# P3

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## P3A - Speed

AVERAGE SPEED = DISTANCE X TIME

• GREATER THE SPEED OF OBJECT, FURTHER THE DISTANCE IT CAN TRAVEL IN A CERTAIN TIME
• GREATER THE SPEED OF OBJECT, SHORTER TIME IT TAKES TO GO A CERTAIN DISTANCE

AVERAGE SPEED = (U +V) / 2

• = SPEED AT START
• V = SPEED AT END

DISTANCE = AVERAGE SPEED X TIME = ((U+V) X T) / 2

• UNIT OF SPEED = M/S
• MAY NEED TO CHANGE UNITS E.G. IF TIME IS GIVEN IN HOURS OR IF DISTANCE IS GIVEN IN KM
• 1000 M PER KM
• 3600 SECONDS IN AN HOUR
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## P3A - Speed

DISTANCE-TIME GRAPHS

• GRADIENT = SPEED - STEEPER THE GRADIENT, FASTER OBJECT'S GOING
• FLAT SECTIONS - WHERE IT'S STOPPED
• NEGATIVE GRADIENT SECTIONS (DOWNHILL) MEANS OBJECT HAS CHANGED DIRECTION AND IS COMING BACK
• CURVES REPRESENT ACCELERATION AND DECELERATION
• CURVE OF INCREASING GRADIENT (STEEPENING) - ACCELERATING
• CURVE OF DECREASING GRADIENT (LEVELING OFF) - DECCELERATING
• STAIGHT UPHILL/DOWNHILL LINES - OBJECT MOVING AT STEADY SPEED

CALCULATING SPEED FROM A DISTANCE-TIME GRAPH JUST MEANS WORKING OUT THE GRADIENT OF THE LINE

SPEED = GRADIENT = (VERTICAL / HORIZONTAL)

USE SCALES OF AXIS TO DETERMINE VERTICAL AND HORIZONTAL NUMBERS

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## P3B - Changing Speed

ACCELERATION = CHANGE IN SPEED / TIME TAKEN

• ACCELERATION - HOW QUICKELY SPEED IS CHANGING
• UNITS OF ACCELERATION - M/S2

SPEED AND VELOCITY

• SPEED - HOW FAST OBJECT IS GOING E.G. 30 MPH
• VELOCITY - SPEED AND DIRECTION OF OBJECT E.G. 30 MPH DUE NORTH
• NEGATIVE VELOCITIES - E.G. IF A CAR TRAVELING AT 20MPH TURNS AROUND, IT'S SPEED IS STILL 20 MPH BUT IT'S VELOCITY IS -20 MPH
• RELATIVE VELOCITY - DIFFERENCE IN VELOCITIES OF TWO OBJECTS TRAVELLING IN PARALLEL TO EACHOTHER E.G. TWO CARS TRAVELING AT 30 MPH PARALLEL TO EACHOTHER IN OPPISITE DIRECTION - RELATIVE VELOCITY IS THE DIFFERENCE BETWEEN THE TWO VELOCITIES = 30 AND -30 = 60 MPH
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## P3B - Changing Speed

SPEED-TIME GRAPHS

• GRADIENT = ACCELERATION - THE STEEPER THE GRADIENT, THE GREATER THE ACCELERATION
• FLAT SECTIONS - STEADY SPEED
• POSITIVE GRADIENTS (UPHILL SECTIONS) - ACCELERATION
• NEGATIVE GRADIENTS (DOWNHILL SECTIONS) - DECELERATION
• AREA UNDER ANY SECTION OF GRAPH - DISTANCE TRAVELLED IN THAT TIME INTERVAL
• CURVE - NON UNIFORM ACCELERATION
• ACCELERATION - WORK OUT GRADIENT OF LINE - (VERTICAL / HORIZONTAL)
• SPEED - READ VALUE OFF SPEED AXIS
• DISTANCE TRAVELLED - AREA UNDER ANY PART OF GRAPH
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## P3C - Forces and Motion

FORCE = MASS X ACCELERATION

BALANCED FORCES - OBJECT WILL KEEP MOVING AT THE SAME SPEED IN THE SAME DIRECTION - TO KEEP GOING AT A STEADY SPEED, THERE MUST BE ZERO RESULTANT FORCE (IF CAR STARTS OFF STILL, IT'LL STAY STILL)

UNBALANCED FORCE - OBJECT WILL ACCELERATE IN THE DIRECTION OF THE FORCE - NEWTONS 2ND LAW OF MOTION - THERE WOULD BE A RESULTANT FORCE IF FORCES ARE UNBALANCED

ACCELERATION/DECELERATION - 5 DIFFERENT FORMS: STOPPING, STARTING, SPEEDING UP, SLOWING DOWN, CHANGING DIRECTION - ALL HAPPEN WHEN ARROWS ON FORCE DIAGRAM UNEQUAL

ANY RESULTANT FORCE PRODUCES ACCELERATION - IN MOST REAL SITUATIONS THERE ARE AT LEAST TWO FORCES ACTING ON OBJECT

RESULTANT FORCE OF TWO OBJECTS MOVING PARALLEL TO EACHOTHER - ADD OR SUBTRACT TWO FORCES

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## P3C - Forces and Motion

STOPPING DISTANCE = THINKING DISTANCE + BREAKING DISTANCE

THINKING DISTANCE

THE DISTANCE A CAR TAVELS IN THE TIME BETWEEN THE DRIVER NOTICING THE HAZARD AND APPLYING THE BREAKS

FACTORS WHICH EFFECT THINKING DISTANCE

• HOW FAST YOU'RE GOING - HIGHER YOUR SPEED, HIGHER THE DISTANCE TRAVELLED IN THE TIME IT TAKES TO APPLY BREAKS
• HOW DOPEY YOU ARE - AFFECTED BY TIREDNESS, DRUGS, ALCOHOL, DISTRACTIONS, LACK OF CONCERNTRATION, CARELESS ATTITUDE

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## P3C - Forces and Motion

BREAKING DISTANCE

DISTANCE TRAVELLED IN TIME IT TAKES TO STOP ONCE BREAKS HAVE BEEN APPLIES

FACTORS WHICH EFFECT BREAKING DISTANCE

• HOW FAST YOU'RE GOING - SPEED EFFECTS TIME IT TAKES TO STOP
• MASS OF VEHICLE - WITH SOME BREAKS, BREAKING DISTANCE IS LONGER WHEN VEHICLE HEAVILY LOADED
• HOW GOOD THE BREAKS ARE - HOW MUCH FORCE APPLIED TO BREAKS, WHETHER BREAKS ARE FAULTY - BREAKS NEED TO BE CHECKED REGULARLY
• HOW GOOD THE GRIP IS - DEPENDS ON THREE THINGS
• - ROAD SURFACE - LEAVES, DIESEL SPILLS AND MUD ON THE ROAD - INCREASE BREAKING DISTANCE
• - WEATHER - WET OR ICY ROADS ARE SLIPPERY - INCREASE BREAKING DISTANCE
• - TYRES - TREAD DEPTH OF TYRES SHOULD BE 1.6 MM MINIMUM - ESSENTIAL FOR GETTING RID OF WATER IN     WET CONDITIONS - TYRE WITH NO TREAD WILL RIDE ON SURFACE OF WATER AND EASILY SKID -                          AQUAPLANING - DANGEROUS
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## P3C - Forces and Motion

THE HIGHWAY CODE

• TO AVOID ACCIDENT, DRIVERS NEED TO LEAVE ENOUGH SPACE BETWEEN THEM AND THE CAR IN FRONT, RELATIVE TO THE SPEED THEY'RE GOING AT
• SPEED LIMITS - IMPORTANT - STOPPING DISTANCE IS HEAVILY EFFECTED BY SPEED
• ROAD CONDITIONS, WEATHER CONDITIONS AND TYRES CAN ALSO AFFECT THE STOPPING DISTANCE
• POLICE CALL DRIVING WITHIN STOPPING DISTANCE OF ANOTHER CAR "TAIL GATING"

EFFECT OF SPEED ON STOPPING DISTANCE

• THINKING DISTANCE - LINEAR - THINKING RATE INCREASES AT THE SAME RATE AS SPEED INCREASES - THIS IS BECAUSE THINKING TIME OF THE DRIVER STAYS PRETTY CONSTANT BUT THE HIGHER THE SPEED, THE MORE DISTANCE YOU TRAVEL IN THIS TIME (STRAIGHT LINE ON GRAPH)
• BRAKING DISTANCE - SQUARED RELATIONSHIP - INCREASES FASTER THE MORE YOU SPEED UP - AS SPEED DOUBLES, BREAKING DISTANCE INCREASES FOUR FOLD, WHEN SPEED TRBLES, BREAKING DISTANCE INCREASES 9 FOLD (CURVED LINE ON GRAPH)
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## P3D - Work and Power

WORK DONE = FORCE X DISTANCE

WHEN A FORCE MAKES AN OBJECT MOVE, ENERGY IS TRANSFERED AND WORK IS DONE

• WHEN SOMETHING MOVES, IT NEEDS ENERGY SUPPLIED BY SOMETHING ELSE TO MOVE IT
• THE THING WHICH MOVES THE OBJECTS A SUPPLY OF ENERGY E.G. FUEL, FOOD, ELECTRICITY
• WHEN IT DOES WORK TO MOVE THE OBJECT, IT TRANSFERS THE ENERGY IT'S RECIEVED (AS FUEL) INTO OTHER FORMS
• WHETHER ENERGY IS TRANSFERED USEFULLY (E.G. LIFTING A LOAD) OR WASTED (E.G. BY HEAT FROM FRICTION), YOU CAN STILL SAY THAT WORK IS DONE
• EXAMPLES OF WHEN WORK IS DONE INCLUDE LIFTING WEIGHTS, CLIMBING STAIRS, PUSHING A SHOPPING TROLLEY, PULLING A SLEDGE
• MEASURED IN JOULES
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## P3D - Work and Power

POWER = WORK DONE / TIME TAKEN

• POWER - THE MEASURE OF HOW QUICKLY WORK IS BEING DONE
• A POWERFUL MACHINE IS ONE THAT TRANSFERS A LOT OF ENERGY IN A SHORT SPACE OF TIME
• MEASURED IN WATTS - 1 WATT IS ONE JOULE OF ENERGY TRANSFERRED PER SECOND - 1 W = 1 J/S

POWER = FORCE X SPEED

• WORK DONE IS FORCE X DISTANCE
• POWER = (FORCE X DISTANCE) / TIME
• DISTANCE / TIME IS ANOTHER WAY OF WRITING SPEED
• POWER = FORCE X SPEED

FUEL CONSUMPTION

• CAR WITH LOW FUEL CONSUMPTION - E.G. 1L PER 100 KM - DOESN'T NEED MUCH FUEL TO TRAVEL 100KM - GOOD FOR ENVIRONMENT (LESS CO2 EMISSIONS) AND CHEAPER TO RUN
• CAR WITH HIGH FUEL CONSUMPTION - E.G. 1 MILE PER GALLON - ONLY TRAVELS 1 MILE FOR A GALLON OF FUEL - BAD FOR ENVIRONMENT, MORE EXPENSIVE
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## P3E - Energy on the Move

KINETIC ENERGY = 1/2 X MASS X SQUARED SPEED

• KINETIC ENERGY - ENERGY IT HAS WHEN MOVING - DEPENDS ON MASS AND SPEED OF OBJECT
• THE GREATER IT'S MASS AND THE FASTER IT'S GOING, THE BIGGER THE KINETIC ENERGY WILL BE

KINETIC ENERGY AND STOPPING DISTANCES

• KINETIC ENERGY TRANSFERRED = WORK DONE BY BRAKES
• 1/2 X M X V SQUARED = MAXIMUM BREAKING FORCE X BREAKING DISTANCE
• BREAKING DISTANCE INCREASES AS SPEED SQUARED INCREASES - IT'S A SQUARED RELATIONSHIP
• BECAUSE THE MAXIMUM BREAKING FORCE IS THE MAXIMUM AND CAN'T BE INCREASED, BREAKING DISTANCE MUST INCREASE BY A FACTOR OF FOUR TO MAKE THE EQUASION BALANCE
• IF YOU GO TWICE AS FAST, THE BREAKING DISTANCE MUST INCREASE BY A FACTOR OF FOUR TO CONVERT THE EXTRA KINETIC ENERGY
• INCREASING SPEED BY A FACTOR OF 3 INCREASES KE BY FACTOR OF 9 - BRAKING DISTANCE BECOMES 9 TIMES AS LONG
• DOUBLING THE MASS OF AN OBJECT DOUBLES THE KE - DOUBLE THE BREAKING DISTANCE
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## P3E - Energy on the Move

FOSSIL FUELS

• MOST CARS RUN ON FOSSIL FUELS - PETROL OR DIESEL MADE FROM OIL (A FOSSIL FUEL)
• EMMISSIONS RELEASED WHEN FUELS ARE BURNED CAUSE ENVIRONMENTAL PROBLEMS - E.G. RELEASE CO2 WHICH LEADS TO GLOBAL WARMING, RELEASE SULFUR DIOXIDE WHICH LEADS TO ACID RAIN
• NON-RENEWABLE - ONE DAY THEY'LL RUN OUT

BIOFUELS

• CARS RUN ON FUELS MADE FROM PLANTS AND ORGANIC WASTE
• SCIENTISTS WORKKING ON ALTERNATIVES TO FOSSIL FUELS
• ADVANTAGES - RENEWABLE, CARBON NUETREL - RELEASE AS MUCH CARBON DIOXIDE AS PLANTS TAKE IN WHEN GROWING - OVERALL CO2 EMISSIONS WOULD BE REDUCED IF WE SWITCHED TO BIOFUELS
• DOESN'T PRODUCE MUCH OTHER POLLUTION BUT CARS THEMSELVES PRODUCE POLLUTION WHEN MADE

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## P3E - Energy on the Move

ELECTRIC CARS

• CARS THAT RUN ON LARGE BATTERIES THAT POWER ELECTRIC MOTORS
• DON'T RELEASE POLLUTION WHEN DRIVING BUT NEED TO BE CHARGED - CHARGED WITH ELECTRICITY GENERATED IN POWER STATIONS WHICH DO POLLUTE
• WAY ROUND THIS - SOLAR POWER - COULD REDUCE OVERALL CO2 EMMISSIONS - DISADVANTAGE - SOLAR PANELS EXPENSIVE TO MAKE AND BUY
• DISADVANTAGES OF ELECTRIC CARS - OVERALL PRODUCTION OF CARS STILL POLLUTE AND ELECTRIC CARS ARE CURRENTLY LIMITED IN PERFORMANCE COMPAIRED TO FOSSIL FUELED CARS
• THIS IS CHANGING, HOWEVER, WITH ADVANCES IN TECHNOLOGY AND NEW DESIGNS
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## P3E - Energy on the Move

FACTORS WHICH EFFECT FUEL CONSUMPTION

• MASS AND SPEED -TO MOVE A CAR, FUEL NEEDS TO BE CHANGED INTO KINETIC ENERGY - KINETIC ENERGY = MASS X SPEED SQUARED X 1/2 SO THE HIGHER THE SPEED AND HIGHER THE MASS, THE MORE KINETIC ENERGY IT WILL NEED AND THE MORE FUEL IT WILL NEED TO BE TURNED INTO K.E.
• CARS WORK MORE EFFICIENTLY AT CERTAIN SPEEDS - MOST EFFICIENT SPEED BETWEEN 40 AND 55 MPH
• DRIVING STYLE - ACCELERATION USES MORE K.E. SO MORE FUEL WILL NEED TO BE TURNED INTO K.E. - CONSTANT BRAKING AND ACCELERATING ALSO INCREASES K.E. NEEDED
• WEATHER CONDITIONS - DIFFERENT WEATHER AND ROAD CONDITIONS MAY REQUIRE MORE FREQUENT BRAKING AND ACCELERATION
• FRICTION - CAR USES K.E. FROM FUEL TO WORK AGAINST FRICTION BETWEEN TYRES AND ROAD AND BETWEEN THE CAR ITSELF AND THE AIR AROUND IT - OPENING WINDOWS, HAVING A ROOF BOX ETC. WILL HAVE AN EFFECT - INCREASES AIR RESISTANCE AND DRAG
• CARS DESIGNED TO BE MORE FUEL EFFICIENT - MORE EFFICIENT ENGINES, STREAMLINED
• HIGHER FUEL CONSUMPTION RELEASES MORE EMMISSIONS - WORSE FOR ENVIRONMENT - CAR MANUFACTURERS CHANGING CAR AND ENGINE DESIGNS TO REDUCE EMISSIONS
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## P3F - Crumple Zones

MOMENTUM (KGM/S) = MASS (KG) X VELOCITY (M/S)

• HIGHER THE SPEED AND LARGER THE MASS OF AN OBJECT, THE MORE MOMENTUM IT HAS

FORCE ACTING = CHANGE IN MOMENTUM (KGM/S) / TIME TAKEN FOR CHANGE TO HAPPEN (S)

• CAN BE EXPLAINED BY NEWTONS SECOND LAW OF MOTION (FORCE = MASS X ACCELERATION)
• ANY FORCE APPLIED TO OBJECT INCREASES IT'S ACCELERATION (F = MASS X A)
• ACCELERATION IS A CHANGE IN VELOCITY OVER TIME (A = CHANGE IN V / T)
• THEREFORE A FORCE APPLIED TO AN OBJECT CHANGES IT'S VELOCITY OVER TIME (F = CHANGE V X MASS / T)
• A CHANGE IN MOMENTUM CAN BE CAUSED BY A CHANGE IN VELOCITY (CHANGE IN M = MASS X CHANGE IN V) SO ANY FORCE APPLIED TO AN OBJECT OVER A CERTAIN TIME CAUSES A CHANGE IN MOMENTUM (F = CHANGE IN M / T)

EFFECT OF TIME TAKEN FOR CHANGE IN MOMENTUM ON FORCE

• IF MOMENTUM CHANGES VERY QUICKLY, FORCE APPLIED WILL BE VERY LARGE - DANGEROUS
• LONGER IT TAKES FOR CHANGE IN MOMENTUM, SMALLER THE FORCE
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## P3F - Crumple Zones

CAR SAFETY FEATURES

• COLLISION - FORCE ON OBJECT CAN BE LOWERED BY SLOWING OBJECT DOWN OVER LONGER TIME - LONGER IT TAKES FOR CHANGE IN MOMENTUM, SMALLER FORCE ACTING - SOME INJURIES CAUSED BY RAPID DECELLERATION OF PARTS OF BODY - INCREASING COLLISION TIME REDUCES DECELERATION
• SAFETY FEATURES INCREASE COLLISION TIME - REDUCE FORCES AND DECELLERATION - REDUCE INJURY - ALSO REDUCE INJURIES BY STOPPING PERSON HITTING HARD SURFACES INSIDE CAR - SOME FEATURES CHANGE SHAPE DURING CRASH - ABSORB KINETIC ENERGY
• CRUMPLE ZONES - CRUMPLE AND CHANGE SHAPE ON IMPACT - INCREASE TIME TAKES CAR TO STOP
• SEAT BELTS - STRETCH - INCREASE TIME TAKEN FOR WEARER TO STOP - REDUCES FORCE ACTING ON CHEST - NEED TO BE REPLACED AFTER CRASH
• AIR BAGS - SLOW PERSON DOWN MORE GRADUALLY
• ROADS MADE SAFER - PLACING CRASH BARRIERS AND ESCAPE LANES IN DANGEROUS LOCATIONS - DESIGNED TO INCREASE TIME AND DISTANCE OF COLLISION - FORCE REDUCED

ABS BRAKES - ANTI-LOCK BRAKING SYSTEM BRAKES - KEEP CONTROL OF CARS STEERING WHEN BRAKES HARD

• DRIVER BRAKES HARD - ORDINARY BRAKES LOCK WHEELS - CAN'T TURN - CAN CAUSE SKID
• ABS PUMP ON, OFF - STOP WHEELS LOCKING - PREVENT SKIDDING - GIVE CAR SHORTER BREAKING DISTANCE
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## P3F - Crumple Zones

TESTING SAFETY FEATURES

• SAFETY FEATURES RIGOROUSLY TESTED - SEE HOW EFFECTIVELY THEY SAVE LIVES OR STOP INJURIES
• TEST INVOLVES CRASHING CARS CONTAINING CRASH TEST DUMMIES WITH AND WITHOUT SAFETY FEATURES - WATCHING SLOW MOTION FILM FOOTAGE TO SEE RESULTS - SEE HOW BAD INJURY WOULD BE
• REPEATED USING DIFFERENT CARS, SPEEDS, SIZED DUMMIES
• RESULTS COMPARED WITH REAL DATA FROM ACTUAL CAR ACCIDENTS - TAKEN INTO ACCOUNT WHEN DECIDING WHETHER TO FIT SAFETY FEATURE
• CRASH TESTS - SHOWM WEARING SEATBELTS REDUCES FATALITIES BY 50% - AIRBAGS REDUCE 30%
• DEPARTMENT FOR TRANSPORT PRODUCE REPORTS ON ROAD TRAFFIC ACCIDENTS IN UK EACH YEAR - SHOW SIGNIFICANT REDUCTION IN DEATHS AND INJURIES SINCE 1980S - DUE TO WIDE RANGE OF SAFETY FEATURES
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## P3G - Falling Safely

FRICTION - FORCE WHICH ACTS AGAINST OBJECTS THAT ARE MOVING, SLOWING THEM DOWN

• FRICTIONAL FORCE - MATCH SIZE OF FORCE TRYING TO MOVE IT UP TO POINT - AFTER POINT FRICTION WILL BE LESS
• FRICTION ACTS TO MAKE OBJECT SLOW OR STOP - ALWAYS NEED DRIVING FORCE TO KEEP STEADY SPEED
• WAY IN WHICH FRICTION OCCURS:LARGER AREA OF OBJECT, GREATER DRAG - DRAG REDUCED BY BY STREAMLINING E.G. SPORTS CARS ARE WEDGE SHAPED - ROOF BOXES AND DRIVING WITH WINDOWS OPEN RUIN THIS - INCREASE DRAG
• BETWEEN SOLID SURFACES WHICH ARE GRIPPING
• BETWEEN SOLID SURFACES WHICH ARE GLIDING PAST EACHOTHER
• RESISTANCE OR DRAG FROM FLUIDS
• SOMETHING DESIGNED TO REDUCE SPEED E.G. PARACHUTE - LARGE SURFACE AREA - MORE AIR RESISTANCE
• IN A FLUID, FRICTION ALWAYS INCREASES AS SPEED INCREASES
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## P3G - Falling Safely

TERMINAL SPEED - MAXIMUM SPEED REACHED BY FALLING OBJECTS WHERE THEY NO LONGER ACCELERATE

• OBJECT FIRST SETS OFF - MORE FORCE ACCELERATING OBJECT THAN INCREASING SPEED
• AS SPEED INCREASES, AIR RESISTANCE INCREASES - GRADUALLY REDUCES ACCELERATION UNTIL RESISTING FORCE EQUAL TO ACCELERATING FORCE - FORCES BALANCED - NO FURTHER ACCELERATION

TERMINAL SPEED IN RELATION TO DRAG

• TERMINAL SPEED OF ANY MOVING OBJECT DEPENDS ON DRAG COMPARED TO DRIVING FORCE
• GREATER DRAG (DEPENDS ON SHAPE AND AREA OF OBJECT) - LOWER TERMINAL SPEED
• SKYDIVERS HAVE PARACHUTES - INCREASE AIR RESISTANCE DUE TO LARGE SURFACE AREA BUT SAME AMOUNT OF DRIVING FORCE - EQUAL OUT QUICKER - DECREASE TERMINAL SPEED - MAKE LANDING SAFE

FORCES AND SPEED

• STEADY HORIZONTAL SPEED - REACTION, WEIGHT, THRUST, WEIGHT BALANCED
• STEADY VERTICAL SPEED - WEIGHT AND DRAG BALANCED
• HORIZONTAL ACCELERATION - UNBALANCED FORCES - THRUST BIGGER THAN DRAG
• VERTICAL ACCELERATION - FORCES UNBALANCED - WEIGHT BIGGER THAN DRAG
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## P3H - The Energy of Games and Theme Rides

GRAVITATIONAL POTENTIAL ENERGY = MASS X G X HEIGHT

• GPE - ENERGY THAT SOMETHING HAS BECAUSE OF IT'S HEIGHT ABOVE THE GROUND - ENERGY USED TO RAISE IT STORED AND CONVERTED TO KINETIC ENERGY AS IT FALLS
• G = GRAVITATIONAL FEILD STRENGTH - ON EARTH IT'S ABOUT 10

K.E GAINED = G.P.E LOST - mgh = 1/2 mv2

• WHEN FALLING OBJECT REACHES TERMINAL SPEED, G.P.E CAN'T BE CONVERTED TO K.E TO MAKE IT ACCELERATE ANYMORE - CONVERTED TO INTERNAL ENERGY OF OBJECT OR USED TO HEAT UP AIR PARTICLES SURROUNDING IT THROUGH FRICTION
• EQUASION CAN BE REARRANGED TO H = V SQUARED / 2G (AS LONG AS MASS DOESN'T CHANGE WHEN FALLING)
• CAN BE USED TO FIND HEIGHT SOMETHING IS DROPPED FROM TO REACH CERTAIN SPEED E.G. WHEN DESIGNING ROLLAR COASTER
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## P3H - The Energy of Games and Theme Rides

ROLLAR COASTERS

• AT TOP OF ROLLARCOASTER - CARRIAGE HAS LOTS OF GPE
• CARRIAGE DESCENDS - GPE CONVERTED TO KE - CARRIAGE SPEEDS UP
• IGNORING AIR RESISTANCE AND FRICTION BETWEEN TRACK AND CART, MINIMUM GPE AND MAXIMUM KE AT LOWEST POINT OF ROLLARCOASTER
• REAL ROLLAR COASTER - DOES HAVE FRICTION - CARRIAGE HAS TO HAVE ENOUGH KE TO GET UP HILL AGAIN
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## Comments

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Just what I needed! Thank you loads! =)

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Exam in like less than 12 hours, thought I could leave P3 due to calculations but I realized that I cannot. Helped so much :D

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