Dynamics and Space
St Luke’s High School
National 4 Physics
Name :
___________________
Teacher : ___________________
Room :
_______
N4 Dynamics & Space – revision checklist
Speed and acceleration
1. Calculations involving the relationship between speed, distance, and time.
2. Determination of average and instantaneous speed.
3. Interpretation of speed-time graphs to describe motion including calculation of distance
(for objects which are speeding up, slowing down, stationary and moving with constant
speed.) Motion in one direction only.
4. Use of relationship of acceleration, change in speed and time.
Relationship between forces, motion and energy
1. The use of Newton’s first law and balanced forces to explain constant speed, making
reference to frictional forces.
2. The use of Newton’s second law to explain the movement of objects in situations
involving constant acceleration.
3. Calculations using the relationship between force, mass and acceleration in situations
where only one force is acting.
4. Calculations using the relationship between weight, mass and gravitational field strength
within our solar system.
5. Risks and benefits associated with space exploration including challenges of re-entry to a
planet’s atmosphere. The use of thermal protection systems to protect spacecraft on reentry
.
Satellites
1. The range of heights and functions of satellites in orbit around the earth, including
geostationary and natural satellites. Range of applications of satellite including
telecommunications; weather monitoring; the use of satellites in environmental
monitoring. The use of satellites in developing our understanding of the global impact of
mankind’s actions.
2. The dependence of period of orbit on height.
3. The use of parabolic reflectors to send and receive signals.
4. Use of the relationship between distance, speed and time applied to satellite
communication.
Cosmology
1. Description of planet, moon, star, solar systems, exo-planet, galaxy and universe
2. Scale of the solar system and universe measured in light years.
3. Space exploration and its impact on our understanding of the universe and planet Earth.
4. Conditions required for an exo-planet to sustain life.
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KINEMATICS
Speed, distance, time
Average Speed
Average speed is a measure of the distance travelled in a unit of time. Average speed is
calculated by using this formula:
distance travelled (m)
𝒔̅ =
average speed
(m/s)
𝒅
𝒕
time taken (s)
Units of speed
Speed can be measured in many different units. Usually the unit is metres per second, m/s or
ms-1. This means the distance must be measured in metres and the time taken in seconds. Note:
these notes will use the solidus for multiple units, e.g. m/s. However, you can use the negative
index, e.g. ms-1, if you prefer.
Measurement of average Speed
To measure an average speed, you must:



measure the distance travelled with a measuring tape or metre stick
measure the time taken with a stop clock
calculate the speed by dividing the distance by the time
Calculations involving distance, time and average speed
Note: care must be taken to use the correct units for time and distance.
Example
Calculate the average speed in metres per second of a runner who runs 1500 m in 5 minutes.
s =1500m
t = 5 minutes = 5 x 60 seconds = 300 s
𝑠̅ =
𝑑 1500
=
= 5𝑚𝑠 −1
𝑡
300
Instantaneous speed
The instantaneous speed of a vehicle at a given point can be measured by finding the average
speed during a very short time as the vehicle passes that point.
Average speed and instantaneous speed are often very different e.g. the average speed of a
runner during a race will be less than the instantaneous speed as the winning line is crossed.
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Measuring instantaneous speeds
To measure instantaneous speeds it is necessary to be able to measure very short times. With an
ordinary stopclock, human reaction time introduces large errors. These can be avoided by using
electronic timers. The most usual is a light gate connected to an electronic timer.
A light gate consists of a light source aimed at a photocell. The photocell is connected to an
electronic timer or computer. The timer measures how long an object takes to pass through the
light beam. The distance travelled is the length of the object which passes through the beam.
Often a card is attached so that the card passes through the beam. The length of the card is easy
to measure. The instantaneous speed as the vehicle passes through the light gate is then
calculated using:
𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝑣𝑒ℎ𝑖𝑐𝑙𝑒 =
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑐𝑎𝑟𝑑 𝑜𝑟 𝑣𝑒ℎ𝑖𝑐𝑙𝑒
𝑡𝑖𝑚𝑒 𝑡𝑜 𝑐𝑢𝑡 𝑏𝑒𝑎𝑚
Example
A vehicle moves through a light gate as shown in the diagram. Using the data from the diagram,
calculate the instantaneous speed of the vehicle as it passes the light gate.
𝑠𝑝𝑒𝑒𝑑 =
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑐𝑎𝑟𝑑
𝑡𝑖𝑚𝑒 𝑡𝑜 𝑐𝑢𝑡 𝑏𝑒𝑎𝑚
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=
10
0.25
=
0.10
0.25
= 0.4 𝑚/𝑠
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Acceleration
Most vehicles do not travel at the same speed all the time. If they speed up, they are said to
accelerate. If they slow down, they decelerate. Acceleration describes how quickly speed
changes. Acceleration is a vector quantity. However, only the acceleration of vehicles travelling
in straight lines will be considered.
Acceleration is the change in speed in unit time.
𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑠𝑝𝑒𝑒𝑑
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
Units of Acceleration
The units of acceleration are the units of velocity divided by the units of time (seconds). If the
velocity is in m/s, acceleration is in m/s2 (metres per second squared). An acceleration of 2m/s2
means that every second, the velocity increases by 2m/s.
Formula for Acceleration
𝒂=
𝒗−𝒖
𝒕
a = acceleration in m/s2
u = initial speed in m/s
v = final speed in m/s
t - time taken in s
Note: If a vehicle is slowing down, the final velocity will be smaller than the initial velocity, and
so the acceleration will be negative. A negative acceleration is a deceleration.
The equation for acceleration can be rearranged to give an alternative version:
𝒗 = 𝒖 + 𝒂𝒕
Example
A car is moving at 15 m/s, when it starts to accelerate at 2 m/s2. What will be its speed after
accelerating at this rate for 4 seconds?
u=
15 m/s
v =u+at
a=
2m/s2
=15+(2 x 4)
t=
4s
=23
The car will reach a speed of 23 m/s
Speed-time graphs
A velocity-time graph is a useful way to describe the motion of a vehicle. Time is always plotted
along the x-axis, and velocity is plotted along the y-axis.
The shape of the graph indicates whether the vehicle is accelerating, decelerating or moving
at a constant speed.
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(m/s)
(m/s)
(m/s)
0
0
(s)
constant speed
0
(s)
(s)
increasing speed
decreasing speed
= acceleration
= deceleration
The slope (or gradient) of the line on a speed-time graph indicates the acceleration. While the
slope is steady, the acceleration is constant. If the line gets steeper, the acceleration (or
deceleration) gets greater. Acceleration can be calculated using data from the graph and the
formula. The area vertically below a section of the graph is equal to the distance during that
time.
Example
The graph describes the motion of a car during 35 seconds.
a) What was the initial acceleration of the car?
b) What was the deceleration?
c) How far did the car travel in the 35 seconds?
d) Calculate the average distance
a. Initial acceleration lasts from 0 -10s:
𝑎=
u = 0, v = 20m/s, t = 10s
𝑣 − 𝑢 20 − 0
=
= 2𝑚/𝑠 2
𝑡
10
b. Deceleration was from 30-35s:
𝑎=
u = 20m/s, v = 0, t= 5s
𝑣 − 𝑢 0 − 20
=
= −4𝑚/𝑠 2
𝑡
5
c. Distance travelled = area under the graph:
Divide into sections of rectangles and triangles: X + Y + Z: use scale for sizes.
Area X = ½ x base X height = ½ x 10 x 20
Area Y = length x breadth
= 20 x 20
Area Z = ½ x base x height = ½ x 5 x20
=100m
=400m
=50m
Distance travelled = total area = 550m.
d. 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 =
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𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑
𝑡𝑖𝑚𝑒
=
550
35
= 15.7𝑚/𝑠
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DYNAMICS
Forces
Effects of forces
Forces can only be detected by their effects.
They can change:
• the shape of an object (stretch it, squeeze it etc)
• the speed of an object
• the direction of movement of an object
Measurement of Forces
Forces are measured in units called newtons (N), (see later for definition). Forces can be
measured with a newton balance. This instrument depends on the effect of a force on the shape
(length) of a spring.
A newton balance has a spring
inside. The force to be measured is
applied to the hook which is
attached to the spring. The force
causes the spring to stretch. The
greater the force, the greater the
stretch of the spring and the further
the marker moves across the scale.
Mass and Weight
Weight is a force caused by gravity acting on an object's mass. On Earth, it measures the pull of
the Earth on the object. It is measured in newtons. Weight always acts vertically downwards. Its
size does not just depend on the mass of the object, but on the strength of gravity at that place.
Mass measures the amount of matter in an object. It is measured in kilograms (kg). The value of
mass does not change from place to place. The strength of gravity in a particular place is called
the gravitational field strength and tells you the weight (or force) per unit mass. Its symbol is g
and its unit is N/kg. On Earth, g = 9.8 N/kg; this means that every 1kg will be subjected to a
weight(force) of 9.8N.
Mass and weight are connected by the following formula:Weight in N
W = mg
gravitational field strength in N/kg
Mass in kg
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Example
a) What is the weight of a 50 kg girl on Earth?
b) What would she weigh on the moon where the gravitational field strength is 1.6 N/kg?
a) W=mg
b) W=mg
= 50x9.8
=50x1.6
=490N
=80N
The Force of Friction
Friction is a resistive force, which opposes the motion of an object. This means that it acts in the
opposite direction to motion.
Friction acts between any two surfaces in contact. When one surface moves over another, the
force of friction acts between the surfaces and the size of the force depends on the surfaces, e.g.
a rough surface will give a lot of friction.
Air friction is usually called air resistance. It depends mainly on two factors:


the shape and size of the object
the speed of the moving object.
Air resistance increases as the speed of movement increases.
Increasing and Decreasing Friction
Where friction is making movement difficult, friction should be reduced.
This can be achieved by:
 lubricating the surfaces with oil or grease
 separating the surfaces with air, e.g. a hovercraft or airtrack
 making the surfaces roll instead of slide, e.g. use ball bearings
 streamlining to reduce air resistance.
Where friction is used to slow an object down, it should be increased.
This can be achieved by:
 choosing surfaces which cause high friction e.g. sections of road before traffic
 lights have higher friction than normal roads
 increasing surface area and choosing shape to increase air friction, e.g. parachute.
Newton's First Law
When the forces on an object are balanced (or when there are no forces at all), then neither the
speed nor direction of movement will change. Balanced forces mean constant speed or the
object is stationary. E.g a spacecraft will continue at a constant speed through space because no
forces act on it.
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Newton's Second Law of Motion
This law deals with the situation when there is an unbalanced force acting on an object. The
velocity cannot remain constant, and the acceleration produced will depend on the mass of the
object and the value of the unbalanced force. As the unbalanced force acting on an object
increases, the acceleration increases also. As the accelerated mass increases, the acceleration
decreases for a given force. The newton is defined as the force which makes a mass of 1 kg
accelerate at 1m/s2.These facts can be summarised in an equation:
Acceleration in m/s2
Unbalanced force in N
𝐹 = 𝑚𝑎
Mass in kg
Example
A car of mass 1000 kg has an unbalanced force of 1600 N acting on it.
What will be its acceleration?
m= 1000kg F = 1600N
𝑎=
𝐹
1600
=
= 1.6𝑚/𝑠 2
𝑚
1000
Resultant Forces
When several forces act on one object, they can be replaced by one force which has the same
effect. This single force is called the resultant or unbalanced force.
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Combining forces in a straight line
Draw a diagram of the object and mark in all the forces acting, using an arrow to represent
each force. (Do not forget weight, which is often not specifically mentioned in the question).
Use arithmetic to find the resultant:


add together forces which act in the same direction
subtract forces which act in the opposite direction.
A diagram like this is called a free body diagram.
Example
A short time after take off a rocket of mass 10000 kg has a thrust of 350000 N and experiences
air resistance of 30000 N. Draw a free body diagram and find the resultant force
acting on the rocket.
Air resistance 30000N
Total upward force =
Total downward force =
Resultant force upwards =
350000N
100000N + 30000N =
350000 – 130000
=
130000N
220000N
Calculations using F = ma for more than one force
Draw a free body diagram and mark in all the known forces. Use this to calculate the resultant
force (F in the equation) before using the equation.
Example: A car of mass 1000 kg
experiences friction equal to 500 N. If
the engine force is 1300 N,
what will be the cars acceleration?
Resultant force = 1300 - 500
𝑎=
𝐹
𝑚
=
800
1000
=
800N
= 0.8𝑚/𝑠 2
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Acceleration due to gravity and gravitational field strength
Weight is the force which causes an object to accelerate downwards and has the value mg, where
g is the gravitational field strength, see page 5. The value of the acceleration caused by weight
can be calculated from Newton's second law, using the equation F = ma where F is now the
weight W, and W = mg.
𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑔𝑟𝑎𝑣𝑖𝑡𝑦 = 𝑎 =
𝐹
𝑚𝑔
=
= 𝑔 𝑤ℎ𝑒𝑟𝑒 𝑔 𝑖𝑠 𝑖𝑛 𝑚/𝑠 2
𝑚
𝑚
The numerical values of the acceleration due to gravity and gravitational field strength are equal.
Their units, N/kg and m/s2 are also equivalent. This means that on earth a falling object will
accelerate at 9.8m/s2 (in the absence of air resistance).
Principle of Conservation of energy
The total amount of energy remains constant during energy transfers. Energy cannot be created
or destroyed but simply transformed to one of its many forms.
When a rocket comes in to land the kinetic energy is changed to heat due to friction between its
surface and the air. The side of the rocket in contact with the air is protected with heat proof
insulating panels.
Heat Insulators
September 2015
Heat Conductors
Page 10
Space Exploration
Our Universe
Most astronomers believe that the universe began in a big bang about 14 billion years ago.
Matter, time and space all began with the big bang. In a fraction of a second, the Universe grew
from smaller than a single atom to bigger than a galaxy. And it kept on growing at a fantastic
rate. It is still expanding today.

The universe consists of many galaxies separated by empty space.

A galaxy is a large cluster of stars (e.g. the Milky Way).

A star is a large ball of matter that is undergoing nuclear fusion and emitting light. The
sun is a star. The sun and many other stars have a solar system.

A solar system consists of a central star orbited by planets.

A planet is a large ball of matter that orbits a star (e.g. Earth or Jupiter). Planets do not
emit light themselves. Many planets have moons.

A moon is a lump of matter that orbits a planet (e.g. the Moon orbits the Earth or Deimos
and Phobos orbit Mars)
Our Solar System
Our solar system consists of the Sun, the eight official planets and at least three "dwarf planets"
(Pluto was downgraded to a dwarf planet in 2008). The planets orbit the sun and in turn other
smaller satellites or moons orbit the planets.
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Exploring Space
Rockets
A simple rocket is shown in the diagram. The two liquids mix
and burn in the combustion chamber, where the hot gases
produced expand rapidly and are forced out through the nozzle.
These hot gases are pushed downwards and exert an upwards
force on the rocket.
Interplanetary Flight
During interplanetary flight there is no need for the engines to be
kept on. Since space is a vacuum there is no friction acting on
the space vehicle. With no unbalanced forces acting on the
vehicle it will continue to move at a steady speed (Newton’s
First Law of Motion). If acceleration or deceleration is required,
then the only force acting on the space vehicle is its engine
thrust.
liquid
fuel
liquid
oxidant
turbo
pumps
combustion
chamber
exhaust
Space Craft Re-entry
When a spacecraft re-enters the Earth’s atmosphere it experiences friction with the atmosphere.
This results in kinetic energy being changed into heat energy. For this reason spacecraft have to
be covered with heat shielding to prevent them from burning up on re-entry.
Cosmology
Light-years
Since distances in space are so enormous, it is useful to think about how long it takes light to
reach us from an object. For example:
Object
Sun
Proxima Centauri (nearest
star)
Edge of galaxy
Time for light to reach Earth
8 minutes
4.3 years
100,000 years
A useful measurement of distances in space is the light-year. A light-year is the distance
travelled by light in one year. 1 light-year = 9,460,730,472,580,800 m (9.46 x 1015 m).
This means that when we look at things in space we see them as they were many years ago. It is
not possible to see anything as it is now. Even someone walking past you – you see them where
they were a fraction of a second ago not where they are at the moment you look!
Satellites
We have learned to make use of space in many ways, but most of the benefits affecting people
on Earth are brought about by unmanned satellites.

Communication Satellites:
A company called Intelsat owns the majority of
communication satellites which relay TV and telephone signals. Each one is about the
size of a house.
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
Science Satellites: These have varying purposes including the study of the Van Allen
radiation belts around the Earth, the density, pressure and chemical composition of the
upper atmosphere, the magnetic field around the Earth and even to monitor meteorites
approaching the Earth.

Astronomy and Solar Satellites: One of the problems of observing the Sun, planets and
distant galaxies from Earth is the absorption and bending of light and other radiations by
the atmosphere. By putting a telescope on a satellite, a much clearer view of the
Universe is obtained.

Military Satellites: Spy satellites orbit the Earth taking pictures of shipyards, research
stations, rocket bases and other military locations. Some spy satellites are used to
intercept telephone calls, and radio signals.

Navigation Satellites: Cars, planes and ships can receive signals from navigation
satellites. The user has a receiver computer which locks on to the signals from the
satellites and uses this to calculate position and speed. The United States' Global
Positioning System (GPS) consists of up to 32 medium Earth orbit satellites in six
different orbital planes. GPS is currently the world's most utilised satellite navigation
system.

Weather Satellites: Scanners on the satellites build up visible light and infrared pictures
of the Earth, which are transmitted back to weather stations. This information can be
used to make more accurate short-term weather forecasts.

Earth Resource Satellite: These can be used to analyse the health of crops (using
infrared), monitoring pollution, looking for forest fires and even locating natural
resources such as oil.

Geostationary Satellites: These stay above the same point on the Earth’s surface
(above the equator) and have an orbital period of 24 hours.
 The further out a satellite is the longer it takes to orbit
 The further out a satellite is the longer it takes to send a signal
there and get a signal back. Eg it takes about ¼ of a second to send
and receive a signal to and from a geostationary satellite. It takes
2.5 seconds to send and receive a message back from the moon.
 Communication signals travel at the speed of light which is
300,000,000 m/s.
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Receiver
SPACE
Transmitter
Space exploration
Where we’ve been – what we have learned about the universe and the Earth.
Exo-planets
Conditions for life
 Suitable star which must produce a stable energy source for a long time.
 Liquid water on the surface.
 Oxygen for life like that on the Earth.
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