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A.4 – Relativistic mechanics (HL only)
Description
Nature of science:
Paradigm shift: Einstein realized that the law of conservation of momentum could not be maintained as a law of physics. He therefore deduced that in order for momentum to be conserved under all conditions, the definition of momentum had to change and along with it the definitions of other mechanics quantities such as kinetic energy and total energy of a particle. This was a major paradigm shift. (2.3)
Understandings:
- Total energy and rest energy
- Relativistic momentum
- Particle acceleration
- Electric charge as an invariant quantity
- Photons
- MeV c –2 as the unit of mass and MeV c –1 as the unit of momentum
Applications and skills:
- Describing the laws of conservation of momentum and conservation of energy within special relativity
- Determining the potential difference necessary to accelerate a particle to a given speed or energy
- Solving problems involving relativistic energy and momentum conservation in collisions and particle decays
Guidance:
- Applications will involve relativistic decays such as calculating the wavelengths of photons in the decay of a moving pion
- The symbol m 0 refers to the invariant rest mass of a particle
- The concept of a relativistic mass that varies with speed will not be used
- Problems will be limited to one dimension
Data booklet reference:
Theory of knowledge:
- In what ways do laws in the natural sciences differ from laws in economics?
Utilization:
- The laws of relativistic mechanics are routinely used in order to manage the operation of nuclear power plants, particle accelerators and particle detectors
Aims:
- Aim 4: relativistic mechanics synthesizes knowledge on the behaviour of matter at speeds close to the speed of light
- Aim 9: the theory of relativity imposes one severe limitation: nothing can exceed the speed of light
Directly related questions
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17N.3.HL.TZ0.7b:
Determine, using your answer to (a), the initial speed of the particle.
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17N.3.HL.TZ0.7b:
Determine, using your answer to (a), the initial speed of the particle.
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17N.3.HL.TZ0.b:
Determine, using your answer to (a), the initial speed of the particle.
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18M.3.HL.TZ1.6b:
State the rest mass of the pion with an appropriate unit.
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18M.3.HL.TZ1.6b:
State the rest mass of the pion with an appropriate unit.
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18M.3.HL.TZ1.b:
State the rest mass of the pion with an appropriate unit.
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18M.3.HL.TZ2.6b.i:
Determine, in terms of MeV c–1, the momentum of the pion.
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18M.3.HL.TZ2.6b.i:
Determine, in terms of MeV c–1, the momentum of the pion.
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18M.3.HL.TZ2.b.i:
Determine, in terms of MeV c–1, the momentum of the pion.
- 18N.3.HL.TZ0.6b.i: Explain the origin of each equation.
- 18N.3.HL.TZ0.6b.i: Explain the origin of each equation.
- 18N.3.HL.TZ0.b.i: Explain the origin of each equation.
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18N.3.HL.TZ0.6a:
Show that the momentum of the electron is 1.41 MeV c–1.
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18N.3.HL.TZ0.6a:
Show that the momentum of the electron is 1.41 MeV c–1.
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18N.3.HL.TZ0.a:
Show that the momentum of the electron is 1.41 MeV c–1.
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19M.3.HL.TZ2.8biii:
Calculate the potential difference V.
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19M.3.HL.TZ2.8biii:
Calculate the potential difference V.
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19M.3.HL.TZ2.biii:
Calculate the potential difference V.
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19M.3.HL.TZ1.6b:
Calculate the speed of the pion.
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19M.3.HL.TZ1.6b:
Calculate the speed of the pion.
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19M.3.HL.TZ1.b:
Calculate the speed of the pion.
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19N.3.HL.TZ0.5a(i):
the total energy.
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19N.3.HL.TZ0.5a(i):
the total energy.
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19N.3.HL.TZ0.a(i):
the total energy.
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17N.3.HL.TZ0.7a:
Determine the rest mass of the particle.
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17N.3.HL.TZ0.7a:
Determine the rest mass of the particle.
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17N.3.HL.TZ0.a:
Determine the rest mass of the particle.
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18M.3.HL.TZ1.6a.ii:
show that the energy of the pion is about 140 MeV.
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18M.3.HL.TZ1.6a.ii:
show that the energy of the pion is about 140 MeV.
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18M.3.HL.TZ1.a.ii:
show that the energy of the pion is about 140 MeV.
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18M.3.HL.TZ2.6a:
Calculate the gamma (γ) factor for one of the protons.
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18M.3.HL.TZ2.6a:
Calculate the gamma (γ) factor for one of the protons.
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18M.3.HL.TZ2.a:
Calculate the gamma (γ) factor for one of the protons.
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18M.3.HL.TZ2.6b.ii:
The diagram shows the paths of the incident protons together with the proton and neutron created in the interaction. On the diagram, draw the path of the pion.
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18M.3.HL.TZ2.6b.ii:
The diagram shows the paths of the incident protons together with the proton and neutron created in the interaction. On the diagram, draw the path of the pion.
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18M.3.HL.TZ2.b.ii:
The diagram shows the paths of the incident protons together with the proton and neutron created in the interaction. On the diagram, draw the path of the pion.
- 18N.3.HL.TZ0.6b.ii: Calculate, in MeV c–1, p1 and p2.
- 18N.3.HL.TZ0.6b.ii: Calculate, in MeV c–1, p1 and p2.
- 18N.3.HL.TZ0.b.ii: Calculate, in MeV c–1, p1 and p2.
- 19M.3.HL.TZ2.8a: Define total energy.
- 19M.3.HL.TZ2.8a: Define total energy.
- 19M.3.HL.TZ2.a: Define total energy.
- 19M.3.HL.TZ2.8bi: Determine the momentum of the proton.
- 19M.3.HL.TZ2.8bi: Determine the momentum of the proton.
- 19M.3.HL.TZ2.bi: Determine the momentum of the proton.
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19M.3.HL.TZ2.8bii:
Determine the speed of the proton.
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19M.3.HL.TZ2.8bii:
Determine the speed of the proton.
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19M.3.HL.TZ2.bii:
Determine the speed of the proton.
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19M.3.HL.TZ1.6a:
Show that energy is conserved in this decay.
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19M.3.HL.TZ1.6a:
Show that energy is conserved in this decay.
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19M.3.HL.TZ1.a:
Show that energy is conserved in this decay.
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19N.3.HL.TZ0.5a(ii):
the speed.
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19N.3.HL.TZ0.5a(ii):
the speed.
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19N.3.HL.TZ0.a(ii):
the speed.
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19N.3.HL.TZ0.5b:
Determine the rest mass of X.
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19N.3.HL.TZ0.5b:
Determine the rest mass of X.
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19N.3.HL.TZ0.b:
Determine the rest mass of X.
- 20N.3.HL.TZ0.6a: Define rest mass.
- 20N.3.HL.TZ0.6a: Define rest mass.
- 20N.3.HL.TZ0.a: Define rest mass.
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20N.3.HL.TZ0.6b:
Calculate the total energy of the deuterium particle in .
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20N.3.HL.TZ0.6b:
Calculate the total energy of the deuterium particle in .
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20N.3.HL.TZ0.b:
Calculate the total energy of the deuterium particle in .
- 20N.3.HL.TZ0.6c: In relativistic reactions the mass of the products may be less than the mass of the reactants....
- 20N.3.HL.TZ0.6c: In relativistic reactions the mass of the products may be less than the mass of the reactants....
- 20N.3.HL.TZ0.c: In relativistic reactions the mass of the products may be less than the mass of the reactants....