Average Speed

2 variables are measured :

The total journey distance , d, and

The total time for the journey ,t.

Average speed

t

dv

Metres per second , m s-1

Metres, m

Seconds , s

Instantaneous Speed

This is the speed at an instant. This is measured over a very short time interval, as close to 0 as possible. Hence electronic timing is used as our reaction time is too big if stopclocks were used.

t

dv

Instantaneous Speed

Apparatus

0.025 s

Light gate timer

mask

Mask cuts light beam and time is recorded

Use s = v x t to calculate instantaneous speed

Where s = width of mask

Vector and Scalar Quantities

Scalar quantities have magnitude only

e.g. temperature

Vector quantities have magnitude and direction

e.g. force of 10 N to the right

Distance and Displacement

Distance is a scalar quantity but displacement is a vector and has a direction associated with it. E.g.

A person walks 3 km north then 4 km east. Calculate the distance traveled and the displacement.

Draw a vector diagram

Distance and Displacement

Draw a line from the start to the finish. This is the displacement. Use Pythagoras theorem to calculate the magnitude of the displacement

c2 = a2 + b2 c2 = 32 + 42 = 25 c = 5.

north3 km north

4 km east

Use Trig to calculate angle Ɵ cos Ɵ= a/h cos Ɵ = 3/5 =0.6

Ɵ = cos-1 0.6 = 530

Displacement = 5 km , 0530

Distance traveled = 3 + 4 = 7 km

Speed and velocity

Speed is a scalar

Velocity is a vector

time

cedisspeed

tan

time

ntdisplacemevelocity

Speed and velocity

Calculate the average velocity and speed of the walker who travels as shown in a time of 2 hours. 4 km east North

3 km north

15.32

7tan hkmtime

cedisspeed

Acceleration

Unbalanced forces cause vehicles to accelerate hence it is a VECTOR quantity.

t

uva

changefortime

velocityinchangeonaccelerati

Units m s-2

Units m s-1

s

Acceleration

Rearrange the acceleration formula

a

uvt

atvu

atuv

The quantity a.t is how much the speed increases by.

Velocity time graphs

Slope = accelerationArea under graph = displacement

Displacement = area 1 + area 2 + area 3

speed time graph

0

2

4

6

8

10

12

0 5 10 15 20 25 30 35

time (s )

spee

d (

m/

s )

1 2 3

Area = ½ b x h + b x h + ½ b x h

= ½ x 5 x 10 + 25 x 10 + ½ x 2 x 10

= 25 + 250 + 10

= 285 m

( we have no indication of direction here )

Change of DirectionConstant Acceleration (Direction Change)

-6

-4

-2

0

2

4

6

8

10

0 1 2 3 4 5 6 7

Time (s)

Vel

oci

ty (

m/s

)

• If the line of a velocity/time graph crosses the “x” axis then the object has changed direction of travel.

• In the graph above the velocity of the object changes from negative to positive at 2 seconds.

• This means it “stopped” and changed direction in an instant of time.

• This graph could represent a ball travelling up a slope, stopping then travelling downwards .

• The movement down the slope has been designated as positive.

• The total displacement after six seconds is the area under the line.

• S = (½ x 4 x 8) – (½ x 2 x 4) = 12m

Forces

A Force is a push or pull and can change the speed / shape / and /or direction of an object.

Newton balance is used to measure pulling forces

Units are Newtons, N

Mass and Weight

Mass : measure of a body’s inertia, its resistance to change. Units, kg ,Scalar

Weight : gravitational force acting on an object, Units , N, vector

Weight = Mass x gravitational field strength

W = m x g

Mass and Weight

Gravitational field strength,g,

= force acting per unit mass ( N kg-1 )

On earth g = 9.8 Nkg-1 i.e. every 1 kg is pulled towards the centre of the earth by a force of 9.8 N.

The bigger the mass of a planet the bigger g is. The smaller the radius the bigger g is.

Friction

This arises when two surfaces rub against each other.

Can often slow objects down.

Decrease friction via lubrication , use of bearings , making cars more streamlined,wearing tight clothing…

Increase friction by increasing area of tyres / brake pads / parachutes

Balanced Forces

• Same magnitude of force but act in opposite direction

• Equivalent to NO force acting

500 N friction force 500 N engine force

Balanced Forces

• Newton’s First Law of Motion : an object remains at rest or continues to move at a constant velocity unless the forces acting on it are unbalanced.

Newton’s Second Law

• If the forces acting on an object are unbalanced it will accelerate.

200 N friction force

500 N engine force

Unbalanced force, Fun = 500 -200 = 300 N

Newton’s Second Law

axmFun Unbalanced force mass x acceleration

Newtons kilograms metres per second per second

Example.

Calculate the acceleration of a car , 750 kg, when an engine force of 500 N acts and a frictional force of 250 N acts against the motion.

500 N250 N

Fun = 500 – 250 = 250 N

Newton 2

Newton

Defined as ; 1 N is the force required to accelerate a 1kg mass at 1 ms-2.

Free Body Diagrams

Arrows to show which way the forces act e.g. a person who weighs 500 N in a lift is acted on by a 650 N force upwards.

Upward force = 650 N

Weight = 500 N

Fun = 650 – 500 = 150 N

Mass, m = weight/gravitational field strength

Mass = 500 / 9.8 = 51 kg.

Gravitational field strength and acceleration due to gravity

Consider a 1kg mass falling vertically with NO frictional forces acting against it.

The force acting downward = gravitational force

This causes the mass to accelerate :

Acceleration due to gravity and gravitational field strength are the same value.

1 kg mass

Fg = m.g

= 1x9.8

= 9.8 N

Free FallObjects accelerating downwards at the same rate at which gravity force accelerates them downwards are in free fall. They appear weightless.

Newton’s Third Law

The rocket exerts a force on the gases, pushing them down

The gases exert a force on the rocket, pushing it upwards

Newton’s Third Law

• To every force there is an equal and opposite reaction force. i.e. the rocket pushes the gases downwards and the gases push back up on the rocket with the same size of force. The rocket has a bigger mass than the gases so the rocket moves up slower than the gases move downwards.

Work

• Work done is a measure of the energy transferred. E.g. when lifting a pencil I do work against the earth’s gravity force, energy has been transferred: chemical energy in my body has been turned into kinetic energy which is turned into potential energy as the pencil gains height.

Work

Work done = Force x distance

W = F x d

Joules, J Newtons, N metres, m

Example

Calculate the work done by the brakes of a car if a 4.5kN average force are applied over a distance of 20 m.

Work done W = F x dF = 45 kN = 4.5x104 N, d = 20 mW = 4.5 x 104 x 20 W = 9.0 x105 J The car originally had 9.0 x105 J of kinetic energy. To bring the car to rest the brakes must do the exact same amount of work, 9.0 x 105 J.

Power• This is the rate of doing work ( transferring energy )• i.e. work done per second• Units are Watts, W• 1 W = 1 J s-1

• i.e. a 2000 W heater transfers 2000 J of electrical energy into heat energy every second

Power

Calculate the work done by a 75kW motor running for 5 mins.

P = 75 kW = 75 000 W

t = 5 mins = 5 x 60 = 300 s

JxxxtxPEt

EP 71025.260575000

Potential Energy

Energy stored in an object as it is lifted of the ground.

hxgxmEp

Potential Energy mass gravitational field strength

( joules, J ) (kilograms ,kg ) ( Newtons per kilogram, N kg-1 )

Change in height

( metres, m )

Potential energy This is really a special case of ‘doing work’Work done = average force x distance moved

If we lift something vertically at uniform speed then the forces acting on it are balanced

Fup = Fgravity = m x g

For a vertical distance we normally write h instead of d Therefore W = f x d W = m x g x h

Potential energyCalculate the potential energy you gain as you climb the stairs in the school.m = 78 kg, h = 3.5 m, g = 9.8 N kg-1.

Ep = m x g x hEp = 78 x 9.8 x 3.5Ep = 2675.4 JRound to 2 sig figs 2.7 x 102 J

Kinetic EnergyMoving objects have kinetic energy, Ek,

25.0 vxmxEk

Kinetic energy mass speed squared

( joules, J ) ( kilograms, kg ) ( metres per second squared 21sm

Kinetic energy

Calculate the speed a 1000 kg van is moving at if it has 50 000 J of Ek.

Ek = 50 000 J, m = 1000 kg v = ?25.0 vxmxEk

1

2

10100

1000

50000222

smvv

xv

m

Exv

m

Exv kk

Cosmology

Signals from Space

We live on a planet called Earth, this is a big lump of rock that orbits the sun. There are 7 other planets orbiting the sun. They make up the solar system along with the moons , asteroids and dwarf planets.

Signals from Space

The sun is a star, it is our source of heat and light energy.

Our sun is one of millions of stars that make up the Milky Way galaxy ( a group of stars ).

The milky way galaxy is one of

millions of galaxies that make

up the universe

Electromagnetic Spectrum

This is a group of radiations ( waves ) that travel at 3 x 108 ms-1 through air / vacuum. They are grouped according to their frequency / wavelength , have different properties and are detected by different detectors.

The different signals convey different types of information e.g. search for ET life uses radio waves but black holes can be detected by searching for gamma rays.

Electromagnetic Spectrum

Remember that

Radiation Detector

TV and Radio Aerial

Microwaves Aerial

Infrared Photodiode/ (hand)

Visible Light Eye

Ultra Violet Fluorescence of chemicals

X Rays Photographic film

Gamma rays Geiger Muller tube

xfv Increasing frequency

Electromagnetic Spectrum

Calculate the frequency of 300 m radio waves. Remember that all members of the electromagnetic radiation travel at 3 x 108ms-1.

V = 3x108 ms-1 λ = 300 m f = ?

xfv

Hzxxv

f 68

101300

103

Light Year

This is the distance that light would travel in one year:

Distance = speed x time

( this is equivalent to going around the earth 250 million times )

mxxxxxxtxvd 158 1046.9606024365100.3

Light YearObject Time for

light to travel from earth

Distance

( m )

moon 1.2 seconds

sun 8 minutes

Next nearest star

4.7 years

Edge of Milky Way Galaxy

100 000 years

Telescopes

Used to gather signals from distant objects ( signals can be any member of electromagnetic spectrum ):

Spectroscopy

White light can be split into its spectrum by a prism. The shorter the wavelength of light the more refraction and bending of the light.

Blue λ = 450 nm

Green λ = 550 nm

Red λ = 650 nm

Red

Green

Blue

Continuous spectrum• All colours merge into each other , like a rainbow. • Hot objects emit a continuous spectrum• Temperature of star can be calculated by looking

at spectrum• Cool objects emit red light but as the temp

increases , red, green and blue light are emitted :it glows white

Line Spectrum

• Emitted by low pressure gases• Chemical composition of stars can be evaluated• Each element has its unique spectrum• These are called emission spectrum

The Big BangBig Bang theory states approximately 14 billion years ago the universe came into existence . It started as a single point and a rapid expansion occured. Initially the temperature was very hot and only ‘energy existed’. As it expanded , it cooled and ‘matter’ was formed . Initially particles called quarks and electrons were formed then eventually protons and neutrons. The simplest elements then followed : Hydrogen then helium.

Big Bang : The EvidenceOther galaxies are moving away from us , this suggests that at one time all the ‘matter’ in the universe must have been at a single point. This time was approximately 13.7 billion years ago.Cosmic Microwave background radiation is detected coming from all directions : This is the remnants of the ‘Big Bang’.

Advantages of Space ExplorationApart from allowing us to better understand ‘where we come from’ Space Exploration has had a huge impact on society :Use of satellites to predict weather/ storms/GPSUse of sensors to monitor volcanoes/ investigate the bodyUse of new materials in insulation/ replacement body parts/ scratch resistant lensesImprovements in computing…………

Space flightProjectile MotionNewton’s thought exptReentryA heat shield protected the two-man Gemini spacecraft against the enormous heat of reentry into the atmosphere

beginning at a velocity of more than 27,500 kilometers (17,000 miles) per hour. Like those of other early human spacecraft, Gemini's heat shield derived from ballistic-missile warhead technology. The dish-shaped shield created a shock wave in the atmosphere that held off most of the heat. The rest dissipated by ablation: charring and evaporation of the shield's surface. Ablative heat shields are not reusable.

The ablative substance of the Gemini heat shield is a paste-like silicone elastomer material which hardens after being poured into a

honeycomb form. Spacecraft that enter planetary atmospheres are fitted with heat shields to protect them against the high heating loads experienced during entry. Heat shields fitted to deal with very high speed entry are designed to ablate, that is evaporate in response to the heating loads. The ablation products carry away heat in the form of latent heat of vaporisation. They also blanket the surface with an insulating layer of gases and fine particulates which helps protect the surface from further convective and radiative heating. The interaction between the shock layer flow, the high temperature gases and particles present and the radiation they emit and absorb is highly complex and poorly understood. A barrier to understanding is the difficulty of simulating the high speed flow, the radiation field and the ablative products cloud behaviours in the one flow in the laboratory. Experiments carried out with colleagues at the University of Queensland (UQ) have demonstrated that this can be achieved in the UQ expansion tunnels with models whose exposed surfaces are coated with epoxy resin. The figure shows the spatial distribution of the visible radiative power density, in arbitrary units, deduced from high speed video images of the flow round a model of the Japanese Hyabusa spacecraft coated with epoxy resin. UV and IR spectra, integrated along the line of sight, were also taken along the stagnation streamline in this flow.

Shielding that must be fitted to a spacecraft, such as a manned capsule or the Space Shuttle, if it is to survive the intense heat generated during reentry. The high heating experienced by a spacecraft when entering the atmosphere is caused by a high-pressure bow shock in front of the vehicle (not, as is sometimes supposed, friction with the air). This strong shock wave is caused by the craft flying at hypersonic speeds, or high supersonic speeds. Hypersonic means greater than Mach 5. The shock wave is where the atmosphere is rapidly compressed by a factor of 50 to 100, depending on the speed of the vehicle. Because of this rapid compression the gas is heated to temperatures of 6,000 K or more. This hot gas then impinges on the front of the spacecraft, transferring heat to the surface. 

Ablative heat shieldsOne way to dissipate this large amount of thermal energy is with a heat shield that works by ablation, that is by parts of it melting or vaporizing and breaking off in order to carry the heat harmlessly away. This technique was used by reentering Mercury, Gemini, and Apollo spacecraft. Early manned capsules, which were spherical in shape and not orientated in any special way for reentry, simply had an all-over ablative covering.

Projectile MotionThis has two components : a constant horizontal velocity and a

vertical velocity that accelerates uniformly at 9.8 m s-2.

Horizontal velocity remains constant if we ignore frictional forces and spin.

Vertical velocity changes uniformly as gravitational force acts on object.

This results in a curved

trajectory :

Projectile motionExample

Calculate the horizontal distance,s, traveled

( range )and the height,h,of the cliff if the car takes 5 s to hit the ground.

20 ms-1

Height of cliff, h,

Range,s,

Now that’s what I call a speed bump.

Area under graph = ½ b x h = ½ x 5 x 49 = 122.5 m

Calculate the resultant velocity of the car as it hits the sea :Draw a vector diagram:

20 ms-1

Ɵ49 ms-1

Use Pythagoras to work out hypotenuse 52.9 ms-1

Use trig to work out angle , Ɵ67.80

Resultant velocity is 52.9 ms-1 , 67.80 below the horizontal.

Newton’s Thought Expt

The ball is fired horizontally but gravitational force accelerates it towards the earth. It crashes at point A

If the horizontal velocity is increased it can ‘reach ‘ a little further around the earth to B.

If the horizontal velocity is increased further it can travel right round the earth.

Newton’s Thought Expt 3

If the horizontal velocity of the ball is increased further it flies off into space.The ball orbits the earth because gravitational force is pulling it towards the centre. The ball wants to travel in a straight line but gravitational force pulls it inwards.This is why satellites , natural and man made orbit planets.

Re entryWhen the space shuttle re enters the earth’s atmosphere there are huge frictional forces acting against it.Some of the shuttle’s kinetic energy is turned into heat energy.To stop the craft becoming too hot inside, the underside is painted black, this is a good emitter of infra red radiation. The underside is also covered with tiles that have a low specific heat capacity and a low thermal conductivity. This ensures that the temperature of the tiles rises quickly( but lots of heat is radiated to the surroundings ) and a small amount of heat energy is transferred into the cabin.

Example energy change

The space shuttle, 100 tonnes, slows down from 7 500 ms-1 to 750 m s-1 when it hits the earth’s atmosphere. Assume that all this change in kinetic energy is turned into heat energy Calculate the maximum temperature rise if the specific heat capacity of the thermal tiles, 2000kg, is 50 J kg-10C-1.

ExampleUse Ek = 0.5mv2 to calculate kinetic energy change.

Ek before = 2.8125 x 1012

Ek after = 2.8125 x 1010

Ek change = 2.78 x1012 J

Use Eh = Ek = cm T

Cxx

x

mxc

ET h 07

12

1078.2200050

1078.2

Obviously a lot of the heat energy is re radiated otherwise the shuttle would melt.

Ablative Heat Shields

When a material turns from a solid to a liquid or from a liquid to a gas energy is required. When water evaporates off your skin you cool down. This idea is used to cool down some space craft on re entry.

Part of the heat shield is designed to burn away, the gases produced carry some heat energy away