1. Topic 4 Motion of particles
Unit P3: Applications of physics
Topic 4 Motion of particles
Student Notes

2. Unit P3: Applications of physics
W.A.L.T
We Are Learning To
Unit P3: Applications of physics
Topic 4
Motion of particles
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

3. 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.

4. Physics to help cure people
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.

5. Why?
CERN
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.

6. Unit P3: Applications of physics
W.A.L.T
We Are Learning To
Unit P3: Applications of physics
Topic 4
Motion of particles
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

7. 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

8. 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!
The velocity of a body is its speed in a given direction.

9. 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

10. 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

11. Pet scans Cost: £2,000,000 Cost: £2,000,000 PET scanner A cyclotron
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
PET Scan of Normal Brain

12. O F H + n F O β + 2. Radioactive Fluorine-18 is made Cyclotron9 H 1 + n
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.
Cyclotron F 18 9 O 8 β 1 +
A positron is a positively-charged electron
Fluorine-18 has a half-life of minutes.

13. Unit P3: Applications of physics
W.A.L.T
We Are Learning To
Unit P3: Applications of physics
Topic 4
Motion of particles
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)

14. Momentum = mass x velocityOn
Move p m v
Momentum = mass x velocity
p = mv
(kg m/s)
(kg)
(m/s)
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.

15. 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
In a perfectly elastic collision (first trolley stops) kinetic energy is conserved.

16. 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.

17. p = mv E.g.2 Explosion Before explosion After explosion p = mv
v = 1m/s
v = 0.5m/s
1kg
2kg
1kg
2kg
p = mv
p = 1 x 1
p = -1 kgm/s
p = mv
p = 1 kgm/s
p = 2 x 0.5
p = mv
p = 0 kgm/s
Total momentum = = 0 kgm/s

18. p = mv E.g.1 Inelastic collision After collision Before collision
(trolleys join)
2kg
v = ?m/s
Before collision
v = 2m/s
v = 0m/s
1kg
1kg
p = mv
p = 1 x 2
p = 2 kgm/s
p = mv
p = 1 x 0
p = 0 kgm/s
p = mv
2 = 2 x v
v = 1m/s
Total momentum = = 2 kgm/s

19. p = mv elastic collision Before collision After collision v = ? m/s
5kg
8kg
v = ? m/s
v = 3m/s
v = 6m/s
v = 0m/s
5kg
8kg
p = mv
6 = 5 x v
v = 1.2 m/s
p = mv
p = 24 kgm/s
p = 8 x 3
p = mv
p = 5 x 6
p = 30 kgm/s
p = mv
p = 8 x 0
p = 0 kgm/s
Total momentum
= = 30 kgm/s
= 6 kgm/s

20. Unit P3: Applications of physics
W.A.L.T
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

21. How PET Scanners work
1. Metabolically-active organs or tumors use glucose (sugar) at high rates

22. p O + F + n F O e + 2. Radioactive Fluorine-18 is made Cyclotron9
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.
Cyclotron F 18 9 O 8 e 1 +
A positron is a positively-charged electron
Fluorine-18 has a half-life of minutes.

23. Fluoro-Deoxy-D-Glucose (FDG)
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)

24. F O e + 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. F 18 9 O 8 e 1 +
A positron is a positively-charged electron
Fluorine-18 has a half-life of minutes.

25. 6. A PET scanner detects the gamma rays from electron-positron 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. e 1 + -1  2
electron
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.

26. Conservation of momentum - PET scansγ
positron e+, e, + or 
0 1
electron e-, e, - or 
0 -1 γ e 1 + -1  2
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 Total momentum = 0
After: left momentum = right momentum Total momentum = left - right = 0

27. Conservation of energy - PET scans1 + -1  2 . .
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
E=mc2
energy
mass of BOTH electron and positron, 2me
speed of light

28. Conservation of charge - PET scans1 + -1  2 . .
Charge before
Charge after
Electron = -1
Positron = +1
Overall = 0
gamma = 0
Overall = 0

29. Unit P3: Applications of physics
W.A.L.T
We Are Learning To
Unit P3: Applications of physics
Topic 4
Motion of particles
4.12 Investigate factors affecting the height of rebound of bouncing balls

30. A super ball is a toy that was invented in 1965 by Norman Stingley
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.

31. 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
In a perfectly elastic collision (first trolley stops) kinetic energy is conserved.

32. Investigate the factors affecting the height of rebound of bouncing balls