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Unit P3: Applications of physics
Topic 4 Motion of particles
Student Notes
Unit P3: Applications of physics
Topic 4
Motion of particles
We Are Learning To
4.1 Discuss how instruments, including particle accelerators, can
help scientists develop better explanations about the physical
world
4.2 Discuss reasons for collaborative, international research into
big scientific questions, including particle physics
CERN is the European Organisation for Nuclear Research
Conseil Européen pour la Recherche Nucléaire (French)
The biggest experiment in history,
CERN’s Large Hadron Collider
(LHC), began operating in 2007.
$7 billion investment
Costs the UK taxpayer
£34 million per year
Half the world’s particle physicists, from 80 nations, are collaborating to
analyse the results.
The four collision sites to detect particles are ATLAS, ALICE, CMS and LHC-B.
Sir Tim Berners-Lee
Sir Tim Berners-Lee invented the World Wide
Web in 1990 to help CERN particle physicists
communicate via computers on a global scale.
Physics to help cure people
Particle beams for radiation therapy in hospitals
Ugo Amaldi was well known as a particle physicist at
CERN when he decided to work towards promoting the
creation in Europe of a network of centres for cancer
therapy using beams of ions, in particular carbon ions.
CERN
Why?
CERN is the European Organisation for Nuclear Research, the world’s largest particle physics
centre. At CERN, physicists build large machines to study high-energy particles. Sometimes the
machines they make can be used by people in different ways.
The World Wide Web was invented by physicists at CERN to communicate with one another from all
over the world about projects at CERN. But now many people use the Web to gather information about
many things, and to communicate with one another.
Detectors and accelerators were used at CERN to study the properties of colliding high-speed particles.
But hospitals can use detectors and accelerators to see inside people in order to diagnose illnesses,
and also to treat illnesses by killing tumours without surgery. CERN employs just under 3000
people – physicists, engineers, technicians, craftsmen, administrators, secretaries and workmen.
Some 6500 visiting scientists, half of the world’s particle physicists, come to CERN for their
research. They represent 500 universities and over 80 nationalities. Using proton–proton collisions
inside the Large Hadron Collider (LHC), particle physicists aim to answer the questions:
l What are the elementary constituents of matter?
l What are the forces that control their behaviour at the most basic level?
The LHC can reconstruct the enormous energies that existed just after the Big Bang. Studying its
particle collisions is like ‘looking back in time’, recreating the environment present at the origin of our
universe. By accelerating and smashing particles together, physicists can identify their components or
create new particles, revealing the nature of the interactions between them. What for? To understand
the formation of stars, earth, trees, everything you see around – and, finally, us.
Unit P3: Applications of physics
Topic 4
Motion of particles
We Are Learning To
4.3 Explain how for motion in a circle there must be a resultant
force known as a centripetal force that acts towards the centre of
the circle
4.4 Explain how particle accelerators called cyclotrons cause
charged particles to move in a circular or spiral path, due to a
magnetic field
Centripetal Force
If something is moving in a circle, its velocity is changing, even if its
speed is constant. This is because it is changing direction. If the velocity
is changing the object must be accelerating. We know from Newton’s 2nd
Law (F=ma) of motion that an object will accelerate when there is a
resultant force. The law goes on to state that the object will accelerate in
the direction of the resultant force.
.
We call the force that
keeps things moving in
a circle a centripetal
force. A centripetal
force can be provided
in a number of ways
Acceleration (m/s2) =
change in velocity (m/s)
time taken for change (s)
velocity
Important:
An object moving in a circular
motion is changing its direction and
hence its velocity is changing. It is
therefore accelerating even though
its speed is staying the same!
velocity
velocity
The velocity of a body is its speed in a given direction.
Cyclotrons are particle
accelerators in which
moving charged
particles are bent into
circular paths.
A constant magnetic field applied at right angles to the particle’s
motion produces the centripetal force required
two ‘D-shaped’
A voltage across a gap between two ‘D-shaped’ magnetic field
regions accelerates the charged particles. The path of the
particles spirals outwards as their speed increases. On leaving the
magnetic field, the particles travel in a straight line towards a
specific target. In the LHC, this target is another particle beam
Pet scans
Cost: £2,000,000
Cost: £2,000,000
PET scanner
A cyclotron
PET Scan of
Normal Brain
If a high energy proton is allowed to collide with a
stable element, the nucleus of this element can be
changed into an unstable nucleus of a different
element. This is a radioactive isotope. Small
cyclotrons are now used in hospitals to produce
the short lived isotopes needed in PET scanners
2. Radioactive Fluorine-18 is made
18
8
Cyclotron
1
O + 1H
9
1
F + 0n
In a cyclotron, accelerated
protons are used to bombard
stable Oxygen-18 atoms to
produce the positron-emitting
radioisotope Fluorine-18
used in PET scanning.
18
9
Fluorine-18 has a
half-life of 109.8 minutes.
18
F
18
8
0
O + 1β
A positron is a positively-charged electron
Unit P3: Applications of physics
Topic 4
Motion of particles
We Are Learning To
4.7 Demonstrate an understanding that for inelastic collisions momentum is conserved
but kinetic energy is not conserved
4.8 Demonstrate an understanding that for elastic collisions both momentum and kinetic
energy are conserved
4.9 Analyse collisions in one dimension in terms of momentum and kinetic energy
4.10 Carry out calculations using momentum conservation for a two-body
collision (in one dimension only)
4.11 Carry out calculations using conservation of kinetic energy for a two-body
elastic collision (in one dimension only)
Momentum
Mass
On
Move
p
m
v
Momentum = mass x velocity
(kg m/s)
(kg)
(m/s)
p = mv
Momentum can be defined as "mass in motion.“ The amount of momentum
which an object has is dependent upon two variables: how much stuff is moving
and how fast the stuff is moving. Momentum depends upon the variables mass
and velocity.
Momentum is a vector quantity. It has size and direction.
Colliding objects have kinetic energy and
momentum.
Momentum is conserved in all explosions and collisions.
In a completely inelastic collision (objects join) kinetic energy is
not conserved
Inelastic collision
Before collision
After collision (trolleys join)
In a perfectly elastic collision (first trolley stops) kinetic energy
is conserved.
elastic collision
Before collision
After collision (trolleys do not join)
Conservation of momentum
As long as no external
forces are acting on the
objects involved, the
total momentum stays
the same in explosions
and collisions. We say
that momentum is
conserved. You can
use this idea to work out
the mass, velocity or
momentum of an object
in an explosion or
collision.
p = mv
Explosion
Before explosion
E.g.2
After explosion
v = 1m/s
1kg
2kg
1kg
v = 0.5m/s
2kg
p = mv
p = mv
p = mv
p = 0 kgm/s
p=1x1
p = 2 x 0.5
p = -1 kgm/s
p = 1 kgm/s
Total momentum = -1 + 1 = 0 kgm/s
Inelastic collision
p = mv
Before collision
v = 2m/s
v = 0m/s
E.g.1
After collision
(trolleys join)
v = ?m/s
2kg
1kg
p = mv
p=1x2
p = 2 kgm/s
1kg
p = mv
p=1x0
p = 0 kgm/s
Total momentum = 2 + 0 = 2 kgm/s
p = mv
2=2xv
v = 1m/s
elastic collision
p = mv
Before collision
After collision
v = 6m/s
v = 0m/s
v = ? m/s
v = 3m/s
5kg
8kg
5kg
8kg
p = mv
p=5x6
p = 30 kgm/s
p = mv
p = mv
p = mv
6=5xv
p=8x3
p=8x0
p = 0 kgm/s v = 1.2 m/s p = 24 kgm/s
Total momentum
= 30 + 0 = 30 kgm/s
30 - 24 = 6 kgm/s
Unit P3: Applications of physics
Topic 4
Motion of particles
We Are Learning To
4.5 Demonstrate an understanding that certain stable elements can be bombarded with
proton radiation to change them into radioactive isotopes
4.6 Describe the use of particle accelerators (cyclotrons) to produce radioactive isotopes
for medical purposes
4.13 Recall that gamma rays can be produced by the annihilation of an electron and a
positron
4.14 Apply conservation of momentum and charge to positron electron annihilation
4.15 Apply the idea of conservation of mass energy for positron electron annihilation
a in a qualitative way (calculations involving E = mc2 will not be required)
b in a quantitive way using the equation E = mc2
4.16 Explain the use of radio isotopes in PET scanners to produce gamma rays
How PET Scanners work
1. Metabolically-active organs or tumors
use glucose (sugar) at high rates
2. Radioactive Fluorine-18 is made
18
1
18
p
O
+
8
1
Cyclotron
F + 0n
In a cyclotron, accelerated
protons are used to bombard
stable Oxygen-18 atoms to
produce the positron-emitting
radioisotope Fluorine-18
used in PET scanning.
18
9
Fluorine-18 has a
half-life of 109.8 minutes.
9
1
F
18
8
0
O + 1e
A positron is a positively-charged electron
3. Fluoro-Deoxy-D-Glucose (FDG) is produced
The radioisotope Fluorine-18 is then
attached to glucose molecules to make
a radioactive ‘tagged’/’labelled’ sugar
called FDG.
Fluoro-Deoxy-D-Glucose
(FDG)
4. The radioactive tracer FDG
is injected into the patient
5. Metabolically-active organs or tumors
use lots of sugar. As the ‘tagged’ sugars
starts to decay, they emit positrons.
18
9
Fluorine-18 has a
half-life of 109.8 minutes.
F
18
8
0
O + 1e
A positron is a positively-charged electron
6. A PET scanner detects the
gamma rays from electronpositron annihilation
A positron collides with an electron from
the patient’s body and they annihilate.
Two gamma rays are produced, travelling
in opposite directions at the speed of light.
0
electron
-1
0
e + 1e
2 0
0
positron
gamma ray
The gamma rays are detected by the PET
scanner. A computer converts
their location into an image of
where they were produced. PET
scans show metabolic ‘hot spots’
- often rapidly-growing tumors.
Conservation of momentum - PET scans
positron
e+, 01e, + or 01
electron
e-, -10e, - or-10 
0
-1
0
e + 1e
γ
2 0
0
γ
The positron is attracted to an electron, due to their opposite charges.
When they collide annihilation takes place and two gamma rays
are released travelling at the speed of light at 180° to each other.
Why two gamma rays? Because momentum is always conserved.
Before: Particles not moving After: left momentum = right momentum
Total momentum = 0
Total momentum = left - right = 0
Conservation of energy - PET scans
0
-1
0
e + 1e
2 0
0
Energy is also conserved.
But where does the light
energy of the two gamma
rays come from?
…From the mass of the electron and the positron
The energy is given by Einstein’s famous
equation
2 speed of light
energy
.
.
E=mc
mass of BOTH electron and positron, 2me
Conservation of charge - PET scans
e + 1e
2 0
Charge
before
Charge
after
0
-1
0
0
Electron
= -1
gamma
=0
Positron
= +1
gamma
=0
Overall
=0
Overall
=0
.
.
Unit P3: Applications of physics
Topic 4
Motion of particles
We Are Learning To
4.12 Investigate factors affecting the height of rebound of
bouncing balls
A super ball is a toy that was invented in 1965 by Norman
Stingley. Its extreme springiness ensured that when dropped it
bounced back to more or less the same height it was dropped
from and when thrown down against the ground it could leap over
a three storey building!
When a ball is dropped onto the ground it undergoes an inelastic
collision. This means some kinetic energy of the ball is
transferred to the surroundings (as heat and sound). The ball
does not rebound to the same height since kinetic energy has
been transferred.
Colliding objects have kinetic energy and
momentum.
Momentum is conserved in all explosions and collisions.
In a completely inelastic collision (objects join) kinetic energy is
not conserved
Inelastic collision
Before collision
After collision (trolleys join)
In a perfectly elastic collision (first trolley stops) kinetic energy
is conserved.
elastic collision
Before collision
After collision (trolleys do not join)
Investigate the factors affecting the
height of rebound of bouncing balls