annoying me!" (reaction). This is NOT an example what is going on here! The action and reaction forces exist at the same time. This statement is correct, but terse and confusing. You need to understand that it means: "action...reaction" means that "equal" means : forces always occur in pairs. Both forces are equal in magnitude. Single, isolated forces never Both forces exist at exactly the same time. happen. They both start at exactly the same instant, and "action " and "reaction " are they both stop at exactly the same instant. unfortunate names for a They are equal in time. couple of reasons : 1. Either force in an interaction can be "opposite" means that the two forces the "action" force or the "reaction" always act in opposite directions - exactly force. 180o apart. Questions Friction is a Force Force on box by person Force on floor by box Force on person by box Force on box by floor It’s the sum of all the forces that determines the acceleration. Every force has an equal & opposite partner. 89 Spring 2008 Friction Mechanism Corrugations in the surfaces grind when things slide. Lubricants fill in the gaps and let things slide more easily. Spring 2008 Why Doesn’t Gravity Make the Box Fall? Force of Floor acting on Box Force from floor on box cancels gravity. If the floor vanished, the box would begin to fall. Force of Earth acting on Box (weight) What’s missing in this picture? Force on box by person Force on floor by box Force on person by box Force on box by floor A pair of forces acting between person and floor. Don’t all forces then cancel? How does anything ever move (accelerate) if every force has an opposing pair? The important thing is the net force on the object of interest Force on box by person Net Force on box Force on box by floor 93 Spring 2008 Newton’s Laws 29. At what speeds are Newton’s Laws applicable ? At speeds way below the speed of light 30. Newton’s First Law: A: Does not distinguish between accelerated motion and constant velocity motion B: Does not distinguish between stationary objects and those moving with constant acceleration C: Does not distinguish between stationary objects and those moving with constant velocity D: None of the above 31. Newton’s Second Law: A: Implies that for a given force, large masses will accelerate faster than small masses B: Implies that for a given force, larger masses will accelerate slower than smaller masses C: Implies that for a given force, the acceleration produced is independent of mass D: Implies that for a given force, no acceleration is produced irrespective of the mass. Newton’s 2nd Law 34. A car of mass 1250 kg is travelling at a constant speed of 78 kmh-1 (21.7 ms-1). It suffers a constant retarding force (from air resistance, friction etc) of 12,000 N (a) What is the net force on the car when travelling at its constant speed of 78 kmh-1 ? At constant velocity, acc = 0 thus ΣF = 0 (b) What driving force is supplied by the car’s engine when travelling at 78 kmh-1 ? At constant velocity ΣF = 0, so driving force = retarding force = 12,000 N (c) If the car took 14.6 sec to reach 78 kmh-1 from rest , what was its acceleration (assumed constant) ? Use eqns of motion u = 0 ms-1 , v = 21.7 ms-1, a = ?, x = ?, t = 14.6 s use v = u + at -> 21.7 = 0 + 14.6(a) -> a = 1.49 ms-2 Momentum Newton described Momentum as the “quality of motion”, a measure of the ease or difficulty of changing the motion of an object. Momentum is a vector quantity having both magnitude and direction. Mathematically, p = mv Where, p = momentum (kgms-1) m = mass (kg) v = velocity (ms-1) In order to change the momentum of an object a mechanism for that change is required. Airbags/Crumple Zones 39. Explain why, in a modern car equipped with seat belts and an air bag , he would likely survive the collision whereas in the past, with no such safety devices, he would most likely have been killed. The change in momentum in any collision is a fixed value thus impulse is also fixed, but the individual values of F and t can vary as long as their product is the that fixed value. In modern vehicles seat belts and crumple zones are designed to increase to time it takes to stop thus necessarily reducing the force needed to be absorbed by the driver because Impulse = Ft. This reduced force will lead to reduced injuries. In the old days the driver would have been “stopped” be some hard object like a metal dashboard and his time to stop would have been much shorter and thus the force experienced would have been larger leading to more severe injury and likely death.