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DynamicsSummary Notes

ampHomework

National 5 Physics

National 5 Physics Summary Notes Dynamics amp Space

Velocity and displacement mdash vectors and scalarsScalars and Vectors

All physical quantities can be categorised into 2 groups

scalars - have only magnitude (size)

vectors - have both magnitude (size )and a direction

Some scalars have a vector equivalent

Examples

Scalars Vectorsdistance displacementspeed velocity

- accelerationtime -

- forcemass weight

energy -

Displacement and VelocityDistance is a scalar quantity which relates the length of the path travelled in a journeyDisplacement is a vector quantity which gives the separation between the start and finish points of the journey in a straight line along with a direction (often a bearing) Speed and velocity can be calculated using the following equations

speed=distancetime

velocity=displacementtime

(scalar) (vector)

Scalar AdditionTwo scalars can be combined as long as they are of the same quantity and unitsFor example

100 m + 50 m = 150 m can be added

1F Kastelein


10 m + 50 cm cannot be added 10 m + 05 m =105 m

2F Kastelein


Vector AdditionAdding vectors is more complicated since they also require consideration to be taken for their direction Vectors should be added tip to tail where the tip of the first vector is the starting point for the tail of the second vector

At this level we only ever need to consider adding 2 vectors positioned at right-angles to one another and even then it is usually a 345 triangle

Helpful Triangle Rules

Pythagoras Theorem

a2=b2+c2

Trigonometry

sin θ=oppositehypotenuse

cos θ=adjacenthypotenuse

tan θ=oppositeadjacent

3F Kastelein


4F Kastelein


MotionSpeed

Speed is the distance travelled by an object in one second (usually expressed in metres per second ms or m s-1)

Measuring Average SpeedMeasure distance travelled with a rulerMeasure time taken to travel with a stop clock

5F Kastelein

Speed Distance and Time

speed=distancetime

v=dt

t=dv

d=vt

Average and Instantaneous Speed

The average speed v of an object is the average for the whole journey (total distance travelled divided by time taken)

Example Travelling 70km in 2 hours by car

The instantaneous speed of an object is its speed at one particular point during the journey


v=dt

Measuring Instantaneous SpeedMeasure length of card with a rulerMeasure time taken for card to pass through light gate with an electronic timer

instantaneous speed= lengthof cardtimeisingate

6F Kastelein

average speed=distancetime


7F Kastelein

Displacement and DistanceDistance is a measure of how far a body has actually travelled

Distance is a scalar as it only requires a magnitude

It has the symbol d

Displacement is the measurement of how far an object has travelled in a straight line from the start to the finish of its journey

Displacement is a vector and so a magnitude and a direction is required

It has the symbol s

If the velocity is measured over the whole journey then it is known as average velocity with the symbol v


v= st

speed=distancetime

v=dt


8F Kastelein


9F Kastelein

Acceleration

Acceleration is the rate at which velocity changes how much it changes each second

It is a vector quantity

Acceleration is usually measured in metres per second per second (ms2 or m s-2) although miles per hour per second (mphs) can also be used sometimes

Acceleration can be calculated by dividing the change in velocity by the time taken for the change

Calculating acceleration

acceleration=change in velocitytime

a=v-u

t

t=v-ua

v=u+at

u=vminusat

Velocity-time graphs

constant velocity

increasing velocity (constant acceleration)

decreasing velocity (constant deceleration)

Using velocity-time graphs

Acceleration and deceleration can be calculated from a velocity-time graph

Acceleration is the gradient of the line If it is positive the object is accelerating If it is negative the object is decelerating

The distance travelled by (or displacement of) an object or vehicle can be calculated by finding the area under the graph

distance travelled = area a + area b + area c

velocity


10F Kastelein


Newtonrsquos laws

ForcesForces can change the shape speed and direction of motion of an

objectForce is measured in units called newtons (N)

11F Kastelein

Newton Spring Balance

The instrument used to measure forces is called a Newton balance

When a force is applied to the balance the spring becomes longer The increase in length is directly proportional to the force applied

Weight

The weight of an object is the force on it due to the Earthrsquos gravitational pull Since it is a force weight is measured in newtons (not kilograms)

The mass of an object is the amount of matter that makes up the object and is measured in kilograms

To calculate the weight (in newtons) of an object on Earth multiply the mass (in kilograms) by 98

The mass of an object remains the same no matter where the object is in the universe but the weight depends on the gravitational field strength at that point in space

Gravitational Field Strength

The gravitational field strength g of a planet is the force exerted per unit of mass of an object (that is on that planet) Gravitational field strength therefore has units of N kg-1

For example on Earth the gravitational field strength g is 98N kg-1 On Mars this would be 38 N kg-1

Calculating Weight

W ndash weightm ndash massg ndash gravitational field strength

W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein

Newtonrsquos First Law of Motion

When equal forces act in opposite directions they are called balanced forces

Balanced forces are equivalent to no forces at all

When balanced forces (or no forces at all) act on an object it remains at rest or continue to move at a constant speed in a straight line This is known as

SeatbeltsWhen a car brakes (or crashes) there is a force acting against the car slowing it down If the passenger was not wearing a seatbelt they would (according to Newtonrsquos First Law of Motion) continue to move forwards at constant speed (until they hit the windscreen or dashboard) A seatbelt is therefore used to provide a backwards force to stop the passenger from continuing to move forward at constant speed

Unbalanced ForcesWhen unbalanced forces act on an object the object changes speed (or direction) The acceleration due to an unbalanced force depends on the mass of the object and can be calculated using Newtonrsquos Second Law

These two forces can be replaced by a single force of 50N acting to the right This is known as the unbalanced or resultant force

Newtonrsquos Second Law of Motionunbalanced force=masstimesacceleration

F=maa= Fm m= F

aIf more than one force is acting on the object it is necessary to determine the unbalanced force acting on it first before using the above equationWhen the unbalanced force stays constant and the mass increases the acceleration decreasesWhen the mass stays constant and the unbalanced force increases the acceleration increases

FrictionFriction is a force that opposes the motion of an object

Air resistance or drag is the force of friction due to an objectrsquos motion through the airSituations in which friction is increased include i) applying the brakes of a carii) opening a parachuteiii) wearing rubber soled shoes for rock climbing

Situations in which friction is decreased include i) making racing cars streamlinedii) oiling moving parts in a car engineiv) using an air cushion on an lsquoair hockeyrsquo table


14F Kastelein


Newtonsrsquos Third Law of Motion

Newtonrsquos Third Law states that

ldquoIn the absence of external forces if object A exerts a force on object B then object B exerts an equal and opposite force on object Ardquo

These two forces are often know as an action force and a reaction force

- When you walk you exert a backwards force on the floor - action - The result is that the floor exerts a forwards force on you - reaction - you move forwards

Rockets and jet engines work on a similar principle

- The engine exerts a backwards force on the gas - action - The gas exerts a forwards for on the engine - reaction - the craft is propelled forwards

Freefall

When a spacecraft is in orbit it is constantly falling Anything inside will fall in the same way As a result the astronauts inside a space capsule will experience ldquoweightlessnessrdquo They are actually in freefall (since they are still in the Earthrsquos gravitational field and still have weight)

This is similar to a passenger in a falling elevator Both fall at the same rate (due to the gravitational field of the Earth) without windows the passenger feels ldquoweightlessrdquo

To be truly weightless you would have to find a place where there is no gravitational field These places are very hard to find

Terminal Velocity

Terminal velocity occurs when a falling object experiences air resistance Eventually the weight of the object will be perfectly balanced by the air resistance and the balanced forces will lead to constant speed This constant speed is known as terminal velocity

15F Kastelein


16F Kastelein


17F Kastelein


EnergyForms of energy

Energy can never be created or destroyed It can only be transformed from one type to another (or other types)There are many different forms of energy

Kinetic (movement) Energy Gravitational Potential Energy Chemical Potential Energy Nuclear Potential Energy Elastic Potential Energy Heat Energy Light Energy Sound Energy Electrical Energy

The units of all types of energy are joules (J)

18F Kastelein

Work Done

Work done is a measure of the energy transferred during an energy transformation

Work done has the symbol Ew and is measured in joules (J)

Work Done Force amp Distance

work done=forcetimesdistance

Ew = Fd

F=EWd

d=EWF

Power

Power is the rate at which energy is transferred during an energy transformationPower has the symbol P and is measured in watts (W)

Power Energy and time

Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein

Gravitational Potential Energy

The change in gravitational potential energyEp of an object is the work done against gravity (lifting) or by gravity (falling)

Gravitational Potential Energy mass

and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg

Kinetic Energy mass and speed

kinetic energy=12masstimesspeed2

EK=12

mv2

v2=2EKm

m=2EKv2

Conservation of Energy

During any energy transformation the total amount of energy stays the same This is known as the principle of conservation of energy

The principle of conservation allows numerical problems involving different forms of energy to be solved For example when a vehicle rolls down a slope gravitational potential energy is converted into kinetic energy and heat (work done by friction) Calculations can be performed on each of the spate forms of energy (EP=mgh EK=frac12mv2 and EW=Fd) but it is also known that the total amount of energy stays the same and so (in this case) EP = EK + EW

Energy ldquoLossrdquo

In some situations it may appear that energy has been lost In these cases it will have been turned into less useful (or sometimes less obvious) forms The most common example is when energy is ldquolostrdquo as heat due to friction

Kinetic Energy

Kinetic energy Ek is the energy an object has due to its motion

Kinetic energy is measured in joules (J)The kinetic energy of an object depends on both its mass and speed Increasing the mass andor the speed of the object increases its kinetic energy


21F Kastelein


ProjectilesProjectile Motion

A projectile is an object that has been launched and is travelling through the air They experience two components to their motion A horizontal one and a vertical one

Vertical Motion - this component is under the influence of the gravitational field in which the object moves This means that it will experience a constant downwards vertical acceleration

Horizontal Motion - this component is not under the influence of external forces This means it will experience a constant horizontal speed

CalculationsFor horizontal motion we can use the speed equation since speed will be a constant Therefore horizontal distance travelled will always be given by d=vt

For vertical motion the projectile accelerates and we can us

22F Kastelein


v = u + at To calculate the distance travelled we would have to use a speed time graph where the gradient is 98 to reflect the acceleration of the projectile distance travelled = area of graph

23F Kastelein


24F Kastelein


Orbits

A satellite orbit is a scaled up version of projectile motion The satellite falls towards the centre of the Earth but misses each time With enough horizontal speed a stable orbit is achieved

The satellite will continue to travel with constant speed and at a constant height

Freefall




Terminal Velocity


25F Kastelein


26F Kastelein


Exercise 1 Average and Instantaneous Speed

1 Explain the difference between average and instantaneous speed

2 State whether the following are average speeds or instantaneous speeds

a The speed of train travelling between Glasgow and Paisleyb The speed of a car on a speedometerc The speed of a roller coaster at bottom of a loopd The speed of a car between two lamp-postse The speed of a golf ball as it leaves the club

3 Describe a method of measuring the instantaneous speed of a trolley in the lab Your description should include

a A diagram of the apparatusb The measurements taken c Any calculations involved

4 A train leaving Glasgow at 900 am arrives in Edinburgh at 1015 am The distance is 84 km

a Calculate the average speed in kilometres per hour b Express the speed in metres per second

5 A jet travels from London to New York at an average speed of 223 msThe flight time is 7 hoursCalculate the distance travelled by the jet

6 A student carries out an experiment to measure the instantaneous speed of a trolley using the apparatus shown below

The length of the trolley is 30 cmThe time recorded on the timer is 015 s

Use the measurements to calculate the instantaneous speed of the trolley

27F Kastelein


Exercise 2 Scalars and Vectors

1 Physical quantities can be categorised as either scalar or vector

a Describe what is meant by a scalar quantityb Describe what is meant by a vector quantityc Sort the following into a table with the headings scalar quantity and vector

quantity

force distance displacement velocity speed time

2 During a race a car makes 25 complete laps of a course of 5 km

a What is the total distance travelled by the car after 25 complete lapsb What is the resultant displacement of the car after 25 complete laps

3 An athlete runs 8 km due west then turns and runs 6 km due north as shown in the diagram

a What is the total distance that the athlete travelled

b By scale diagram or otherwise find the resultant displacement of the athlete

c The run was completed in 75 minutes

i Calculate the average speed of the athlete in kmh

ii Calculate the average velocity of the athlete in kmh

28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START


Exercise 3 Acceleration

1 State the definition of acceleration

2 A Ford KA increases its velocity from 2 ms to 16 ms in 10sA Peugot 106 takes 8s to accelerate to 11 ms from restShow by calculation which car has the greater acceleration

3 A car slows from 70 mph to 30 mph in 5 s when taking the exit from a motorway

a Calculate the deceleration in mph s

b If 1 mile = 16 km what is the deceleration in kmhs

c Calculate the deceleration in ms2

4 During a game of ten-pin bowling a player gives bowling ball an acceleration of 3 ms2 for 12 s Assuming the bowling ball was accelerated from rest calculate the final velocity of the bowling ball

5 A supertanker travelling at 13 ms decelerates at a rate of 003 ms2 How long does it take to come to a complete stop

6 A rocket accelerates at 52 ms2 for 10 minutes to reach a final velocity of 6200 ms Calculate the initial velocity of the rocket

29F Kastelein


Exercise 4 Graphs of Motion

1 The motion of a race car is recorded as follows

Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0

a Using the graph paper provided draw a speed time graph of the race carrsquos journey

b Using the graph you have drawn describe the motion of the race car over the 80 seconds

c Using the graph you have drawn calculate

i The acceleration between 10 and 40 s ii The total distance travelled by the race car

iii The average speed during the 80 seconds

2 The velocity-time graph shown below describes the motion of a ball which has been thrown straight up into the air then allowed to fall to the ground

a At what time does the ball reach its

maximum heightb Calculate the maximum height that the ball reachesc Calculate the height from maximum to the groundd Use your answers to b and c to calculate the height above the ground that

the ball was thrown from

30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)


Exercise 5 Newtonrsquos First Law

1 Copy and complete the following

An object will remain at _ _ _ _ or continue to travel at a _ _ _ _ _ _ _ _ speed in a straight line unless an _ _ _ _ _ _ _ _ _ _ force acts

Therefore if the forces acting on the object are _ _ _ _ _ _ _ _ then the object will either be _ _ _ _ _ _ _ _ _ _ or will be moving at a _ _ _ _ _ _ _ _ speed

2 A weightlifter holds a bar as shown

The mass of the bar is 180 kg

(a) Calculate the weight of the bar(b) What size of force did the weightlifter apply to raise the bar at a

constant speed(c) What is the size of force that the weightlifter applies to hold the bar

stationary

31F Kastelein


Exercise 6 Resultant Force and Newtonrsquos 2 nd Law

1 A fully laden oil tanker of mass 65x107 kg sets off from its port on a bearing of 090degIts engine produces a force of 40x106 N A tugboat pushes against the tanker as shown with a force of 30x106N

a Using a scale diagram or otherwise find the resultant force acting on the tanker

b Calculate the initial acceleration of the tanker

2 A car of mass 1500 kg accelerates at a rate of 23 ms2The engine of the car provides a force of 4000 NCalculate the size of the frictional force acting on the car

3 A firework of mass 02 kg provides an initial upwards thrust of 28 N

a Calculate the weight of the fireworkb Draw a diagram and label the forces acting on the fireworkc Calculate the initial acceleration of the fireworkd As the firework ascends its acceleration increases

Explain why the acceleration increases

32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER


Exercise 7 Weight mass and gravitational field strength

1 Describe how a Newton Balance can be used to measure the size of a force

2 A student takes two identical pieces of paper She crumples one into a ball and leaves the other one as a flat sheetThe student then drops both pieces of paperWhich piece of paper will land first Explain your answer

3 Mass and weight mean different things

a Explain what is meant by massb What are the SI units of massc Explain what is meant by weightd What are the SI units of weight

4 Define the term gravitational field strength

5 A pupil has a mass of 48 kg

a Calculate the weight of the pupil on Earthb What would the mass of the pupil be on Marsc Calculate the weight that the pupil would be on Mars where the gravitational

field strength is 4 Nkg

6 A scientist predicts that a person of mass 75 kg will have a weight of 780 N on a newly-discovered planetCalculate the gravitational field strength of this planet

33F Kastelein


Homework 8 Conservation of Energy

1 An 8 kg boulder rolls down a hill as shown below

(a) How much potential energy does the boulder lose as it rolls assuming that no energy is lost due to friction(b) Calculate the speed of the boulder at the

bottom of the hill

2 A railway train travels uphill between two stations

The train uses 18 MJ of energy during this journey The mass of the train and the passengers is 20 000 kg

(a) Calculate the height gained by the train during the journey

(b) Suggest why the actual height gained by the train is less than the value calculated in part

3 An early method of crash testing involved a car rolling down a slope and colliding with a wall In one test a car of mass 750 kg starts at the top of a 72m high slope

(a) Calculate the gravitational potential energy of the car at the top of the slope(b) (i) State the value of the kinetic energy of the car at the bottom of

the slope assuming no energy losses(ii) Calculate the speed of the car at the bottom of the slope before hitting the wall

4 A diver climbs from water level of a swimming pool to the top of a diving platform The platform is 50 m above the water level and the diver has a mass of 50 kg

(a)Calculate the gain in gravitational potential energy of the diver

(b)The diver drops from the edge of the diving platform and lands in the water

34F Kastelein

8 kg

20 m


(i) State the value of the gain in kinetic energy as the diver enters the water

(ii) Calculate the vertical speed as the diver enters the water

Exercise 9 Newtonrsquos Third Law free-fall and acceleration due to gravity

1 Josie and Kirsty are arguing about how a water rocket water lifts off

Dave knows that what Josie says isnrsquot true but Kirsty has not provided an actual explanation either

Dave reminds Kirsty about Newtonrsquos Third Law and they both go back and offer an explanation to Josie

Copy and complete what they say to Josie

ldquoOK Josie this is to do with Newtonrsquos Third Law action and _ _ _ _ _ _ forces The rocket pushes the water _ _ _ _ _ _ _ _ _ and as a reaction the _ _ _ _ _ pushes the rocket _ _ _ _ _ _ _ with an _ _ _ _ _ sized force ldquo It has nothing to do with the _ _ _ _ _ pushing on the ground

2 The speed-time graph for a sky-dive is shown right

(a) Explain why the gradient of the graph is decreasing between 0 and 20 seconds

(b) At what time is the parachute opened

(c) What is the name given to the constant velocity reached during free-fall

35F Kastelein

Josie Kirsty Dave


Exercise 10 ndash Projectile Motion

1 A javelin is launched horizontally at 5 ms It lands 15 metres horizontally from its launch point

a Calculate the time that the javelin is in the air forb Calculate the final vertical velocity of the javelinc Using a scale diagram or otherwise find the size of the final

resultant velocity of the javelin and the angle of impact

2 A ball rolls off a table top with a horizontal speed of 20 msThe ball hits the ground 03 seconds later

a Calculate the horizontal distance that the ball lands from the table top

b Calculate the final vertical speed of the ballc Sketch a velocity-time graph of the vertical motion of the balld Use the graph to find the height of the table

3 Explain how an artificial satellite such as the International Space Station remains in orbit around the Earth

36F Kastelein

5 ms

15 metres






Exercise 6 Resultant Force and Newtonrsquos 2nd Law






Velocity and displacement mdash vectors and scalarsScalars and Vectors

All physical quantities can be categorised into 2 groups

scalars - have only magnitude (size)

vectors - have both magnitude (size )and a direction

Some scalars have a vector equivalent

Examples

Scalars Vectorsdistance displacementspeed velocity

- accelerationtime -

- forcemass weight

energy -

Displacement and VelocityDistance is a scalar quantity which relates the length of the path travelled in a journeyDisplacement is a vector quantity which gives the separation between the start and finish points of the journey in a straight line along with a direction (often a bearing) Speed and velocity can be calculated using the following equations

speed=distancetime


(scalar) (vector)

Scalar AdditionTwo scalars can be combined as long as they are of the same quantity and unitsFor example

100 m + 50 m = 150 m can be added

1F Kastelein



2F Kastelein





Pythagoras Theorem

a2=b2+c2

Trigonometry




3F Kastelein


4F Kastelein


MotionSpeed



5F Kastelein


speed=distancetime

v=dt

t=dv

d=vt






v=dt



6F Kastelein



7F Kastelein



It has the symbol d



It has the symbol s



v= st

speed=distancetime

v=dt


8F Kastelein


9F Kastelein

Acceleration







a=v-u

t

t=v-ua

v=u+at

u=vminusat


constant velocity








velocity


10F Kastelein


Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres













2F Kastelein





Pythagoras Theorem

a2=b2+c2

Trigonometry




3F Kastelein


4F Kastelein


MotionSpeed



5F Kastelein


speed=distancetime

v=dt

t=dv

d=vt






v=dt



6F Kastelein



7F Kastelein



It has the symbol d



It has the symbol s



v= st

speed=distancetime

v=dt


8F Kastelein


9F Kastelein

Acceleration







a=v-u

t

t=v-ua

v=u+at

u=vminusat


constant velocity








velocity


10F Kastelein


Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres















Pythagoras Theorem

a2=b2+c2

Trigonometry




3F Kastelein


4F Kastelein


MotionSpeed



5F Kastelein


speed=distancetime

v=dt

t=dv

d=vt






v=dt



6F Kastelein



7F Kastelein



It has the symbol d



It has the symbol s



v= st

speed=distancetime

v=dt


8F Kastelein


9F Kastelein

Acceleration







a=v-u

t

t=v-ua

v=u+at

u=vminusat


constant velocity








velocity


10F Kastelein


Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












4F Kastelein


MotionSpeed



5F Kastelein


speed=distancetime

v=dt

t=dv

d=vt






v=dt



6F Kastelein



7F Kastelein



It has the symbol d



It has the symbol s



v= st

speed=distancetime

v=dt


8F Kastelein


9F Kastelein

Acceleration







a=v-u

t

t=v-ua

v=u+at

u=vminusat


constant velocity








velocity


10F Kastelein


Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












MotionSpeed



5F Kastelein


speed=distancetime

v=dt

t=dv

d=vt






v=dt



6F Kastelein



7F Kastelein



It has the symbol d



It has the symbol s



v= st

speed=distancetime

v=dt


8F Kastelein


9F Kastelein

Acceleration







a=v-u

t

t=v-ua

v=u+at

u=vminusat


constant velocity








velocity


10F Kastelein


Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












v=dt



6F Kastelein



7F Kastelein



It has the symbol d



It has the symbol s



v= st

speed=distancetime

v=dt


8F Kastelein


9F Kastelein

Acceleration







a=v-u

t

t=v-ua

v=u+at

u=vminusat


constant velocity








velocity


10F Kastelein


Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












7F Kastelein



It has the symbol d



It has the symbol s



v= st

speed=distancetime

v=dt


8F Kastelein


9F Kastelein

Acceleration







a=v-u

t

t=v-ua

v=u+at

u=vminusat


constant velocity








velocity


10F Kastelein


Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












8F Kastelein


9F Kastelein

Acceleration







a=v-u

t

t=v-ua

v=u+at

u=vminusat


constant velocity








velocity


10F Kastelein


Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












9F Kastelein

Acceleration







a=v-u

t

t=v-ua

v=u+at

u=vminusat


constant velocity








velocity


10F Kastelein


Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












10F Kastelein


Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












Newtonrsquos laws



11F Kastelein




Weight








Calculating Weight


W = mg

m=Wg

g=Wm


12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












12F Kastelein


13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












13F Kastelein









F=maa= Fm m= F






14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












14F Kastelein









Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres



















Freefall




Terminal Velocity


15F Kastelein


16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












16F Kastelein


17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












17F Kastelein






18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres
















18F Kastelein

Work Done





Ew = Fd

F=EWd

d=EWF

Power



Power=Energytime

P= Et

E=Pt

t= EP


19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












19F Kastelein


Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












Mechanical Energy

1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576as1048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576104857610485761048576

20F Kastelein




and height

EP=mgh

m=EPgh

g=EPmh

h=EP

mg



EK=12

mv2

v2=2EKm

m=2EKv2






Kinetic Energy




21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












21F Kastelein








22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres


















22F Kastelein



23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres













23F Kastelein


24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












24F Kastelein


Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












Orbits



Freefall




Terminal Velocity


25F Kastelein


26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres












26F Kastelein














27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres
























27F Kastelein





quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres















quantity










28F Kastelein

270˚

180˚

090˚

000˚

6 km

8 km

FINISH

START












29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres






















29F Kastelein




Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres














Time(s)

0 10 20 30 40 50 60 70 80

Speed (ms)

5 5 20 35 50 50 50 25 0










30F Kastelein

0 05 1 15 2 25

-15

-10

-5

0

5

10

15

time (seconds)

velo

city

(ms

)










stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres




















stationary

31F Kastelein










32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres




















32F Kastelein

30x106 N

270˚

180˚

090˚

000˚

force from tugboat

engine force

40x106 NTANKER












33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres






















33F Kastelein





bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres















bottom of the hill











34F Kastelein

8 kg

20 m














35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres
























35F Kastelein

Josie Kirsty Dave










36F Kastelein

5 ms

15 metres




















36F Kastelein

5 ms

15 metres











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