Basic Physics PH 1 1 S I System

Basic Physics PH 1. 1

S. I. (System Internationale) Units All units can be divided into two groups … base units derived units kg m s K A mol cd J Ω V W N Hz Bq C Pa Wb T ……. • only 7 units • each has a detailed definition

physical quantity unit name SI unit combination of base units force newton N kg m s-2 energy / work joule J kg m 2 s-2 power watt W kg m 2 s-3 voltage volt V kg m 2 s-3 A-1 resistance ohm Ω kg m 2 s-3 A-2 pressure pascal Pa kg m-1 s-2 frequency hertz Hz s-1

For example: the kilogram… © BIPM any object that has a mass of 1 kg has exactly the same mass as that of the international prototype of the kilogram atmospheric pressure inside three layers of glass platinum-iridium alloy at a constant temperature 19± 1 C Why choose platinum-iridium? It is a very dense alloy, so a 1 kg sample has a small volume and hence a small surface area. As a result, very little surface contamination takes place, so the mass of the sample stays constant.

For example: the metre … © Wikipedia 1 m is the distance between two lines scratched ona particular bar of platinum-iridium alloy (that is stored at the Bureau International des Poids et Mesures in Sèvres, France) at the melting point of ice Recently, the definition has been altered … 1 m is the distance travelled by light through a vacuum in 1/ 299792458 s!

one mole is the amount of substance that contains the same number of parts as there atoms in 12 g of the carbon-12 isotope this is number is the Avogadro number = 6. 022 x 1023 …. . an enormous number!! An Avogadro number of soft drink cans would cover the entire surface of the Earth to a depth of 200 miles! If counting atoms at a rate of 10 million per second, it would take 2 billion years to count the atoms in one mole of substance! http: //ysfine. com/einstein/avogadro. jpg For example: the mole …

Scalar and vector Every quantity that is measured in Physics is either … (1) scalar – magnitude (i. e. a figure) only eg. distance, time, mass, temperature, speed, density, …. (2) vector – magnitude and direction eg. force, displacement, velocity, magnetic field strength, …. We use arrows to represent vectors in diagrams … 12 N to right the length of the arrow represents the size of 4 N upwards the vector

Combining the effect of more than one vector … displacement distance = +

The effect of more than one vector … Any two vectors combine like this to give a single vector that has exactly the same effect, eg. two forces, two velocities. . aeroplane’s velocity wind velocity relative to the ground resultant force

The Paralelogram Law – adding vectors A and B C A B B A C C = A +B vector C can be obtained by a drawing scale diagram or by using the cosine and sine rules to calculate it

Pythagoras’s Law – adding perpendicular vectors A C C = A +B θ B To calculate the magnitude of C … and its direction … C 2 = A 2 + B 2 tanθ = A B

Resolving vectors – splitting a vector into two components … the number of combinations is infinite!

Resolving a vector – splitting a vector into two components concentrate on two perpendicular vectors y F θ x y = F·sinθ x = F·cosθ

Newton’s First Law in the absence of a force, an object either stays at rest or continues to move with constant velocity in other words … all objects have inertia (an inbuilt reluctance to change their motion) © The Estate of Harold E. Edgerton It also defines a force … that which is needed to accelerate an object

Newton’s First Law a force stops the van / motor cycle / car … but the stepladder / cyclist / driver continue to move at constant velocity !! © Tom Henderson

Newton’s First Law Without a force to change its direction , the ball moves at constant speed in a straight line © Tom Henderson

What is a centrifugal force? an imaginary force that ‘appears’ as a result of Newton’s First Law eg. when a car corners …. . there is no friction between the tape and the car’s dashboard, so there is no force to change its direction, until the side of the car is in contact with it

What is a centrifugal force? © Tom Henderson …. the passenger ( ) is under the impression that he is being pushed towards the driver ( ), but this is an imaginary force (note that the car is a left-hand drive!)

Newton’s Second Law the rate of change of momentum is directly proportional to the applied force and takes place in the direction of the force i. e. it relates the size of the acceleration with the force that causes it acceleration smaller mass larger mass force

From the • the acceleration is directly proportional graph … to the force that gives rise to it • the acceleration is inversely proportional to the applied force i. e. force mass × acceleration force = k · mass × acceleration k - constant 1 N is the force that gives a 1 kg mass an acceleration of 1 ms-2 resultant force when there is more than one force acting k=1 force = mass × acceleration ΣF = ma

acceleration driving force drag G D force = mass × acceleration G-D=m×a acceleration a = G-D m the acceleration is directly proportional to the magnitude of the resultant force

Newton’s Third Law In contrast to the first two laws, we are looking at the forces that are acting on two interacting objects … to every action there is an equal but opposite reaction if A exerts a force (FAB) on B, then B exerts an equal but opposite force (FBA ) on A B A 5 N 5 N action: A pulls B to the left with a force 5 N reaction: B pulls A to the right with a force 5 N http: //www. bbc. co. uk/schools/ks 3 bitesize/ or

Examples: action: the boy pulls the girl to the left reaction: the girl pulls the boy to the right © Tom Henderson

action: the gun pushes the bullet forwards reaction: the bullet pushes the gun backwards (recoil) action: the man pushes the boat backwards www. allstar. fiu. edu reaction: the boat pushes the man forwards

action: the man pushes the ground downwards and backwards reaction: the ground pushes the man upwards and forwards action: the man pushes the ground downwards reaction: the ground pushes the man upwards

Some peculiar examples … action: the balloon pushes the air to the left reaction: the air pushes the balloon to the right © teachertech. rice. edu action: the rocket pushes the gases backwards reaction: the gases push the rocket forwards

Some peculiar examples … action: the Earth pulls the parachutist downwards reaction: the parachutist pulls the Earth upwards!! action: the girl pulls the wall to the right reaction: the wall pulls the girl to the left!! © Tom Henderson

In any situation, there are many forces acting. In order to analyse the effects of these forces, we draw free body diagrams In a FBD, there is only one object shown, along with all of the forces that are acting on it How many forces are there acting in this situation?

FBD for the boy: B C A A – the Earth pulling the boy downwards (i. e. gravity) B – the chair pushing the boy upwards C – the book pushing the boy downwards

FBD for the chair: E D B′ D – the Earth pulling the chair downwards (i. e. gravity) B′ – the boy pushing the chair downwards (force B’s partner) E – the ground pushing the chair upwards (a contact force) Even though they exist, we ignore the gravitational forces that act between small masses e. g. the boy and the chair

FBD for the book: C′ F F – the Earth pulling the book downwards (i. e. gravity) C′ – the boy pushing the book upwards (force C’s partner)

FBD for the Earth: D′ F′ A ′ E′ A′ – the boy pulling the Earth upwards (force A’s partner) F′ – the book pulling the Earth upwards (force F’s partner) D′ - the chair pulling the Earth upwards (force D’s partner) E′ – the chair pushing the ground downwards (force E’s partner) 12 forces identified in total (always an even number)

Another example … a car accelerating • we use a double arrow to show acceleration • we don not distinguish between the friction and air resistance that try to prevent the motion

FBD for the car: B D C E A A – the Earth pulling the car downwards (i. e. gravity) B – the ground pushing the car upwards (contact force) C – the ground pushing the car forwards (driving force) D – the ground pushing the car backwards (friction) E – the carvan pulling the car backwards • the car accelerates if force C > forces (D+E) • acceleration a = (C-D-E)/m (m – mass of car only)

G FBD for the caravan: H E′ F E′ - the car pulling the caravan forward (force E’s partner) F – the Earth pulling the caravan downwards (gravity) G – the ground pushing the caravan upwards (contact force) H – the ground pushing the caravan backwards (friction) • the caravan accelerates if force E′ > force H • acceleration a = (E′-H)/m (m – mass of caravan only)

A′ F′ FBD for the Earth: A′ - car pulling the Earth upwards (A’s partner) H′ D′ B′ – car pushing the ground downwards (force B’s partner) C′ B′ G′ C′ – car pushing the ground backwards (force C’s partner) D′ – car pushing the ground forwards (force D’s partner) F′ - caravan pulling the Earth upwards (force F’s partner) G′ - caravan pushing the ground downwards (force G’s partner) H′ - caravan pushing the ground forwards (force H’s partner) We ignore any resultant forces that act on the Earth. Their effects would be negligible since the mass of the Earth is enormous.

The moment of a force (or torque) is the turning effect that a force has bout a pivot distance to be exact … force http: //www. splung. com/content/sid/2/page/moments moment = force × distance from the pivot moment = force × distance of the line of action of the force from the pivot

The Principle of Moments an object is in equilibrium provided the total clockwise moments about any point is equal to the total anticlockwise moments about that point or ∑(Fd)clockwise = ∑(Fd)anticlockwise

In its simplest form … clockwise moment about the pivot = 20 1 = 20 Nm anticlockwise moment about the pivot = 10 2 = 20 Nm clockwise moment = anticlockwise moment about the pivot therefore the beam balances

When there is more than one clockwise and anticlockwise moment … ∑clockwise moments about the pivot = (20 1) + (12 1. 8) = 20 + 21. 6 = 41. 6 Nm ∑anticlockwise moments about the pivot = (10 2) + (30 0. 7) = 20 + 21 = 41 Nm total clockwise moments > total anticlockwise moments therefore it does not balance – the beam tilts in the clockwise direction

When considering the free body diagram for the beam … G G - force of pivot pushing beam upwards If the beam is not accelerating upwards or downwards … upward force = G = total of forces acting downwards = 10 + 30 + 20 + 12 = 72 N Therefore for any object to be truly in equilibrium … (1) there is no resultant force acting on it (2) there is no unbalanced moment about any point

The centre of gravity the centre of gravity is that point from which all of an object’s weight can be considered to act Rather than considering the weight (w) of each individual particle, we combine all of the weights… W = ∑w and consider W acting from one point (the centre of gravity) W

An object is stable provided its weight does not produce a moment that causes it to topple … inverted cone on its side www. webdesign. org upright cone W W stable equilibrium unstable equilibrium W neutral equilibrium

What is the effect of the position of the centre of gravity on an object’s stability? low C of G unstable equilibrium at a smaller angle higher C of G

lower centre of gravity – more stable

What is the effect of the width of the base on stability? wider base – greater stability

http: //nexus 404. com http: //www. bhcyachts. com When designing for stability … low centre of gravity large mass (greater inertia) http: //www. jpmagazine. com/ en. wikivisual. com wide base

q the density of a substance is the mass of 1 cm 3 of the material q it can also defined as the mass of 1 m 3 of a substance the reading will be the density in gcm-3 q density is a scalar quantity – its unit is either gcm-3 or kgm-3 http: //www. awesomescales. net

The density of some common substances: substance air feathers wood density (gcm-3) 0. 0013 0. 003 ~ 0. 7 density (kgm-3) 1. 3 3. 0 ~ 700 ice water bricks aluminum steel silver mercury 0. 9 1. 0 1. 8 2. 7 7. 8 10. 5 13. 6 900 1000 1800 2700 7800 10500 13600

The density of a material can be measured using the equation … mass density = ───── volume the units of density are g/cm 3 and kg/m 3

Measuring the volumes of regular shapes www. grc. nasa. gov