Forces

& Motion Movement and Position: Displacement-Time and Velocity-Time Graphs ................................................... 2

Scalars and Vectors ................................................................................................................................... 2

Displacement (Distance) –Time ................................................................................................................ 2

Some problems ......................................................................................................................................... 6

Velocity-Time Graphs ................................................................................................................................ 7

Forces, Movement and Shape .................................................................................................................... 11

Addition of Forces, Balanced and Unbalanced Forces, Resultant Force ................................................ 11

Force, Mass and Acceleration ................................................................................................................. 12

Mass & Weight ........................................................................................................................................ 12

Terminal Velocity .................................................................................................................................... 14

Stopping Distances .................................................................................................................................. 15

Momentum ............................................................................................................................................. 15

Momentum and Force ........................................................................................................................ 16

Momentum, Collisions and Explosion ................................................................................................. 18

Newton’s Laws of Motion ....................................................................................................................... 19

Moments – The Turning Effect of a Force .............................................................................................. 19

Centre of Gravity ..................................................................................................................................... 21

Stability and centre of gravity ............................................................................................................. 22

Forces on a light beam ............................................................................................................................ 23

Force-Extension Graphs .......................................................................................................................... 25

Hooke’s Law ............................................................................................................................................ 26

Astronomy ................................................................................................................................................... 27

Moons ..................................................................................................................................................... 27

Gravitational Field Strength .................................................................................................................... 28

Gravity ..................................................................................................................................................... 28

Comets .................................................................................................................................................... 29

Orbital Speed, Orbital Radius and Time Period ...................................................................................... 29

Galaxies ................................................................................................................................................... 30

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Movement and Position: Displacement-Time and Velocity-Time Graphs

Scalars and Vectors

Scalars are quantities like energy, power or speed. They have no direction. Vectors do have a direction.

Speed in a given direction is called velocity. Velocity is a vector, speed is not. Acceleration always has a

direction and hence is a vector as well. Distance is a scalar. Distance in a given direction is a vector and

called ‘displacement’.

Time seems to have a direction, but not in the three dimensions. The time cannot go ‘up’ or ‘left’, it is

therefore a scalar. The scientific definition of a vector is a ‘quantity that has magnitude and a direction’.

A scalar is a ‘quantity with magnitude, but no direction’.

Below is a list of vectors and scalars.

Scalars Vectors

Energy Acceleration

Power Force

Voltage Velocity

Current Displacement

Time

Speed

distance

As vectors have a direction, they can be represented by arrows. The length of the arrow is proportional

to its magnitude.

Displacement (Distance) –Time

WARNING: In terms of language – non-physicists use the term distance most of

the time! This is OK !!! Although – when the direction counts, i.e. we talk about

objects moving forward and backwards or up and down then we need to use the

term displacement. The graphs below use displacement but with all bar one you

can replace that term easily with Distance. However, have a look at the last graph

in this section. It slopes downwards!!! Why ?

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The above graph shows an object which is not moving (at rest). Its displacement stays the same as time goes by because it is not moving.

The above graph shows that the objects displacement increases as time goes by. The object is moving and so it has velocity. The straight line shows it is a constant velocity.

The gradient (slope) of the line shows how fast the object is going.

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The above graph shows an object moving with constant velocity. Compare this with the graph on the last one. and you will see that the slope is down rather than up. This means that the object is moving in the opposite direction. As before, the slope of the line shows how fast the object is moving.

Speed is a measure of how fast an object is moving. It is measured in metres per second, written as m/s.

Speed = Distance ÷ Time.

In a formula speed and velocity are written as v:

t

dv

This equation is important!

If an object is stationary (not moving), then its speed is zero.

Velocity is similar to speed. It is a measure of how fast an object is moving, and is also measured in m/s.

Velocity = Displacement ÷ Time.

The difference between velocity and speed is that velocity is speed in a certain direction. It is a vector quantity. If an object is moving in a straight line, then its speed and velocity will be the same. If the moving object stays at the same speed but changes direction, then we say that the velocity has changed (because the direction has changed) but the speed has stayed the same.

In most of the examples of motion that you will come across, the object will be moving in a straight line. In this case, use the word velocity rather than speed.

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If an object moving in a straight line travels 25 metres in 5 seconds, then its velocity = 25 ÷ 5 = 5 m/s.

You must always say what the units are! (in this case m/s, called "metres per second").

Always check what units are given in the question.

If the time is given in hours or minutes, then convert it to seconds before doing the calculation.

If an objects velocity does not change, we say it has a constant velocity. In the above example, we are not told whether the object has a constant velocity, or whether its velocity has changed during the 5 seconds. If the velocity has changed, then the answer we have calculated is an average velocity of 5 m/s. If the velocity has not changed, then the object had a constant velocity of 5 m/s.

When an objects velocity changes, it is called acceleration.

The curve in the above graph shows that an objects velocity is changing as time goes by. This is acceleration.

Acceleration = Change in Velocity ÷ Time.

This equation is written as a = (v-u) ÷ t

where a = acceleration, v = final velocity (the one it ended up with), u = initial velocity (the one it started with), t = time

This equation is important!

The units of acceleration are m/s2 or ms-2, called "metres per second squared".

If an object gets faster, it will have a positive acceleration. If an object gets slower, it will have a negative acceleration (this is sometimes called "deceleration" but the term "negative acceleration" is preferred).

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Some problems

1. If a car changes from 10 m/s to 30 m/s in 8 seconds, what is its acceleration?

v = 30 u = 10 t = 8

a = (30 - 10) ÷ 8 = 20 ÷ 8 = 2·5 m/s2

2. If a bicycle moving at 15 m/s takes 10 seconds to stop, what is its acceleration?

In this example, the final velocity is zero because the bicycle has stopped.

v = 0 u = 15 t = 10

a = (0 - 15) ÷ 10 = -15 ÷ 10 = -1·5 m/s2

The acceleration is negative because the bicycle has slowed down.

Acceleration is the rate of change of an objects velocity. The object is said to have constant acceleration if it gets faster (or slower, or its direction changes) at the same rate.

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Velocity-Time Graphs

WARNING: In terms of language – non-physicists use the term speed most of the

time! This is OK !!! Although – when the direction counts, i.e. we talk about

objects moving forward and backwards or up and down then we need to use the

term velocity.

The above graph shows that the objects velocity does not change as time goes by. It is constant velocity. Compare this with the displacement - time graph for constant velocity.

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The above graph shows that the objects velocity is increasing as time goes by. This is acceleration. The straight line shows that it is constant acceleration. The slope of the line shows (i) the acceleration is positive because the line slopes upwards (ii) how fast the acceleration is.

The above graph shows that the objects velocity is decreasing as time goes by. This is negative acceleration. The straight line shows that it is constant negative acceleration. The slope of the line shows

(i) the acceleration is negative because the line slopes downwards (ii) how fast the negative acceleration is.

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The curve in the above graph shows that the acceleration is not constant. It is changing acceleration.

You may be shown a graph like the one below and be asked to describe the motion of the object.

In region A the object is moving with constant acceleration.

In region B the object is moving with constant velocity.

In region C the object is again moving with constant acceleration but compared with region A (i) the acceleration is slower because the slope is less steep (ii) the acceleration is negative because the slope is downwards.

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The total displacement travelled by the object can be calculated by measuring the area under the graph.

The total displacement travelled by the object can be calculated by measuring the area between the graph and the baseline. This is called the area under the graph.

The area under the previous graph can be divided into two triangles and one rectangle.

The area of triangle A is half base x height

= 0·5 x 10 x 20 = 100.

The area of triangle C = 0·5 x (70 - 30) x 20 = 400.

The area of rectangle B = (30 - 10) x 20 = 400.

The distance travelled is the total area = A + B + C = 100 + 400 + 400= 900 m.

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Forces, Movement and Shape

Forces can be expressed as a push or pull of one body on another.

As you are sitting on your chair, your weight pulls you down. This is the gravitational pull of the Earth on

you. At the same time there is a gravitational pull of your body on the Earth. Exactly, this sounds

surprising. And: as your weight pushes down on the chair you sit on, the chair pushes upwards onto

your body to keep you ‘stationary’. These interactions of forces can be applied to many other situations,

e.g. a car pulling a trailer.

There are various types of forces. Here is a selection of them:

Gravitational force (as mentioned)

Electrostatic force

Magnetic force

Friction, drag, air resistance

Elastic force/force of a spring

Normal reaction force (e.g. of the ground on a car or on your chair)

Friction, drag and air resistance always oppose the motion of an object. This applies to falling apples as

well as to speeding cars.

Addition of Forces, Balanced and Unbalanced Forces, Resultant Force

The tractor has a larger forward force (driving force = 3000N) than drag (1500N). The two forces

(vectors) can be represented by arrows as shown above. The resultant force acting on the tractor is the

difference between the two forces. It can be calculated by subtracting the two vectors. In this case the

resultant force will be F = 3000 – 1500 = 2000N.

Resultant force Drag

Driving force

Pull from trailer Drag

Driving force

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In this second example a trailer (only its pull is shown as an arrow) is connected to the tractor. Now the

sum of the pull of the trailer and the drag are equal and opposite to the driving force. The resultant

force is therefore 0N.

In the first case the forward and backward forces are unbalanced, in the second case the forces are

overall balanced.

Force, Mass and Acceleration

When the forces on an object are balanced it will remain stationary if it was stationary before. If it was

moving at constant velocity before, it will continue to do so. This is Newton’s first law of motion. Objects

only accelerate or decelerate when an unbalanced force acts on them. The greater the unbalanced

force, the greater the acceleration.

The acceleration of the object also depends on a second factor. A force of 1000N will accelerate a

bicycle very quickly, but it will very little effect on a coach, let alone a train. Hence mass is the second

factor that influences acceleration. The following formula joins these factors:

Force = mass x acceleration

F = m x a

Units:

F: N (newtons)

m: kg

a: m/s2

The formula shows that 1N = 1kgm/s2. This means that a force of 1N accelerates a mass of 1kg at a rate

of 1 m/s2. In other words, the velocity will increase by 1m/s every second.

Mass & Weight

In Physics the word weight has a different meaning than in daily life. Mass is what you mean when you

talk about ‘losing weight’. From a Physics point of view, you are losing mass, measured in kg (or stones).

Weight is the gravitational pull on an object, it is a force, measured in newtons. You could lose weight by

flying to the moon where the gravitational pull is less.

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Weight is calculated as

Weight = mass x acceleration due to gravity

W = m x g

Units:

W: N

m: kg

g: m/s2

On Earth: g = 10 m/s2

If you have a close look at the formula you will find that it is just a special case of F=ma.

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21/03/2010

Terminal Velocity

Consider a skydiver:

4) When he opens his parachute the air resistance suddenly ________, causing him to start _____ ____.

5) Because he is slowing down his air resistance will _______ again until it balances his _________. The skydiver has now reached a new, lower ________ _______.

Words – slowing down, decrease, increases, terminal velocity, weight

Terminal Velocity

When a skydiver jumps out of a plane only his weight (W = mg) will act on his

body) in the very first instance. As she accelerates and her speed increases, the

air resistance or drag increases as well. The resultant force becomes less. Finally

drag and weight balance each other out. The skydiver falls at a constant

velocity. This is called terminal velocity.

The velocity-time graph looks like this.

The skydiver here reaches a second terminal velocity after the parachute has been opened.

Due to the initial high velocity the drag is now much bigger than the weight. Once the

skydiver has slowed down, she reaches terminal velocity again, which is much lower this

time as the graph shows. Eventually she lands and her velocity is zero.

Terminal velocity occurs on falling objects in liquid as well, e.g. when a stone is thrown into

a lake.

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Stopping Distances

The distance it takes to bring a car or a bicycle to a halt is called stopping distance. The stopping

distance consists of the thinking distance and the braking distance. The thinking distance is the distance

covered during the reaction time. The vehicle continues travelling at the same speed. Once the brakes

have been applied, the vehicle will slow down and stop. In this time the braking distance is covered.

The following diagram shows how the speed influences the two distances.

The thinking distance increases proportionally to the speed as d = v x t. If you double the speed, the

distance covered in your reaction time doubles as well.

The braking distance increases approximately with the square of the speed (ntk).

The diagram above relates to specific conditions. There are a number of factors that influence both

thinking distance and braking distance.

Factors influencing Thinking Distance Factors influencing Braking Distance

Tiredness Road conditions (wet, icy, gravel, dry tarmac, etc.)

Alcohol Quality of tyres

Drugs Quality of brakes

Distractions (e.g. mobile phone)

Momentum

Momentum is a measure of how difficult it is to stop a moving object. A flying football has a smaller

momentum than a rugby player running at full speed, a train has a larger momentum than a lorry. These

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two examples suggest that there are two quantities that determine the momentum of an object: mass

and velocity.

momentum = mass x velocity

p = m x v

p: momentum (in kgm/s or Ns)

m: mass (in kg)

v: velocity (in m/s)

Momentum is therefore defined as the product of mass and velocity of an object. It is a vector quantity.

Example:

A Golf of mass 1100kg drives at a speed of 13m/s (approx 30mph).

The momentum of the Golf is:

p= mv = 1100 x 13 = 14300 kgm/s

Momentum and Force

If momentum is a measure of how difficult it is to stop a moving object, then force and momentum must

be linked. The force to stop a moving object can be calculated using the following formula:

Force = change in momentum / time taken

t

mumvF

v: final velocity, u: initial velocity

This means that if an object is stopped within a short time, a large force is applied.

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Example:

Find the force it takes to stop a Golf of mass 1100kg at a velocity of 14m/s within 5s.

u = 14m/s v = 0m/s m = 1100kg t = 5s

Nt

mumvF 3080

5

01100141100

Application:

In road accidents cars are usually stopped within a very short period of time. That means that the forces

acting on the passengers are very high. Even if a person wears a seatbelt, the pull of the seatbelt on the

person could be so high that the person could be injured. Seatbelts are therefore made of slightly

stretchy materials (you cannot notice this when pulling on the material). As they stretch the momentum

of the person is changed over a longer period of time, hence reducing the impact force.

The crumple zones of cars have the same purpose: it takes longer to

stop a car hitting another car when the front crumples than when

there is no crumple zone. Hence the impact forces on the

passengers are smaller. Ntk: A more robust, tank-like car would

probably maintain its shape, but be more harmful to the passengers

inside.

One of the disadvantages of the great Smart

car is that the crumple zone is minimal and therefore the potential harm to

driver/passengers greater. However, in the city the speeds are also

lower than on the motorway.

The formula t

mumvF

can be rewritten as F=ma:

mat

vm

t

uvm

t

mumvF

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Momentum, Collisions and Explosion

Momentum is conserved in collisions. That means that the total momentum before a collision equals the

total momentum after the collision.

Total momentum before the collision = total momentum after the collision

The conservation of momentum can be demonstrated with Newton’s

cradle. When one steel ball hits the balls in the middle, one ball on the

right will be moving away with the same momentum as the momentum

of the ball hitting the balls from the left.

In the following example two balls collide. The left one has a mass of

0.5kg, the right one has a mass of 0.2kg. You are supposed to find the velocity of the left one after their

collision.

m1u1+m2u2 = m1v1 + m2v2

u2 = 0m/s. Therefore:

0.5 x 10 = 0.5 x 5 + 0.2 x v2

5 = 2.5 + 0.2 x v2

2.5 = 0.2 x v2

v2 = 12.5 m/s

When one of the objects bounces back after the collision, its

velocity will be negative!

In an elastic collision, the kinetic energy is conserved as well.

This means that the total kinetic energy before and after the

collision will be the same.

In an inelastic collision the two objects stick together after the collision. Kinetic energy is not conserved,

but momentum always is.

u1=10m/s u2=0m/s collision v1=5m/s v2=?

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Conservation of momentum is also used to calculate velocities in explosions or rockets.

The change in momentum of the exhaust fumes of the rocket is the same as the change in momentum

of the rocket. As the gas particles in the exhaust fumes are small and light, they have to be pushed out

at very high speeds to have a significant change in momentum of the rocket itself.

Note: if two parts fly away from each other in an explosion, one of the velocities has to be negative.

Newton’s Laws of Motion

Newton developed three laws of motion and you have already understood them all without knowing

what they are. This is so you know what each one of them states explicitely.

1st law of motion: An object at rest will remain at rest unless acted on by an unbalanced force. An object

in motion continues in motion with the same speed and in the same direction unless acted upon by an

unbalanced force.

We said earlier that an object only accelerates (changes its speed) when an unbalanced or resultant

force acts on it. This is the same thing.

2nd law of motion: Acceleration is produced when a force acts on a mass. The greater the mass (of the

object being accelerated) the greater the amount of force needed (to accelerate the object).

This is the formula F = ma put into words. Note: the force here is the resultant force.

3rd law of motion: For every action there is an equal and opposite reaction.

The weight of your body pushing on the chair you are sitting on is the same as the reaction force of the

chair onto your body.

Moments – The Turning Effect of a Force

A force can have a turning effect – it can make an object turn around a fixed pivot

point. The turning effect of a force is called moment.

You pull a spanner at its end rather than close to the nut.

This feels easier. In Physics terms the moment is higher

when you pull the spanner with the same force at the far

end from the nut.

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A pivot or fulcrum is the point around which an object turns, e.g. the nut or in case of a door the hinge.

The moment depends on two factors: the distance of the force from the pivot and the size of the force.

The moment can therefore be calculated as

moment = force x perpendicular distance from pivot

M = F x d

Units:

M: Nm (Newton meters)

F: N

d: m

Examples:

1.

M = F d

M = 20 x 0.6

M = 12Nm

2. Here the object has been moved and therefore the perpendicular distance between force and pivot

has been shortened from 0.6m to 0.5m.

The moment will now be different:

M = 20 x 0.5

d = 0.6m

F = 20N

pivot

d = 0.5m

F = 20N

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M = 10Nm

Often there are several forces acting on an object. Each force causes a moment. The system will remain

stationary when the moments are balanced. That means that the sum of the moments in clockwise

direction will be equal to the sum of the moments in anti-clockwise direction. The principle of moments

states: The sum of the clockwise moments equals the sum of the anti-clockwise moments for a system

in equilibrium. Equilibrium means balanced forces/moments.

The sum principle of moments can be written as following: Σ is the Greek capital letter ‘sigma’, which

stands for ‘sum of’. The arrows show clockwise and anti-clockwise directions.

Σ↺M = Σ↻M

F1 x d1 = F2 x d2 + F3 x d3

10 x 0.2 = 5 x 0.2 + F3 x 0.3

2 = 1 + 0.3 F3

1 = 0.3 F3

F3 = 1/0.3 = 3.33N

The same method can be used to find an unknown distance, if all forces are given.

Centre of Gravity

The centre of gravity is the point through which the whole weight of an object seems to act. For a

symmetrical object this will be in the centre of the object, like on the ruler shown. The weight arrow is

usually shown as an arrow through this point. You might have done this in the past without knowing

that this was the centre of gravity, or centre of mass as it is sometimes called.

If you have an irregularly shaped body, the centre of gravity can even lie outside the body itself:

F1=10N

F2=5N F3=? d1=0.2m d2=0.2m d2=0.2m

d3=0.3m

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Example:

Σ↺M = Σ↻M

W d3 = F1 d1 + F2 x d2

20 x 0.1 = 10 x 0.1 + F2 x 0.3

2 = 1 + F2 x 0.3

1 = F2 x 0.3

F2 = 3.33N

Stability and centre of gravity

Intuitively we know that it is easier to topple over the vase than the umbrella base. The Physics behind

this is that the moment needed to topple over the vase is much lower than the moment needed to

topple over the base. Generally speaking objects with a low centre of gravity and a broad base are more

difficult to topple over than objects with a high centre of gravity and a small base.

F1=10N

F2=?

W=20N

d2=0.3m

d3=0.1m d1=0.1m

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Forces on a light beam

A light beam is considered to be so light that its own weight is negligible in comparison with the forces

acting on the beam. A light beam could be a beam across a stream with a person walking across it. Or it

could be a very light bridge with a lorry driving across it. No, you don't need to worry whether the very

light bridge will hold the lorry or whether it will collapse ... This is someone else's problem, but you are

right, this idea of the 'light beam' only applies within certain limits.

If a girl stands in the middle of a light beam, half of her weight will be supported by either end.

If she stands just above the support of the light beam on either end, then this end will support her full

weight, while there will be no force on the other end.

W

F = -½ W F = -½ W

W

F = -W

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However, the girl could also stand somewhere in between. Then the support force on either end of the

beam could be calculated using the principle of moments and the fact that the sum of the upwards

forces will equal the sum of the downwards forces (in this case only one, the weight of the girl) as the

object is in equlibrium. However, all you need to know for the exam is that as the girl walks towards the

left end, the support force on the left increases and the support force on the right decreases. If she

walked towards the right, the opposite would be the case.

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Force-Extension Graphs

When another person stands on your foot, it gets squashed. The weight of the other person compresses

your foot. Materials that go back to their original shapes show elastic behaviour, materials that remain

permanently deformed show plastic behaviour. The word plastic in this context has nothing to do with

the material that shopping bags are made of. When a new phone is designed, it is important that the

casing shows elastic behaviour to a certain extent, e.g. when it is dropped, so that you pick it up and it

looks unchanged. When the impact force on the phone is too high, it would break.

In this context we only look at very simple cases: the extension of a rubber band, of metal helical springs

and of metal wires. A force-extension graph shows how the shape of the rubber changes as the force is

applied.

The force here is not proportional the extension as the line is not straight. (Ntk: This has to do with the

untangling of the polymers as the rubber is stretched.)

Many of us have played with the metal spring in a ballpen. When stretched, the spring goes back to its

original length unless it is stretched too much. The following graph shows the behaviour of a metal

spring under load:

Limit of

proportionality

Elastic limit (when stretched further, plastic

deformation occurs: the spring will not go back to

its original shape

Breaking point

Hooke’s law applies

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At the beginning the force is directly proportional to the extension. The point at the end of the straight

line is called the limit of proportionality. The spring can be stretched a little further and still go back to

its original length when released. The point beyond which the deformation will be plastic is called the

elastic limit. Between the elastic limit and the breaking point of the spring more plastic deformation

takes place.

Hooke’s Law

The first part of the graph is a straight line graph through the origin. The force (or load) is directly

proportional to the extension. Directly proportional means that if you double the force, the extension

will also double.

Hooke’s law describes this behaviour mathematically:

Force = spring constant x extension

F = kx

k: spring constant (in N/m or N/cm)

x: extension (in m or cm)

Note: the extension is the amount by which the spring gets longer, it is not to be confused with the

length of the spring.

Note: the spring constant is the gradient of the graph.

Wires do not seem to stretch as we usually do not notice it with the naked eye. However, they do

stretch just like a spring, just less. The stiffness of a metal wire would therefore be far higher.

How would the graph of a wire look like?

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Astronomy

Moons

Not only does the Earth orbit the Sun, but the Moon also orbits the Earth. Our planet is not the only one orbited by a moon. Below is a list of various planets and their moons.

Moons are often called ‘natural satellites’ as they orbit a planet. What we call a satellite in daily life would be an ‘artificial satellite’ in Physics.

Note: for the exam you only need to know that some other planets than the Earth have moons.

Planet Moons Names of Moons

Mercury 0 -

Venus 0 -

Earth 1 Luna

Mars 2 Phobos, Deimos

Jupiter 63 Io, Europa, Ganymede, Callisto (Galilean moons); Amalthea, Himalia, Elara, Pasiphae, Sinope, Lysithea, Carme, Ananke, Leda; Metis, Adrastea (shepherd moons); Thebe, Callirrhoe, Themisto, Kalyke, Iocaste, Erinome, Harpalyke, Isonoe, Praxidike, Megaclite, Taygete, Chaldene, Autonoe, Thyone, Hermippe, Eurydome, Sponde, Pasithee, Euanthe, Kale, Orthosie, Euporie, Aitne (+ 25 other moons)

Saturn 61 Titan, Rhea, Iapetus, Dione, Tethys, Enceladus, Mimas, Hyperion; Prometheus, Pandora (shepherd moons); Phoebe, Janus, Epimetheus, Helene, Telesto, Calypso, Atlas, Pan, Ymir, Paaliaq, Siarnaq, Tarvos, Kiviuq, Ijiraq, Thrymr, Skathi, Mundilfari, Erriapo, Albiorox, Suttung (+ 30 other moons)

Uranus 27 Cordelia, Ophelia, (shepherd moons); Bianca, Cressida, Desdemona, Juliet, Portia, Rosalind, Belinda, Puck, Miranda, Ariel, Umbriel, Titania, Oberon, Caliban, Sycorax, Prospero, Setebos, Stephano, Trinculo (+ 6 unnamed moons)

Neptune 13 Triton, Nereid, Naiad, Thalassa, Despina, Larissa, Proteus, Galatea (shepherd moon) (+ 5 unnamed moons)

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Gravitational Field Strength

The gravitational field strength on Earth is about 10m/s2 or 10N/kg. As shown above the weight can be

calculated from the mass using the gravitational field strength. The mass will be the same anywhere in

the universe, but the weight changes. On the moon g is only about 1/6 of its value on Earth (about

1.6N/kg). That means that you would weigh only 1/6. You could jump six times

higher than on Earth and you would be able to lift up masses which are six

times as high. Lifting up small rocks would be no problem.

On the bigger, heavier planets the gravitational field strength is higher as they

have a greater mass. On Jupiter it is about 23N/kg, while it is less than 4N/kg on Mars.

Gravity

The Sun and all the planets exist in empty space. The ‘magic’ force that keeps the planets in their orbits around the Sun is called gravity.

Gravity is the attractive force between masses. It only has a noticeable effect when at least one of the two masses is huge. Sitting next to your neighbour you do not feel any gravitational attraction. That is because you do not weigh enough. However, the Earth with its big mass pulls you towards its centre and keeps you on its surface.

The gravitational force not only keeps planets in their orbit around the sun, but also causes the moon and artificial satellites to orbit the Earth. The diagram below shows the elliptical paths of the planets around the Sun. It is an old diagram still containing Pluto as a planet, which obviously no longer is the case.

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Comets

The paths of comets are also determined by the gravitational pull of the Sun. The diagram below shows the orbit of the comet Ikeya-Zhang. While the planets’ orbits are close to circular paths, those of the comets are far more elliptical.

Comets are about 1-30km in diameter and are made up of dust and ice. As they get closer to the sun, some of the frozen gases evaporate and are blown away from the Sun (by so called solar wind). Hence the tail of a comet always points away from the Sun.

Probably the most famous comet is Halley’s comet. It comes close to the Sun every 76 years and was last

visible from Earth in 1986.

Orbital Speed, Orbital Radius and Time Period

Speed = distance/time

The distance covered in one orbit is the circumference of a circle (we assume here that the orbits are circular): distance = 2πr

The time taken for one orbit is called the ‘time period’ (symbol: T).

Therefore: periodtime

radiusxorbitalxv

2

T

rv

2

Example: Find the orbital speed of the Earth.

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Since the orbit of the Earth around the Sun follows an ellipse, the distance between Sun and Earth varies. Therefore we take an average here, which is 149,000,000km.

The time period is obviously 1year. To get the speed in km/s (!) we need to convert 1 year into seconds.

T = 1 year = 365days x 24h/day x 60min/h x 60s/min = 31,536,000s

Therefore the speed will be

skmskmx

v /30/69.29000,536,31

000,000,1492

Think: Would the velocity of the Earth be a constant 30km/s as well?

Galaxies

A galaxy is a huge collection of billions of stars. The galaxy that we belong to is called the Milky Way. It is a spiral type of galaxy similar to that in the image. As it is so big and we are 2/3 out from the centre, it is absolutely impossible to obtain any pictures like the one on the right side of our own galaxy. However, when you are out in the countryside, you can see what looks like clouds on a clear night sky. There are so many stars and many of them are so far away, that we just see a lighter stretch across the entire sky.

The universe again is believed to consist of billions of galaxies. If you are about to get a headache now, you know that you are getting a grasp of space and its vastness.

This is just scratching the surface of an incredibly topic.