P2 topic 3 notes

Topic 3 – Motions and forces • •

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VECTORS AND VELOCITY Displacement: o In a 200m race, all runners cover a 200m distance o However, the track is curvedàthe distance in a straight line between the start and finish is less than this – this distance is called the ‘displacement’ o Displacement is measured in a straight lineàunlike distance (which only has a size), displacement has both a size and direction Speed: o The speed of an object tells you how quickly it will take to travel a certain distance o Speed can be calculated from the equation: § speed (m/s) = distance (m) / time (s) o Like distance, speed only has a size (magnitude) but no direction Velocity: o Velocity tells you how quickly an object is moving, and it also tells you in which direction it’s moving § If object is moving forwards – positive velocity § If object is moving backwards – negative velocity o Velocity, like speed, is measured in m/s Quantities like displacement and velocity – which have a size and direction – are called vector quantities Distance-time graphs: A graph in which distance is plotted against time is called a distance-time graph Time and distance are used to calculate speedàfrom a distance-time graph, we can tell how fast an object is moving: o Horizontal lines mean object is stationary o Straight, sloping lines mean the object is travelling at a constant speed § The steeper the line, the faster the object is travelling o The speed of the object can be calculated from the gradient of the line… § I.e speed = gradient = change in distance / change in time

E.g graph above…: o Between A and B and between C and D, person is jogging at a steady speed o The person is stationary (not moving) between points B and C o Speed person is jogging at between points C and D: § Point C: 35 minutes, 6km

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§ Point D: 45minutes, 8km § àspeed = gradient = change distance / change in time § àspeed = gradient = 2 / 10 = 0.2 km/min = 12 km/hour ACCELERATION Moving things speed up or slow down all the time – this change in velocity is called acceleration Acceleration has both a size and directionàis a vector quantity: o Positive acceleration means the object is speeding up o Negative acceleration means the object is slowing down Acceleration can be calculated from the equation: o acceleration (m/s2) = change in velocity (m/s) / time taken (s) o change in velocity = final velocity (v) - initial velocity (u) o à a = (v – u) / t E.g racing car starts from 0 m/s and reaches a velocity of 50 m/s in 5 seconds.

What is its acceleration? o Acceleration = (50 – 0) / 5 = 10 m/s2 o 10 m/s2 means that each second the velocity of the car increases by 10 m/s (i.e 10 metres per second, per second àunits of acceleration are m/s2) E.g2 during landing, a space shuttle slows down from 70 m/s to 20 m/s in 20s.

Calculate its acceleration: o Acceleration = (20 – 70) / 20 = -50/20 = -2.5 m/s2 o The minus sign shows that the space shuttle is slowing down (i.e negative acceleration) VELOCITY-TIME GRAPHS A velocity-time graph shows how the velocity of an object changes with time: o A horizontal line means the object is travelling at a constant velocity § The higher the line, the higher the velocity o A straight sloping line shows the object is accelerating: § The steeper the line, the greater the acceleration § If line slopes upwards, object is speeding up (positive acceleration) § If line slopes downwards, object is slowing down (negative acceleration)

E.g: o At point A - car is stationary o Between points A and B, C and D, E and F, and, G and H – car is accelerating

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Between points A and B, C and D and G and H – positive acceleration (car is speeding up) § Between points E and F – negative acceleration (car is slowing down) o Between B and C, D and E, and F and G – car is travelling at a constant velocity o The car is travelling at the highest velocity between points D and E Calculating acceleration from a velocity-time graph: The acceleration of an object between two points can be calculated from a velocity-time graph, using the equation on the previous page E.g acceleration between points C and D (on diagram above): o final velocity = 40 m/s……initial velocity = 20 m/s……time = 1 second o àacceleration = 20 / 1 = 20 m/s2 Calculating distance from a velocity-time graph: The area under a velocity-time graph tells us the distance the object has travelled To calculate the area under a velocity-time graph… o you split the area under the graph into shapes (squares and triangles), calculate each bit separately, and then add everything together

E.g (for diagram directly above): o Area of triangle = ½ base x height…à area = 1 x 4 = 4m o Area of square = base x height…àarea = 2 x 4 = 8m o àdistance travelled = 8m + 4m = 12m FORCES Forces can make objects change speed, shape or direction A force is a vector quantity because it has both a size and direction Forces are measured in newtons (N) There are lots of different types of forces: o Upthrust/lift – these act upwards (in air) o Weight (gravity) – this acts downwards o friction/air resistance/drag – these act against the direction of movement (friction – on land, air resistance – in air, drag – in water) o Thrust/driving force – these act in the direction of movement…they are forces produced by engines that push vehicles forwards (thrust – in air, driving force – on land) o Push/pull – these are forces that also act in the direction of movement, but are generated by direct contact between objects (not by engine power) Action and reaction forces: Whenever two objects touch, they interact with each other...: o the forces they exert on each other are equal in size and opposite in direction

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o These forces are known as ‘action’ and ‘reaction’ forces o As a pair they’re called an ‘action-reaction’ pair E.g a book resting on a table: o The weight of the book exerts a downward force on the table – this is the ‘action force’ o The table exerts an equal and opposite (i.e upward) pushing force on the book - this is the ‘reaction force’ o Without this reaction force, the book would fall through the table Action and reaction forces are used to propel rockets: o Gases are pushed out from the rear of the rocket – this is the action force o The reaction force from the gases pushes the rocket forwards Free-body force diagrams: A free-body diagram shows the different forces acting on an object:

The arrows show the direction in which the forces act The length of the arrows shows the size of the forces (the longer the arrow, the bigger the size of the force) RESULTANT FORCES Resultant force: When more than one force acts on an object, the effect is the same as if they were combined into a single force – the ‘resultant force’ To work out the resultant force, you add together all the forces acting in one direction, and then subtract them from all the forces acting in the opposite direction E.g for the diagram above: o Total thrust force to the left = 100,000 N o Total air resistance force to the right = 25,000 N o àresultant force = 100,000 – 25,000 = 75,000 N of force to the left Balanced forces: Forces that are equal but act in opposite directions are ‘balanced’ When all forces are balanced, the resultant force on an object is zero: o àthe object’s movement, shape or direction will not change o So if object was stationary, it will remain stationary…if it was moving, it will continue to move at the same velocity (i.e it will continue to move at the same speed and in the same direction) Unbalanced forces: If forces acting in opposite directions are not equal, the forces are ‘unbalanced’ When forces are unbalanced, the resultant force on an object is not zeroàthe object will accelerate in the direction of the resultant force In the diagram above…: o The thrust is the force produced by the plane’s engines, moving the plane forwards

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o As the plane flies, air molecules push against the plane, producing an opposite force called air resistance o The thrust is greater than the air resistance (as thrust arrow is longer): § àforces are unbalancedàthere’s a resultant force in the direction of the thrust force § àplane accelerates in the direction of the thrust force (left) (i.e plane’s velocity increases) If thrust and air resistance forces were balanced, then the resultant force would be zero and the plane would continue to fly at the same velocity If air resistance was greater than the thrust force…: o there would be a resultant force in the direction of air resistance o àthere would be a (negative) acceleration in the direction of the air resistance (right) (i.e the plane’s velocity would decrease) Note: remember when answering questions on forces that there are no air particles in space (space is a vacuum)àthere is no air resistance in space FORCES AND ACCELERATION The rate at which an object accelerates depends on…: o the size of the (resultant) force – the greater the resultant force, the greater the acceleration of the object o the mass of the object – the greater the mass of the object, the smaller its acceleration àequation linking acceleration, force and mass: o Force (N) = mass (kg) x acceleration (m/s2) o F=mxa o 1 newton is the force needed to accelerate a mass of 1kg by 1m/s2 E.g a car’s acceleration is 3 m/s2. It weighs 1500kg. What is the force provided by the engine? o Force = 1500 x 3 = 4,500 N TERMINAL VELOCITY Mass and weight: Mass (measured in kg) is the quantity of matter there is in an object and does not change Weight (measured in N) is a measure of the pull of gravity on an object…àif gravity changes, weight also changes The strength of gravity is called the ‘gravitational field strength’ (measured in N/kg) On earth, the gravitational field strength is 10N/kgàeach kilogram is pulled down with a force of 10N The weight of any object on earth can be calculated using the equation: o weight (N) = mass (kg) x gravitational field strength (N/kg) o W=mxg E.g what is the weight of a 75kg person on Earth? o weight = 75 x 10 = 750 N E.g2 what is the weight of a 75kg person on the moon? The moon’s gravitational field strength is about 1.5N/kg… o Weight = 75 x 1.5 = 112.5 N o Notice how person’s mass (75kg) is the same on the moon as it is on Earth - mass never changes (it’s not affected by gravitational field strength)

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o Person’s weight instead is much lower on the moon (112.5 N) than on Earth (750 N) because the gravitational field strength is much smaller on the moon than on the Earth Acceleration of falling objects: Larger masses need more force to get them to accelerate than smaller masses (recall the equation: force = mass x acceleration) But as the mass increases, so does the force from gravity (weight) (recall the equation: weight = mass x gravitational field strength) On Earth, there are air particles, which generate air resistance: o àif a hammer and a feather are dropped, the hammer hits the ground first because it is slowed down less by air resistance However, in space there are no air particles and so no air resistance…: o àin a vacuum, all objects (regardless of their mass) accelerate down towards the Earth by the same amount o àif a hammer and a feather are dropped in space, they hit the ground at the same time Terminal velocity – skydiver example: When a skydiver first starts to fall, the main force acting on the skydiver is his own weight (acting downwards)…there is very little air resistance acting in the opposite direction (i.e upwards)… o àlarge resultant force downwards o àskydiver accelerates quickly towards the ground As the skydiver gains velocity, the size of the air resistance force increases… o àthe resultant force downwards is smaller o àskydiver is still accelerating down towards the ground, but the size of the acceleration is smaller Eventually the weight and air resistance become balanced… o àresultant force is now zero o àskydiver stops accelerating…i.e the skydiver continues to fall towards the ground, but now at a constant velocity This constant (maximum) velocity reached when the air resistance force balances the weight is called the ‘terminal velocity’