1. Nuclear
radiation
Waves
Waves Dynamics
National 5
Revision
Kinross High School
Space Energy

2. Types of waves:
Longitudinal (e.g. sound) - the direction of vibration Definitions:
is the same as the direction of the wave. Frequency - the number of waves produced (or pass a point) each second.
Transverse (e.g. light) - the direction of vibration is at Speed - the distance a wave travels in one second.
right angles to the direction of the wave. Wavelength - the distance between two neighbouring crests (or troughs) / distance
from one point on a wave to the same point on the next wave.
Amplitude - the height of the wave, from the centre position to the crest (or trough)
Period - the time taken to produce one complete wave / the time taken for one wave
to pass a point.
The wave equation:
speed = frequency x wavelength
speed, v, in m/s Speed, distance and time:
frequency. f. in Hz speed = distance / time; time is always in seconds.
wavelength, lambda, in m.
WAVES
WAVES Period:
Diffraction: period = 1/frequency; period is in seconds.
Waves that can bend around obstacles in its path.
Waves with longer wavelengths (lower frequencies)
will diffract more than waves with shorter Electromagnetic spectrum:
wavelengths (higher frequencies). (in order of increasing wavelength/decreasing frequency)
From that rule, radio waves diffract more than TV •gamma rays (used to sterilise surgical instruments)
waves. •X-rays (used to find broken bones and in luggage security)
•ultraviolet (used to treat skin problems and sterilise medical instruments)
•visible light (used in medicine for eye surgery, to remove birthmarks and
Energy: cancerous tumours)
All waves transfer energy. •infrared (used to speed up the recovery of injured muscles and tissues)
The higher the amplitude of a wave the greater the •microwaves (mobile phones use this type of radiation to carry signals)
energy transferred by that wave. •TV and radio waves
Each of the radiations travel at 300,000,000 m/s in a vacuum (or air).
Click: They are all transverse waves.
Satellites The energy of radiation is directly proportional to its frequency.
Click:
Click: Light
Reflectors
Speed,
Speed,
Wave equation distance and Period Menu
Menu
Wave equation distance and Period
calculation
calculation time
time calculation
calculation
calculation
calculation

3. Wave equation calculations
1. A radio wave has a wavelength of 200 m. Calculate its frequency. 2. A radio wave has a frequency of 900 kHz. Calculate its wavelength.
frequency = speed / wavelength wavelength = speed / frequency
= 300,000,000 / 200 = 300,000,000 / 900,000
= 1,500,000 Hz = 333 m
3. Red light has wavelength of 600 nm. Calculate (a) its frequency, (b) its period, (c) the time taken for red light to travel 36000 km.
(a) frequency = speed / wavelength
= 300,000,000 / 0.0000006
= 500,000,000,000,000 Hz
(b) period = 1 / frequency
= 1 / 500,000,000,000,000
= 0.000000000000002 s
(c) time = distance / speed
= 36,000,000 / 300,000,000
= 0.12 s.
Back to waves
Back to waves

4. Speed, distance and time calculations
1. Calculate how far a gamma ray has travelled in 0.0005 seconds. Express your answer in kilometres.
distance = speed x time
= 300,000,000 x 0.0005
= 150000 m
Since 1 km = 1000 m, then 150000 / 1000 = 150 km
2. The Sun is 150,000,000 km away from the Earth.
(a) Calculate how long it takes light to travel from the Sun to the Earth.
time = distance / speed
= 150,000,000,000 / 300,000,000
= 500 s
(b) During a solar flare, the light ray and infrared radiation leave the Sun's photosphere at the same time and travel through
a vacuum towards the Earth. Will the infrared ray reach the Earth before, after or at the same time as the light ray?
Explain your answer.
At the same time, because light and infrared travel at the same speed in a vacuum.
Back to waves
Back to waves

5. Period and frequency calculations
A water wave travels at a speed of 0.8 m/s. The distance between points A and B of the water
waves is 0.6 m.
Calculate the water wave's (a) wavelength
(b) frequency
(c) period.
(a) 3 wavelengths = 0.6 metres
1 wavelength = 0.2 m
(b) frequency = speed /
wavelength
= 0.8 / 0.2
= 4 Hz
(c) period = 1 / frequency
=1/4
= 0.25 s
Back to waves
Back to waves

6. Curved dishes: receivers
Signals travel long distance and lose energy. This means
Signals from a distant curved reflectors are used to strengthen the received signal
source. from satellites or other sources. The reflector is curved so that
(Note: if signals travel weak signals are collected over a large area and brings to a
long distance, then the point called the focus.
incoming rays are The detector is placed at the focus so that it receives a strong
parallel.) signal.
Radio and microwave telescopes are examples of telescopes
that require a large curved reflector.
detector placed
at focus
Curved dishes: transmitters A parallel beam of signal
Curved reflectors are also used to transmit a strong parallel (any radiation from the
beam of signal (light or other radiations in the electromagnetic electromagnetic
spectrum). In a dish-transmitter, the source is placed at the focus spectrum.) This explains
and the curved reflector produces a parallel beam of signal. why car headlights emit a
parallel beam of light.
detector placed
at focus
Back to waves
Back to waves

7. Space is usually considered to start at an altitude of 100 km.
We need satellites because we cannot just send signals (radio or
microwave) from the UK to Australia. This is because:
* the signals from transmitters travel in straight lines (which
happens with HF TV signals)
* the Earth is curved and these signals cannot travel directly from
Britain to Australia
There are hundreds of satellites orbiting the Earth. For example, a
Sat Nav receiver compares the time it takes to receive radio signals
from a number of satellites.
Satellites are used for telephone
communications, TV
programmes, weather A geostationary satellite takes 24
information, checking on crops, hours to orbit the Earth. Such a
information on the security of
Satellites -
satellite would stay above the
other countries and monitoring same point on the Earth's
Earth's climate surface.
telecommunication and
space exploration The time taken for a satellite to
complete one orbit of the Earth
depends on its height above the
On Earth, a ground station would use a curved Earth: the higher the orbit of the
reflector transmitter to send a parallel beam signal. satellite, the longer its orbital
At the satellite, the signal is received by a curved period.
dish, which is the amplified and re-transmitted (at a
different frequency) back to a different ground station.
Click:
Satellite motion: Projectiles
Satellite motion is an extension of projectile motion.
Spacecrafts: A satellite continually accelerates towards the Earth, just
When a spacecraft re-enters the atmosphere, the craft's kinetic energy like any other projectile.
is converted into heat. This is due to the spacecraft experiencing friction However, the satellite is moving so fast that the Earth
friction with the atmosphere. A spacecraft must be covered with heat curves away from it as quickly as it falls.
shielding to prevent it from burning up on re-entry. This means the satellite never reaches the Earth as it Back to waves
Back to waves
A blunt shaped spacecraft deflects the heat away from the spacecraft. orbits the planet.

8. Advantages of optical fibres:
Reflection of light: Optical fibres: Advantages:
When light is reflected from a flat mirror, the angle of An optical fibre is a thin thread of glass through which light can * cheaper to make
incidence, i, is equal to the angle of reflection, r. travel. Heat, however, is not transmitted along the fibre. The * lighter
optical fibre is said to transmit 'cold light'. * greater signal capacity
Principle of reversibility: Light signals travel along the optical fibre at a speed of * better signal quality
A ray of light will follow the same path in the opposite 200,000,000 m/s. * less energy loss per km of optical fibre (i.e.
direction when it is reversed. Such glass fibres can carry telephone and modern telephone fewer repeater stations)
systems use both optical fibres and electrical cables. * smaller in size
mirror * not affected by interference.
In electrical wires, electrical signals travel at
almost 300,000,000 m/s. Optical fibres are also
difficult to join together.
i r
Light
How does an optical fibre work?
Optical fibres work due to total internal reflection. This means light reflected inside the
glass fibre and none escapes into the air.
Total internal reflection occurs when the angle of incidence is greater than the glass'
critical angle (which is around 42 degrees). From this set-up, light can travel through
optical fibres without ever leaving the fibre.
normal
light is reflected along the fibre
Refraction:
Refraction is when light changes its velocity (speed and direction) as it
passes from one medium into another.
Remember: When light passes from air into glass, the refracted ray
'bends' (should be refract) towards the normal. When light passes from
glass into air, it refracts away from the normal.
Critical angle and total internal
reflection:
Endoscopes:
* When a light ray enters glass,
Light is transmitted along the optical fibre.
along the normal, it does not
They are used to look inside a patient without
change direction.
i * When light passes from glass into
the need for surgery.
An endoscope has two bundles of fibres: one
air, and the angle of refraction is 90
normal to transmit 'cold light' from the source down
r degrees, the angle of incidence is
into the patient; the other bundle is used to
called the critical angle.
send an image back to the surgeon's eye.
* At angles greater than the critical
Endoscopes are flexible and can move
angle, all the light is reflected back
around inside the patient.
Back to waves
Back to waves into the glass. This is called total
air glass internal reflection.

9. Types of radiation:
The atom: * Alpha particles - slow moving helium nucleus.
Most of the mass of an atom is found in a central nucleus. It can travel a few cm in air.
The atom is made up: They can be absorbed by thin paper.
* a nucleus contain positively charged protons (red) * Beta particles - fast moving electrons from the
and neutral charged neutrons (blue) nucleus. They can travel a few metres of air.
* negatively charged electrons orbiting the nucleus It can be blocked by a few mm of aluminium
(green) * Gamma rays - high energy and high frequency
electromagnetic radiation. It is absorbed by a
minimum of a few cm of lead.
Radioactive decay is a random process. Ionisation:
This occurs when an atom loses or gains electrons to
become an ion.
Alpha particles produce much higher ionisation
Half life: density than beta particles or gamma rays.
This is because alpha particles are the largest and
The half-life of a radioactive source is the time taken for its activity to
fall to half of its original value. carry the greatest charge of all types of radiation.
All radioactive sources have their own half-life. Alpha particles can ionise the greatest number of
Click: Half-life atoms near the surface of a body.
calculations NUCLEAR
To measure half-life you would: RADIATION
* measure background count rate first
* then measure the count rate with the radioactive source present Part 1 Activity:
over an appropriate period of time using a Geiger-Muller tube
The activity is the number of decays
and counter.
per second. Activity is measured in
* background activity is subtracted from each reading and a
becquerels (Bq).
graph of count rate against time is drawn.
* the time taken for the activity to half can be determined from the
Click: Activity activity = number of decays / time
graph.
calculations
* activity, A, is in becquerels (Bq)
* number of decays, N
* time, t, is in seconds (s).
Equivalent dose:
This is a measure of biological harm. The equivalent dose is measured in sieverts (Sv).
Typical annual equivalent dose is about 2 mSv. Absorbed dose:
The absorbed dose is the energy absorbed per Part
equivalent dose = absorbed dose x radiation weighting factor kilogram mass (of the absorbing material). 2
* equivalent dose, H, is in sieverts (Sv) absorbed dose = energy / mass
* absorbed dose, D, is in grays (G)
Click: Dosimetry * absorbed dose, D, is in grays (G) or
* radiation weighting factor, wR, is used to compare the ability
calculations joules per kilogram (J/kg)
of different types of radiation to damage living cells.
* energy, E, is in joules (J) Menu
* mass, m, is in kilograms (kg).

10. Medical uses of radiation: Non-medical use of radiation: Background radiation sources:
Radiation can kill or damage (change the nature of) * Beta particles are used to monitor paper Examples are:
living cells. thickness * cosmic radiation
Nuclear radiation can be used in medicine to: * monitor leaks in underground water and * the Earth (soil and rocks - granite)
* sterilise medical instruments sewage pipes (by adding radioactive * the air (radon gas in air, from rocks and
* kill cancerous cells (placing alpha particles next to tracers to the liquids in the pipes and buildings)
the tumour / firing gamma rays at the tumour monitor traces of radioactivity in the soil * the human body (K-40)
* diagnose medical problems (a radioactive tracer surrounding them. * medical sources for X-ray and cancer
is injected and absorbed by an organ, which is * monitoring fertilisers and how it is being treatment
then monitored by a gamma camera) used in plants. * nuclear reactors
Effects of radiation on non-living things: Safety with radiation:
Radiation can cause: * handle radioactive substances with forceps
* ionisation * never point radioactive sources at anyone
* fog photographic film * wash hands thoroughly after using radioactive
* scintillations. sources
NUCLEAR * never bring radioactive sources up to your face
Ionisation is used to detect radiation in the Geiger- (especially your eyes and mouth)
Muller tube. RADIATION * no one under 16 years of age should handle a
When radiation enters the low pressure gas tube, it Part 2 radioactive source
ionises the gas and pulses of current passes * always store radioactive substances in suitable
between the electrodes. This pulse of current is lead-lined containers
recorded on a counter (which is connected to the * keep a record of the use of all radioactive
tube). sources
* return the source to its storage container after it
In a film badge, different sections of the has been used.
photographic film are covered by various thicknesses
and types of absorbers. The type of radiation is
determined by which sections of the film are
blackened. The amount of radiation is determined by
how black the film is. Click: Nuclear Click: Nuclear Reducing the equivalent dose:
fission fusion This can be reduced by:
In scintillation, certain materials absorb the energy of * shielding
the radiation and re-emits it as light. These are used Nuclear reactions: * limiting exposure time
to detect radiation in a gamma camera. Fission and fusion reactions release large * increasing the distance from the source.
amounts of energy.
Part
Menu
1

11. Half-life calculations
1. A radioactive source has a half-life of 30 days. 2. A source has an activity of 60 kBq and a half-life of 20 s.
Calculate its activity 120 days after it was measured at How long will it take for its activity to drop to 7.5 kBq?
2000 kBq.
Number of half-lives: 60 to 30 to 15 to 7.5
120 /30 = 4 half-lives So that is 3 half-lives.
2000 to 1000 to 500 to 250 to 125 1 half-life is 20 s,
3 half-lives is 20 x 3 = 60 s
125 kBq
3. A hospital technician is working with a radioactive source. The graph, on the right, shows the
activity of the source over a period of time.
(a) Use information from the graph to calculate the half-life of the radioactive source.
when t = 0 hours, activity = 160 kBq
find t, when activity drops to 80 kBq
t = 6 hours
(b) Calculate the activity after five half-lives.
160 to 80 to 40 to 20 to 10 to 5
activity after 5 half-lives = 5 kBq
Part
1

12. Activity calculations
1. Calculate the number of decays in the sample in two minutes, when the activity of a source is 1.2 kBq.
number of decays = activity x time
= 1200 x (2 x 60)
= 144000 decays
2. Explain what is meant by an activity of 10 MBq.
10 million decays every second
Part
1

13. Dosimetry calculations
2. A box receives an absorbed dose of 40 mGy from a radioactive
1. A 5 kg block absorbs 10mJ of slow neutrons.
source which emits alpha particles only.
Calculate the absorbed dose received by the box.
Calculate the equivalent dose received by the box.
equivalent dose = absorbed dose x radiation weighting
absorbed dose = energy / mass
factor
= 0.01 / 5
= 0.04 x 20
= 0.002 Gy or 2mGy
= 0.8 Sv
3. A 2 kg box absorbs 40 mJ of radiation. The equivalent dose received by the box is 200 mGy.
Using the information, from the table, which radiation was absorbed by the box?
E = 0.04 J m = 2 kg H = 0.2 Gy Wr = ?
Type of radiation radiation weighting factor
* Find absorbed dose, D, first.
absorbed dose = energy / mass alpha 20
= 0.04 / 2
beta 1
= 0.02 Gy
* Now find Wr. gamma 1
radiation weighting factor = equivalent dose / absorbed dose
fast neutrons 10
= 0.20 / 0.02
slow neutrons 3
= 10
Part
1
From the table, the radiation is fast neutrons.

14. Nuclear fission
1. A bombarding neutron is absorbed by the large nucleus.
2. The large nucleus becomes unstable and breaks apart producing fission fragments.
3. Neutrons are released in this nuclear reaction, which then bombards other large nuclei. This avalanche of nuclear fission is known as a chain reaction.
Back to
nuclear
radiations

15. Nuclear fusion:
1. Two lighter nuclei (two hydrogen nuclei, each consists of two neutrons and one proton) combine (fuse) together
2. The two nuclei fuse to form a heavier nucleus (helium) and energy is released
3. The products (heavy nucleus and the two neutrons) have kinetic energy and move away.
Back to
nuclear
radiations

16. Speed-time graph: Forces:
Speed, distance and time:
Speed is the distance, travelled by an One newton is a force required to accelerate
object, in one second. a kilogram mass at 1 m/s/s.
Click: speed-
time graph A force can change an object's speed,
Average speed (v-bar), of an object, is
the total distance travelled divided by the shape and direction.
time taken.
Friction is a force that acts in a direction
The instantaneous speed, of an object, is opposite to motion.
Click: example
its speed at a particular point during its
journey. Balanced force: two forces, both equal in
size and act in opposite directions are called
balanced forces.
Click: example
Newton's third law of motion:
DYNAMICS: If an object A exerts a force on B,
Acceleration: Part 1 then B exerts and equal and
The acceleration, of a vehicle, is the change in opposite force on A.
speed over the time taken for the change.
acceleration = change in speed / time
OR a = (v - u) / t
Newton's first law of Newton's second law of motion:
a - acceleration (m/s/s) motion: When an object is acted on by a constant
v - final velocity (m/s) Click: example A body will remain at rest or unbalanced force, the body moves with
u - initial velocity (m/s) move at a constant speed in a constant acceleration in the direction of the
t - time taken (s) straight line unless acted on unbalanced force.
by an unbalanced force.
If a = 0 m/s/s, the object is stationary or Basically,
travelling at a constant velocity. Interplanetary flight: Click: example
If a > 0 m/s/s, the object is speeding up During interplanetary flight, there F=mxa
If a < 0 m/s/s/, the object is slowing down. is no need for the engines to be
kept on. F - unbalanced force (N)
Since space is a vacuum, there m - mass (kg)
is no friction acting on the a - acceleration (m/s/s).
vehicle. With no unbalanced
forces acting on it, the vehicle
Part
M enu will continue to move at a steady
2 speed. (Newton's 1st Law of
motion).

17. Velocity and displacement:
Displacement - a measure of how far two points are away from each other, in a Velocity-time graph:
given direction.
Velocity - rate of change of displacement:
velocity = displacement / time Click: velocity-
Acceleration - rate of change of velocity: Click: example
time graph
acceleration = change in velocity / time
Projectiles:
Click: example When an object is projected in a
gravitational field, it will follow a curved
Scalars and vectors: path. This is known as projectile motion.
* Scalar quantity has a size (magnitude)
only e.g. temperature, mass, speed, In projectile motion, there are two types of
distance, time, energy, distance and motion:
power. * vertical - object is accelerating
* Vector quantity has a size and direction downwards due to the object's weight
e.g. velocity, acceleration, force, DYNAMICS:
* horizontal - object is travelling at a
weight, pressure and displacement. Part 2 constant speed (provided air
resistance is negligible)
Click:
Free fall:
Projectiles
When an object is in free fall, it
appears to be weightless. Weight:
Astronauts, inside a spacecraft, The weight of an object is the force on it due to the planet's
appear to be weightless because gravitational pull.
both the astronauts and the craft Weight is measured in newtons.
are falling towards the Earth at the
same rate. The mass of an object is the amount of matter that makes up
that object.It is measured in kilograms. Work done:
Work done is a measure of how much energy is
Weight = mass x gravitational field strength transferred.
W=mxg work done = force x distance Ew = F x
Click: example
d
W -weight in newtons (N)
m - mass in kilograms (kg) work done, Ew, is in joules (J)
g - gravitational field strength in newtons per kilogram (N/kg) force, F, is in newtons (N) Click: example
Part time, t, is in seconds (s).
M enu The gravitational field strength, g, of a planet is the weight per
1 unit mass of an object on that planet.

18. speed (m/s)
speed (m/s)
accelerating
3
2 4
time (s) 1
time (s)
speed (m/s)
The speed-time graph, shown above, consists of four stages. We
can work out how far an object has travelled by working out the area
under the graph.
constant speed The total distance is given as:
distance = area under graph
= area 1 + area 2 + area 3 + area 4
time (s)
The acceleration and deceleration can be worked out by using the
formula:
speed (m/s)
acceleration = (final speed - initial speed) / time taken
decelerating From the above graph:
during stage 1 - the object is accelerating;
stage 2 - acceleration = 0 m/s/s/;
stage 3 - object is accelerating, and
stage 4 - object is decelerating.
time (s)
Part
1

19. velocity (m/s)
velocity (m/s)
accelerating
3
2 4
time (s) 1
time (s)
velocity (m/s)
The velocity-time graph, shown above, consists of four stages. We
can work out how far an object has travelled by working out the area
under the graph.
constant speed The total displacement is given as:
displacement = area under graph
= area 1 + area 2 + area 3 + area 4
time (s)
The acceleration and deceleration can be worked out by using the
formula:
velocity (m/s)
acceleration = (final speed - initial speed) / time taken
decelerating From the above graph:
during stage 1 - the object is accelerating;
stage 2 - acceleration = 0 m/s/s/;
stage 3 - object is accelerating, and
stage 4 - object is decelerating.
time (s)
Part
2

20. A velocity-time graph for the motion of a vehicle is
shown. velocity (m/s)
•Describe the motions represented by each part of
the velocity-time graph.
(b) Calculate the acceleration during each part of the 20
graph.
2
1 3
(c) Calculate the displacement during each part of the
journey. 0
10 30 40 50 60 time (s)
(d) Calculate the length of the journey. 4 5
-20
Solution: 30 to 40 s: u = 20 m/s, v = 0 m/s, t = 10 s
• 0 to 10 s: constant acceleration from 0 to 20 m/s, in 10s. a = (v-u) / t
10 to 30 s: uniform (constant) velocity of 20 m/s for 20 s. = (0 - 20) / 10
30 to 40 s: constant deceleration from 20 m/s to 0 m/s = -2 m/s/s
at 40 s: vehicle changes direction 40 to 50 s: u = 0 m/s, v = -20 m/s, t = 10 s
40 to 50 s: vehicle accelerates in opposite direction, from 0 to 20 m/s, in 10 s. a = (v-u) / t
50 to 60 s: vehicle decelerates (in the same direction as 40 to 50s), from 20 m/s to 0 m/s. = (-20 - 0) / 10
= -2 m/s/s
(c) +
10 to 30 s: acceleration = 0 m/s/s 50 to 60s: u = -20 m/s, v = 0 m/s, t = 10 s (d)
(b) 0 to 10 s: u = 0 m/s, v = 20 m/s, t = 10 s
a = (v-u) / t a = (v-u) / t
= (20 - 0) / 10 = (0 - -20) / 10 Part
2
= 2 m/s/s = 2 m/s/s

21. (c) displacement = area between graph and time axis
from 0 to 10s: displacement = (0.5 x 10 x 20) = 100 m
from 10 to 30s: displacement =(20 x 20) = 400 m
from 30 to 40s: displacement = (0.5 x 10 x 20) = 100 m
from 40 to 50s: displacement =(0.5 x 10 x -20) = -100 m
from 50 to 60s: displacement = (0.5 x 10 x -20) = -100 m
(d) length of journey = displacement
= 100 + 400 + 100 + (-100) + (-100)
= 400 m previous

22. Average speed and instantaneous speed
A runner completes a 400 m race in 50 s. A toy car, of length 5 cm, takes 0.025 s to pass through a light gate.
Calculate her average speed. Calculate the toy car's instantaneous speed.
average speed = distance / time instantaneous speed = length of car / time taken
= 400 ./ 50 = 0.05 / 0.025
= 8 m/s = 2 m/s
Part
1

23. Weight
An astronaut has a mass of 80 kg. Calculate his weight on (a) Earth (g = 9.8 N/kg),
(b) Saturn (g = 3.7 N/kg) and
(c) Mars (g = 3.7 N/kg).
Solutions:
• W=mxg (b) W=mxg (c) W=mxg
= 80 x 9.8 = 80 x 9.0 = 80 x 3.7
= 784 N = 720 N = 296 N
Part
2

24. Work done
1. A man does 40000 J of work in moving a wheel barrow 50 m. 2. There is a frictional force of 1000 N acting on a car and the
What average force does he exert? resultant force is 4000 N.
If the car travels 3 km, what is the work done by the car's engine?
work done = force x distance engine force = 1000 + 4000 = 5000 N
force = work done / distance work done = force x distance
= 40000 / 50 = 5000 x 3000
= 80 N = 15000000 J
Part
2

25. Acceleration
1. A trolley takes 12 s to reach 6 m/s from rest. 2. A car decelerates at 1.5 m/s/s for 14 s from a initial speed of 27 m/s.
Calculate its acceleration. Calculate its final speed.
v=? u = 27 m/s a = -1.5 m/s/s t = 14s
a = (v - u) / t
v = u + at
= (6 - 0) / 12
= 27 + (-1.5 x 14)
= 0.5 m/s/s
= 6 m/s
3. The superhero, Beakman, accelerates at 5 m/s/s 4. A car travelling at 20 m/s decelerates at 4 m/s/s.
for 10 s to reach a final speed of 70 m/s. Calculate the time taken for the car to reach a complete stop.
Calculate Beakman's initial speed.
u = 20 m/s, a = -4 m/s/s, v = 0 m/s, t=?
a = 5 m/s/s, t = 10 s, v = 70 m/s, u=?
v = u + at
v = u + at
0 = 20 + (-4 x t)
70 = u + (5 x 10)
4t = 20
70 = u + 50
t=5s
u = 70 - 50 = 20 m/s
Part
1

26. A rocket has a mass of 10000 kg and sits on a launch pad.
• Calculate the rocket's weight on the Earth's surface. Note: g = 9.8 N/kg.
(b) During lift-off, the rocket's engine thrust is 200 kN. Calculate the rocket's unbalanced force.
(c) Calculate the rocket's initial acceleration during lift-off.
(d) An identical rocket, with the same mass and engine thrust takes off from Mars.
What effect does this have on the rocket's initial acceleration on Mars?
Justify your answer.
Solution:
(a) W=mxg
= 10000 x 9.8
= 98000 N
(b) unbalanced force = 200000 - 98000
= 102000 N
(c) acceleration = unbalanced force / mass ( a = F / m)
= 102000 / 10000
= 10.2 m/s/s
(d) * rocket's weight is smaller, since g on Mars is less than that on Earth
* rocket's unbalanced force increases
Part * acceleration is bigger
1

27. speed (m/s)
25
A car's speed-time graph is shown.
•Describe the car's motion from 0 to 30 s.
(b) Calculate the car's acceleration. 10
(c) Calculate how far the car travelled during the first 30 seconds of its journey.
0 30
time (s)
Solution:
• the car is accelerating from 10 m/s to 30 m/s, in 30 seconds
(b) a = (v - u) / t
= (25 - 10) / 30
= 0.5 m/s/s
(c) distance travelled = area between graph and time axis
= (10 x 30) + (0.5 x 30 x 15)
= 300 + 225
= 525 m
Part
1

28. Velocity and displacement calculation
A car starts from rest, at point S, and travels 240 m due North. It then travels 100 m due East and finishes at point F.
It took the car 25 s to travel from point S to point F.
(a) Calculate the car's displacement at point F relative to point S.
(b) Calculate the car's average velocity between points S and F.
Solution:
(a) Draw a triangle to show the car's motion from start (S) to finish (F).
There are two ways to solve this problem: scale drawing
OR Pythagoras' theorem and trigonometry.
If you use scale drawing and use a scale, for example, 1 cm represents 20 m.
You should find that the length between S and F is 12.5 cm, which represents 250 m.
Since displacement has a direction, then the position F relative to S is 23 degrees.
(b) average velocity = displacement / time
= 250 / 25
= 10 m/s at a bearing of (023)
Part
2

29. Projectiles and free fall.
E Click to show lines
of vertical
displacement
Click to show lines
of horizontal
displacement
Back to
dynamics

30. Vertical motion.
The ball is accelerating
downwards. The lines represent
Click to show lines
the position of the ball after each
of horizontal
second.
displacement
On Earth, all objects free fall. This
is because an object has a mass
and its weight is pulling that object Click to show
towards the ground. The simulation
acceleration due to gravity is 9.8
metres per second squared.
In vertical motion, the initial vertical velocity is 0 m/s. Final vertical velocity is worked out from
v = u + at.
where a = 9.8 m/s/s, u = 0 m/s, t is the time (during its fall) in seconds. Back to
dynamics

31. Horizontal motion.
Assuming that air resistance is negligible,
the horizontal distance travelled each
second is the same.
The ball's horizontal speed is constant.
horizontal distance = horizontal speed x time
Click to show
simulation
Back to
dynamics

32. The Universe:
The Universe:
Solar System: Our Sun, with all the planets,
Solar System: Our Sun, with all the planets,
moons and other objects orbiting around it. Light year (ly): Colour and wavelength:
Colour and wavelength:
moons and other objects orbiting around it. Light year (ly): White light is made up of aarange of colours, which
A galaxy contains billions of stars. Our galaxy The distance, travelled by light (in aavacuum),
The distance, travelled by light (in vacuum), White light is made up of range of colours, which
A galaxy contains billions of stars. Our galaxy can be separated by splitting the white light with aa
is called the Milky Way. in one year.
in one year. can be separated by splitting the white light with
is called the Milky Way. (e.g. Earth is 4.3 ly from Proxima Centauri, prism (to obtain aaspectrum).
A planet is aalarge ball of matter that orbits aa
A planet is large ball of matter that orbits (e.g. Earth is 4.3 ly from Proxima Centauri, prism (to obtain spectrum).
star. Planets do not give off light themselves, 100,000 ly from the edge of our galaxy and
100,000 ly from the edge of our galaxy and Colours of the spectrum (in order of decreasing
Colours of the spectrum (in order of decreasing
star. Planets do not give off light themselves, 2.6 million ly from Andromeda (M31). wavelength are: red, orange, yellow green, blue,
but they do reflect light from its central star.
but they do reflect light from its central star. 2.6 million ly from Andromeda (M31). wavelength are: red, orange, yellow green, blue,
An exoplanet is aaplanet orbiting around indigo and violet.
indigo and violet.
An exoplanet is planet orbiting around Red light has aawavelength of 700nm; violet light - -
another star. For life to exist on an exoplanet,
another star. For life to exist on an exoplanet, Light year Red light has wavelength of 700nm; violet light
the planet should have an atmosphere, liquid
Light year 400 nm.
400 nm.
the planet should have an atmosphere, liquid calculation
calculation
water, and ititis neither too hot or too cold.
water, and is neither too hot or too cold.
A moon is aanatural satellite, which orbits aa
A moon is natural satellite, which orbits
planet.
planet.
A star is aahot dense object, undergoing
A star is hot dense object, undergoing
nuclear fusion, and giving off light. ItItcontains
nuclear fusion, and giving off light. contains
around 90% hydrogen, 9% helium and other
around 90% hydrogen, 9% helium and other Line spectrum:
Line spectrum:
elements.
elements. This consists of aacontinuous spectrum with certain colours
This consists of continuous spectrum with certain colours
The Universe consists of many galaxies
The Universe consists of many galaxies missing which appear as black in the spectrum. Line
missing which appear as black in the spectrum. Line
separated by empty space. SPACE spectra analysis allows the elements present in aastar to
separated by empty space. spectra analysis allows the elements present in star to
be identified.
be identified.
Here is an example.
Here is an example.
Detectors of radiation:
Detectors of radiation:
Celestial objects, such as the stars and galaxies,
Celestial objects, such as the stars and galaxies,
give out energy over the whole range of the
give out energy over the whole range of the
electromagnetic spectrum. Different types of
electromagnetic spectrum. Different types of
telescopes are required to detect different types of
telescopes are required to detect different types of
Cosmic radiation:
Cosmic radiation:
e-m radiation. The Earth is bombarded
The Earth is bombarded
e-m radiation.
with sub-atomic
with sub-atomic Click: Space
* *Gamma rays - -Geiger Muller tube particles called cosmic
particles called cosmic Exploration
Gamma rays Geiger Muller tube
* *X-rays - -photographic film rays. Other types of
rays. Other types of
X-rays photographic film
* *Ultraviolet - -florescent paint particles bombard the
particles bombard the The age of the universe:
Ultraviolet florescent paint The age of the universe:
* *Visible light - -photographic film Earth: electrons,
Earth: electrons, This can be estimated by
Visible light photographic film This can be estimated by
* *Infrared - -blackened thermometer / /thermogram protons, helium nuclei,
protons, helium nuclei, measuring the average
Infrared blackened thermometer thermogram measuring the average
* *Microwaves - -diode probe antimatter and nuclei of
antimatter and nuclei of temperature of space. From
Microwaves diode probe temperature of space. From
* *TV and Radio - -aerial. heavy elements.
heavy elements. this measurement, the age of
TV and Radio aerial. this measurement, the age of
the Universe is 13.8 billion
the Universe is 13.8 billion
years.
years.
Menu
Menu

33. Calculations on the light year.
The distance from Earth to the nearest star, Proxima Centauri, is 4.3 light years
• Calculate the distance light would travel in one year.
distance = speed x time
= 300,000,000 x (365.25 x 24 x 60 x 60)
= 9.45 x 10^15 metres
(b) Calculate the distance between Earth and Proxima Centauri.
distance = 9.45 x 10^15 x 4.3
= 4.07 x 10^16 metres.
(c) Estimate the month and year in which light radiated on 15th May 2014, from Proxima Centauri, will be seen on Earth.
0.3 years = 0.3 x 12 = 4 months
So, 4.3 ly = 4 years and 4 months.
Month and year of observation - September 2018.
Back to space
Back to space

34. Kinetic energy: Conservation of energy (part 1):
Gravitational Potential energy:
This is known as moving energy. This is the work done in lifting a mass,
m, at a height, h, above the ground.
Generating electricity:
* Thermal power stations change
chemical energy of the fuel into
Click: Conservation electrical energy.
of energy * A nuclear power station changes
calculation the nuclear energy of the uranium
Click: Kinetic energy Click: Potential
fuel into electrical energy.
calculations energy calculations
* A hydroelectric power station
changes the gravitational potential
energy of water behind a dam into
electrical energy.
* A nuclear power station produces
radioactive waste.
Efficiency: ENERGY
The energy and power percentage efficiency is
expressed as:
Conservation of energy (part
Click: efficiency Power, energy and time: 2):
calculations Heat energy
power = energy / time Some of the heat energy supplied will
be lost to the surroundings This
means that the substance will take in
Changes of state: less energy than was supplied by the
Change in temperature:
There is no change temperature when a change of state occurs.
The specific heat capacity, of a substance, is heater.
the amount if energy (in joules) needed to
Latent heat of fusion:
change the temperature of 1 kg by 1 degree In most heat problems we can
The energy required to change 1 kg
Celsius. assume no energy is lost to the
from solid at its melting point to liquid surroundings.
without a change in temperature.
Click: Conservation
Latent heat of vaporisation: of energy
The energy required to change 1 kg calculation
of a liquid at its boiling point into 1 kg
Click: heat Click: latent heat
of vapour without a change in temperature.
energy energy
calculations calculations Menu

35. Kinetic energy
1. A 70 kg man on a 20 kg bicycle is moving at a steady speed 2. A toy car of mass 0.1 kg, rolls across the floor.
of 6 m/s when he applies the brakes and comes to rest in 4 Its kinetic energy is 0.45 J.
seconds.
Calculate the toy car's speed..
Calculate the kinetic energy of the man and his bicycle
before he brakes.
Energy

36. Potential energy
1. A ball has a mass of 0.5 kg and is raised 12 m above the 2. An object is raised 20 m above the ground and gains 980 J of
ground. Calculate the ball's gain in potential energy. gravitational potential energy.
Calculate the mass of the object.
Energy

37. Conservation of energy
A 5 kg ball is raised 10 m above the ground. It is then released and hits the ground.
(a) Calculate the potential energy at the top of the cliff.
(b) State the kinetic energy at the bottom of the cliff, assuming that there is no air resistance.
(c) Calculate the speed of the ball at the bottom of the cliff.
(d) Which piece of information given in the question is not required to find the speed?
Energy

38. Efficiency
1. A power station uses up to 300 MJ of chemical energy to produce 2. A power station is 35% efficient. If it produces 400 MJ of
180 MJ of electrical energy. Calculate the efficiency of the power electrical energy per second, calculate the input power to the
station. station.
Energy

39. Conservation of energy
An immersion heater takes 15 minutes to raise the temperature of 0.5 kg of water from 20C to 60C.
•Calculate the power rating of the heater.
(b) The heater is connected to a 12 V supply. Calculate the current in the element.
Energy

40. Latent heat
Calculate the energy required to change 2.6 kg of water at 100 degrees
Celsius into steam at the same temperature.
Calculate the energy required to change 2.6 kg of ice at 0 degrees
Celsius into water at the same temperature.
Energy

41. Changes in temperature
The mass of water is 0.2 kg and its starting temperature is 18 degrees Celsius.
Calculate the final temperature of water when it is suppled by 100000 J of heat energy.
Energy

42. Current: Series circuit rules:
The electric current is the rate of flow of charge. Part M enu
It is measured in amperes (A). * The current is the same at all points in a circuit 2
* The voltage across each component adds up to the supply voltage.
charge = current x time Q = It
charge, Q, in coulombs
current, I, in amperes Parallel circuit rules:
time, t, in seconds.
* The current in each branch adds up to the supply current.
* The voltage across each branch is equal to the supply voltage.
Voltage:
The voltage is the electrical energy given Resistors in series:
to each coulomb of charge. It is
measured in volts (V).
Resistance:
Resistance is a measure of opposition to current in a
circuit. It is measured in ohms. ELECTRICIT
Y: Part 1
resistance = voltage / current R =
V / I
resistance, R, in ohms
voltage, V, in volts
current, I in amperes
Resistors in parallel:
The above expression is known as Ohm's Law.
Power:
This is the energy transferred every
Potential divider: second. It is measured in watts (W).
A potential divider circuit consists of a number of resistors connected
across a supply. The bigger the resistance, the bigger the potential
difference across that resistor.

43. Power:
Earlier, power is defined as the rate at which Transmission lines:
energy is transferred. Transformers are used to reduce power loss in electrical
transmission.
This can be written as: This is done by operating the transmission lines at a high voltage.
Step-up transformers are used to increase the voltage from the power
power = energy / time P = E / t station. The transmission lines then carry electricity round the
M enu
country.. Step-down transformers are then used to reduce the voltage
power, P, is in watts (W) to suitable levels for industries and homes.
energy, E, is in joules (J)
time, t, is in seconds (s) To calculate the power loss, you use the formula:
Part
power loss = current x current x resistance P = I xI xR
1
More about resistance:
* The larger the resistance in a circuit, the smaller the
current in that circuit (provided the supply voltage is the a.c. and d.c.:
same).
* When a conductor heats up, the particles in that a.c. (alternating current) is when current passes
ELECTRICIT round the circuit, back and forth, many times per
conductor vibrate more and its electrical resistance
increases. Y: Part 2 second.
* The resistance of a lamp increases as the current in the The mains supplies a.c.
lamp increases. From that, you can only use Ohm's Law,
for any conductor, at a constant temperature. d.c. (direct current) is when current passes round
* For a resistor, at constant temperature, V/I = constant. the circuit in one direction only. Batteries and cells
* Connecting resistors in series INCREASES the total supply d.c.
resistance.
* Connecting resistors in parallel DECREASES the total The difference between d.c. and a.c. can be seen
resistance. by connecting the supplies to an oscilloscope.
Transistor:
A transistor acts like a switch. d.c.
There are two types of transistor: a.c.
Click: circuit problems npn-transistor and n-channel
enhancement MOSFET.
M ains frequency and voltage:
In the UK, the quoted mains supply is 230 V
and mains frequency is 50 Hz.
The peak value of an a.c. supply is greater
than the declared value (root mean square
value) Click: example

44. Circuit problem 1
A student draws up a circuit and assembles it. The ammeter displays a reading of 3 A.
•Is this a series or a parallel circuit?
(b) The potential difference (voltage) across the resistor, R, is 8 V.
State the voltage across the lamp.
(c) The lamp is fully operated at this voltage. Calculate the lamp's power rating.
(d) Calculate the resistance of the lamp, which operating at this voltage.
(e) The lamp was left on for 15 minutes. Calculate the electrical energy that was
transferred during that time.
----------------------------------------------------------------------------------------------------------------------
Solutions:
•series circuit (e) E = P x t
= 12 x (15 x 60)
(b) 4 V (12 - 8 = 4V) = 10800 W or 10.8 kW
(c) P = V x I
=4x3
= 12 W
(d) R = V / I
=4/3 Part
= 1.33 ohms 2
Click: circuit Click: circuit
problem 2 problem 3

45. Circuit problem 2
(a)Calculate the total resistance in this circuit.
(b) Calculate the current in the 20 ohm resistor.
(c) Calculate the potential difference (voltage) across the 10 ohm resistor.
Solutions:
Part
2
Click: circuit Click: circuit
problem 1 problem 3

46. Circuit problem 3
(a) Calculate the total resistance of the parallel network of resistors.
(b) Calculate the circuit's total resistance.
(c) Calculate the current reading, which should be displayed on the ammeter.
(d) Calculate the potential difference across the 10 ohm resistor.
Part
2
Click: circuit Click: circuit
problem 1 problem 2

47. A circuit diagram of an alarm system is shown.
• From the circuit diagram, Identify an output device.
(b) State the circuit symbol circled yellow.
(c) The device, circled yellow, switches on when the voltage at the
base is 0.7 V. A fixed resistor, R, has a resistance of 10 kilo-
ohms.
Calculate the resistance of the LDR when the potential difference
across it is 0.7 V.
(d) Explain how this alarm system operates..
Solutions:
Part
2