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PHYSICS, M8 EQ-Bank 22

Einstein's equation `E = mc^(2)`  is one of the most important equations in the history of physics.

Justify this statement.   (7 marks)

--- 14 WORK AREA LINES (style=lined) ---

Show Answers Only

Position Statement

  • Einstein’s equation `E=mc^2` is among physics’ most important equations because it reveals mass-energy equivalence and explains fundamental processes from atomic to cosmic scales.

Nuclear Applications

  • The equation explains energy from nuclear fission and fusion processes. It shows how tiny amounts of matter convert to enormous energy in nuclear reactions.
  • The mass defect in atoms directly relates to binding energy through `E=mc^2` and this principle drives nuclear reactors that power cities and nuclear weapons.
  • These applications are responsible for revolutionising both energy production and global politics.

Cosmic and Particle Physics

  • Stars produce energy by converting mass to energy through fusion reactions. The Sun converts 4 million tonnes of mass to energy every second using this principle
  • Particle accelerators create new particles by converting kinetic energy into mass. This allows scientists to study fundamental matter structure and discover new particles.
  • Furthermore, mass dilation near light speed also follows from this mass-energy relationship.

Reinforcement

  • While other equations like Newton’s gravity law are important, they lack the broad applicability of `E=mc^2`.
  • No other single equation explains phenomena from subatomic particles to stellar processes.
  • The equation unified our understanding of matter and energy as different forms of the same thing.
  • This justifies calling `E=mc^2` one of history’s most important physics equations.
Show Worked Solution

Position Statement

  • Einstein’s equation `E=mc^2` is among physics’ most important equations because it reveals mass-energy equivalence and explains fundamental processes from atomic to cosmic scales.

Nuclear Applications

  • The equation explains energy from nuclear fission and fusion processes. It shows how tiny amounts of matter convert to enormous energy in nuclear reactions.
  • The mass defect in atoms directly relates to binding energy through `E=mc^2` and this principle drives nuclear reactors that power cities and nuclear weapons.
  • These applications are responsible for revolutionising both energy production and global politics.

Cosmic and Particle Physics

  • Stars produce energy by converting mass to energy through fusion reactions. The Sun converts 4 million tonnes of mass to energy every second using this principle
  • Particle accelerators create new particles by converting kinetic energy into mass. This allows scientists to study fundamental matter structure and discover new particles.
  • Furthermore, mass dilation near light speed also follows from this mass-energy relationship.

Reinforcement

  • While other equations like Newton’s gravity law are important, they lack the broad applicability of `E=mc^2`.
  • No other single equation explains phenomena from subatomic particles to stellar processes.
  • The equation unified our understanding of matter and energy as different forms of the same thing.
  • This justifies calling `E=mc^2` one of history’s most important physics equations.

Filed Under: Light and Special Relativity, Origins of Elements, Properties of the Nucleus Tagged With: Band 3, Band 4, Band 5, smc-3699-80-E = mc^2, smc-3700-60-Mass-Energy Equivalence, smc-3703-20-Conservation of Mass-Energy

PHYSICS, M7 2021 HSC 16 MC

The Sun has an energy output of `3.85 × 10^{28}\ `W.

By how much does the Sun's mass decrease each minute?

  1. `4.28 × 10^{11}` kg
  2. `2.57 × 10^{13}` kg
  3. `1.28 × 10^{20}` kg
  4. `7.70 × 10^{21}` kg
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`B`

Show Worked Solution

Energy released = `3.85 xx 10^(28) xx 60 = 2.31 xx 10^(30)\` J/min

`E` `=mc^2`  
`m` `=(E)/(c^(2))=(2.31 xx10^(30))/((3xx10^(8))^(2))=2.57 xx10^(13)\ \text{kg}`  

 
`=>B`


♦ Mean mark 45%.

Filed Under: Light and Special Relativity Tagged With: Band 5, smc-3699-80-E = mc^2

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