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## Motion and Forces

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**Outcomes**• 5.6.2a) describe qualitatively the relationship between force, mass and acceleration • 5.6.2b) explain qualitatively the relationship between distance, speed and time • 5.6.2c) relate qualitatively acceleration to a change in speed and/or direction as a result of a net force • 5.6.2d) analyse qualitatively common situations involving motion in terms of Newton’s Laws. • 5.6.6a) distinguish between the terms ‘mass’ and weight**Skills**• 5.13.1e) identify the appropriate units to be used in collecting data • 5.13.1g) formulate a means of recording the data to be gathered or the information to be collected • 5.13.2 a) identify variables that need to be held constant if reliable first-hand data is to be collected • 5.13.2 b) specify the dependent and independent variables when planning controlled experiments • 5.13.2 c) describe a logical procedure for undertaking a simple or controlled experiment • 5.14 a) follow the planned procedure when performing an investigation • 5.14 d) record data using the appropriate units • 5.15 a) make and record observations and measurements accurately over a number of trials • 5.15 b) use independently technologies such as ticker timers • 5.18 d) use symbols to express relationships, including mathematical ones, and appropriate units for physical quantities • 5.18 f) graphs and tables to show relationships and present information clearly and/or succinctly • 5.18 g) select and draw the appropriate type of graph to convey information and relationships clearly and accurately**Motion**Velocity Distance Speed Direction Gravitational Inertia resistance Mass Weight Displacement Qualitative Gravity Calculating Relationship Spelling List**Motion**• Distance is measured in metres (m) for calculations. • time is measured seconds (s). • Note; Displacement is distance with a difference. Displacement is how far you end up from where you started, and in which direction (up, left, north, towards the window). It is distance with direction. You travel a considerable distance each day, but your overall displacement is likely to be zero. You will end up in the same bed that you crawled out of this morning. • Speed is a derived quantity, a measure of how far you can go in a certain time period. (Speed is the rate at which distance is covered.)**Note**• Velocity is speed in a given direction. Wind movement is an example of velocity. • Unit: metres per second • Unit abbreviation: m/s or m s–1**History note; The speed limit for cars in France was 13 km/h**in 1893. Originally all cars in Great Britain had to have a man walking in front of them with a red flag to alert horseriders! In 1896 the speed limit was raised to 20 km/h, and in 1904 to 33 km/h. The first Australian speeding ticket was given to a Tasmanian, • George Innes, who was recklessly driving a car through Sydney at 13 km/h.**Graphing Speed a distance/time graph**The gradient of distance verses time is speed The other graphs show constant speed, slow and faster and stationary (at rest).**In this graph motion is described as**A to B constant speed B to C at rest, stationary. C to D constant speed but slower D to E constant speed to travel back home (fastest speed) This represents the distance travelled D DISTANCE B C E A TIME**Speed–time graph**• A graph of speed against time gives another picture of what is happening in the motion of an object. As before, time is placed on the horizontal axis. If the object is getting faster, the graph rises. If slowing, the graph falls. Constant speed gives a flat graph. The areaunder a speed–time graph gives the distance that theobject has travelled up to that point.**The total distance travelled is the area under the graph.**The area here is 6 + 8 = 14. The object has moved 14 metres.**Problems**1. Light travels at a speed of 300 000 km/s. Calculate how long it takes to travel: • a from the Sun to Earth, a distance of 149 600 000 km • b the 384 403 km distance between the Moon and Earth • c from Earth to Pluto, 5 750 400 000 km away 2. If the distance to the sun is 149600000kms and assume a circular orbit path, then calculate the speed that Earth travels around the Sun. 3. If earths radius is 6750kms, calculate it speed of rotation.**4. For the motions shown in the diagram calculate:**i the distance travelled ii the displacement iii the average speed for the whole trip iv the average velocity for the trip**Calculate the following:**a the total distance Sharnika travelled b her displacement c the time she was away d her speed for the first leg of the trip e her return speed f the times she was at rest g her average speed for the whole trip 5.Sharnie graphed a trip she took. She drew the displacement–time**The ticker-time;- measuring speed**• A ticker-timeris an instrument that breaks movement into a series of small intervals. It gives us a way of accurately measuring distances travelled and times taken, and provides the data from which speeds can be calculated. A small electric hammer strikes a piece of carbon paper at the same frequency as the AC power supply, 50 times a second or 50 Hz. Motion is then recorded as dots on a strip of paper that passes under the hammer. Fifty dots are produced every second, so a space between dots takes only one-fiftieth of a second or 0.02 seconds to produce.**Homework; research how**• ia radar gun or speed camera is used to measure speed • ii a fish finder measures depth and locates schools of fish • iiiWhat isthe meaning of ‘sonic boom’ and the speed at which it occurs.**Ticker Tape Experiment**• Aim To analyse motion using a ticker-timer • Equipment • AC ticker-timer, carbon paper circles and tape, power pack, scissors, ruler, graph paper, paper glue**Method**• 1 Tear off about 1 m of tape and thread it through the timer. • 2 Start the timer, then pull the tape through, changing speed as you go. • 3 Repeat with new tape, so everyone in the group has their own tape. • 4 Draw a line through the first clear dot, then every fifth dot after that. There should be fivespaces per section. This represents a time of 0.1 seconds. • 5 Number each section, then cut along the lines. • 6 Paste the pieces in order onto paper to produce a speed–time graph • 7 Measure the length of each section in millimetres • 8 Add axes to the cut-and-paste graph and use the values in the table to mark appropriate scales along each axis. • 9 On graph paper, plot a distance–time graph for your hand’s motion using the values from your table.**Questions**1 Explain why it was important to number the sections before cutting. 2 Describe any trends or patterns in the graphs you have constructed. 3 State how many dots an AC ticker-timer makes in one second. 4 Once started, describe how long the ticker-timer takes to produce: a a new dot (this is equivalent to a single space between the ‘old’ dot and the new one) b five new dots (equivalent to five spaces**Acceleration**Acceleration is measured in speed units per time unit. The most common unit for acceleration is metres per second per second, m/s2 or m s–2.**Calculating acceleration**• If the speed of a car changes from 0 to 60 km/h in 6 seconds, then its acceleration is (60 – 0) • a = ----------- = 10 6 • The unit here would be speed units (km/h) per time unit (s) or k/h/s: the car gained an extra 10 km/h every second. • For an athlete, speed is better measured in m/s. For example, a runner is jogging along at 2 m/s but then slows her speed over the next 5 seconds until she is running at 1 m/s. Her acceleration would be: (1 – 2) • a = --------- = - 0.2 5 • The units here would be her speed units (m/s) per time unit (s), i.e. m s–2 or m/s2. • You can say that her speed decreased by 0.2 m/s every second, or her speed changed by –0.2 m/s every second. The negative sign tells you that it is a deceleration.**Problems**a. In November 2003, New South Wales dropped the urban street speed limit from 60 km/h to 50 km/h. Contrast the stopping distances at each speed limit. b. It is recommended that the distance between your car and the car in front be equivalent to the reaction distance at that speed. Evaluate how many car lengths a driver travelling at 60 km/h and 100 km/h should leave in front of them.**Calculate the area and the gradient of each section of the**v–t graph in Figure 5.2.8 to find the distance travelled and the acceleration.**Calculating speed**• Let’s say a rocket launches with an acceleration of • 50 m/s2. It started at rest, but 50 m/s is added to its speed every second that passes. • Its speed will then follow the pattern shown in the diagram • If the rocket was already moving at, say, 500 m/s, • then the speeds would be those shown in the figure • another 500 m/s added to them. • You can write this as: • final speed = starting speed + acceleration × time taken • or v = u + at**What is a force?**• a push, pull or twist that causes an object to either: • • increase its speed (accelerate) • • decrease its speed (decelerate) • • change its direction, or • • change its shape. • If any of these things happen, then a force caused it.**Types of forces**Contact and non-contact forces • • Friction: acts between any two surfaces that try and slide over one another. Acts in the opposite direction to the movement or attempted movement. • • Air resistance and drag: friction of air (or liquid or other gases) as it travels across a moving object. Like friction, it acts in a direction opposite to the movement. • • Buoyancy: ‘floating’ force. Acts upwards, opposing the weight force.**• Surface tension: tiny forces between particles on the**surface of a liquid that form a ‘skin’ on the liquid. • • Lift: caused by air moving over a wing or airfoil. Acts at 90° to the surface of the airfoil. • • Thrust: caused by gases or liquid being pushed out the rear of an engine, jet or rocket.**Non-contact forces**• • Weight: caused by gravity. Acts ‘downwards’, towards the centre of the planet. • • Electrostatic: repulsion of like charges (+/+ or –/–) or attraction of unlike charges (+/–). • • Magnetic: repulsion of like poles (N/N or S/S) or attraction of unlike poles (N/S).**Newton’s First Law the law of inertia**• Newton’s First Law examines the forces on an object that is: • at rest ( stopped) or in motion. (moving) • Anything at rest will stay that way unless acted upon by a net unbalanced force. • That is, a force is required to get something moving. • If an object is moving it will continue to do so in a straight line at a constant speed unless acted upon by a net unbalanced force**Crash test dummies have been used for over 30 years to**develop safer cars. Before that, live but anaesthetised pigs were used in crash tests. A large pork BBQ often followed. Human corpses (cadavers) were also used in tests. Accelerometers and force meters were implanted in the cadavers to measure what was occurring. The results from these experiments led to the development of the modern crash test dummy, the Hybrid 3.**Crash test humans**Crash test dummies were first developed by the US Air Force to determine the injuries that pilots would sustain if they ejected from aircraft in flight. Live humans were tested before the invention of the dummies, and Colonel John Stapp underwent 26 tests. In one, he sat in a rocket-powered open sled that accelerated to a speed of 1000 km/h in five seconds, but then was stopped in less than a second. Inertia kept his internal body parts and blood moving and he stated later that he felt as if his eyes would fly out of his skull. Blood vessels in his eyes burst and they bled profusely for 10 minutes after the test. His lungs also collapsed, but he recovered quickly, proving that it was possible to survive such extreme forces.**“I’ve just crashed into a brick wall!”**Newton’s Second Law • Newton’s Second Law states: • Something will happen if a force is applied: the object will accelerate and the acceleration will depend on the mass of the object. • force = mass × acceleration or F = ma • This formula can also be arranged to give: • m = F/a and a = F/m**NEWTON’S THIRD LAW :**“ACTION AND REACTION ARE ALWAYS EQUAL AND OPPOSITE” “IF A BODY A EXERTS A FORCE ON BODY B, THEN B EXERTS AN EQUAL AND OPPOSITELY DIRECTED FORCE ON A”**devishly**clever I’LL PULL HIM WELL ACTION AND REACTION ARE ALWAYS EQUAL AND OPPOSITE!!**Problems**• 1. Calculate the force being applied if: • a a 5 kg box accelerates at 4.1 m/s2 • b a 1.3 tonne car accelerates at 2 m/s2 • c a 400 g ball accelerates at 4 m/s2 • 2. Calculate the acceleration caused by: • a a 40 N force applied to a 0.5 kg mass • b a 0.5 N force applied to a 50 kg mass • 3. A 35 N force causes a mass to accelerate at 7 m/s2. • Calculate the mass.**More problems**• 4. A 3.5 kg body accelerates from rest to 20 m/s in 5 s. • Calculate: • a its acceleration • b the force required • 5. The brakes of a car can exert a stopping force of 3000 N. The car is 1.5 t. Calculate the following: • a the mass of the car in kg (note: 1 t = 1000 kg) • b the deceleration of the car • c how long it would take to stop if it was travelling • initially at 10 m/s**ROCKETS**• Rocket engines are sometimes called reaction engines, as they use the action/reaction pair of forces to provide the thrust needed for launch. Rockets expel massive quantities of gases in one direction, which push the rocket in the opposite direction, usually upwards. The exhaust gases are tiny particles but their effect is dramatic due to their high acceleration. • The exhaust is produced when fuel, called propellant, undergoes chemical combustion**The resulting exhaust stream produces thrust—the force**which propels the rocket. • When thrust equals weight the rocket begins to hover, and when thrust is larger than weight, it lifts off**Flying frozen chickens!**It is estimated that 30 000 birdstrikes occur worldwide each year, leading to damaged aircraft windscreens and even engine failure. The USA designed a unique device for testing the strength of windscreens on aeroplanes. It is a gun that launches a dead chicken at a plane’s windscreen at about the speed the plane flies. The theory is that if the windscreen doesn’t crack from the impact of the carcass, it will survive a real collision with a bird during flight. The British decided to test a windscreen on a new ultra-fast train. They borrowed the FAA’s chicken launcher, loaded a chicken and fired. The ballistic chicken shattered the windscreen, smashed the driver’s seat and embedded itself in the aluminium back wall. The British were stunned and contacted the FAA to see if everything had been done correctly. The FAA reviewed the test and had only one recommendation: ‘Don’t use a frozen chicken’.**Gravity**Is measured as the rate of acceleration at which objects fall. On the Earth’s surface the acceleration of all objects is 9.8 m/s/s. This means that the speed of a falling object increases about 10 m/s every second of its fall. This value is for objects falling in a vacuum. In air, acceleration will be slightly less. An object pushes air out of its way as it falls. The air pushes back with an equal, upward force called air resistance.**Terminal velocity**Air resistance increases as speed increases—the faster you are falling, the more the resistance. Eventually it balances weight, and so the total force acting is zero. There can be no more acceleration and the object falls at a constant speed, called its terminal velocity. All objects have a terminal velocity, but its value will depend on the shape and size of the object. A sheet of paper has high air resistance and a low terminal velocity, while the same paper crumpled has lower air resistance and will reach higher speeds.**Falling from the sky**• Without a parachute humans have a terminal velocity of about 50 m/s. • However, skydivers can control their descent by changing the shape of their body as they fall. An open parachute reduces the terminal velocity to 5 m/s, which is just about the terminal velocity of a raindrop (7 m/s). Pulling on the chute’s strings changes its shape, which changes its speed and direction.**Weight**The force on a mass that is caused by gravity is called weight. It is the force that pulls objects down to the surface of a planet. Weight depends on the mass of the object and the acceleration due to the gravity of the planet itself. You can write this as: weight = mass × acceleration due to gravity or w = mg**Weightlessness**• You have weight whenever gravity is around. True weightlessness (where g = 0) only happens far from the influence of stars and planets. You sometimes ‘feel’ weightless, however, in rides such as the Tower of Terror and the Giant Drop at Dreamworld, when the seat (with you in it) falls. During the fall, the seat cannot push back to give your normal ‘feelings’ of weight. When in orbit, the space shuttle and space stations fall towards Earth. They don’t hit, however, since they are travelling at such high speed ‘horizontally’ that they always miss the planet. • Astronauts aboard them have the ‘feeling’ of weightlessness because both they and the floor fall at the same rate.**Work**• Movement involves energy. Energy is the ability to do work. Work happens whenever things are shifted or rearranged by a force. The bigger the force, the more work done. Likewise if something is shifted a long way, then more work is done than if it only moves slightly. If it doesn’t move, then no work has been done on it. • work = force applied × distance shifted or W = Fs