smc-3700-60-Mass-Energy Equivalence

PHYSICS, M8 2020 VCE 13 MC

Matter is converted to energy by nuclear fusion in stars.

If the star Alpha Centauri converts mass to energy at the rate of 6.6 × 10\(^9\) kg s\(^{-1}\), then the power generated is closest to

\(2.0 \times 10^{18}\ \text{W}\)
\(2.0 \times 10^{18}\ \text{J}\)
\(6.0 \times 10^{26}\ \text{W}\)
\(6.0 \times 10^{26}\ \text{J}\)

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\(C\)

Show Worked Solution

→ The energy produced by the star each second is the power generated by the star.

→ \(E=mc^2=6.6 \times 10^9 \times (3 \times 10^8)^2=6 \times 10^{26}\ \text{Js}^{-1}=6 \times 10^{26}\ \text{W}\)

\(\Rightarrow C\)

Mean mark 56%.

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)

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`E=mc^(2)` at its most basic level, expresses the concept that mass and energy are interchangeable.

Its importance is due to its critical role in explaining and analysing a broad range of ideas, processes and phenomena. These include:

→ The energy sourced from the processes of nuclear fission and fusion, including the energy associated with radioactive decay.

→ The relationship between the binding energy of atoms and their mass defect.

→ Mass dilation of objects approaching the speed of light.

→ The fundamental principles and technology upon which nuclear bombs and nuclear reactors operate.

→ Processes which source energy in stars through the conversion of mass into energy.

→ Processes which allow for particle accelerators to operate, allowing us to investigate into the fundamental structure and properties of matter.

Other equations, such as Newton’s Universal Law of Gravity, do not have the same myriad of applications in fields that make up our current understanding of physics.

It is therefore justified in being called one of the most important equations in the history of physics

Show Worked Solution

`E=mc^(2)` at its most basic level, expresses the concept that mass and energy are interchangeable.

Its importance is due to its critical role in explaining and analysing a broad range of ideas, processes and phenomena. These include:

→ The energy sourced from the processes of nuclear fission and fusion, including the energy associated with radioactive decay.

→ The relationship between the binding energy of atoms and their mass defect.

→ Mass dilation of objects approaching the speed of light.

→ The fundamental principles and technology upon which nuclear bombs and nuclear reactors operate.

→ Processes which source energy in stars through the conversion of mass into energy.

→ Processes which allow for particle accelerators to operate, allowing us to investigate into the fundamental structure and properties of matter.

Other equations, such as Newton’s Universal Law of Gravity, do not have the same myriad of applications in fields that make up our current understanding of physics.

It is therefore justified in being called one of the most important equations in the history of physics

PHYSICS, M8 2015 HSC 33d

The position of the Sun, star `W` and star `Z` are shown on the H-R diagram.

The curves `A` and `B` show intensity versus frequency for star `W` and the Sun, measured from the same distance.

Identify which curve (`A` or `B`) represents star `W` and justify your choice. (2 marks)

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Account for differences between stars `W` and `Z` that can be deduced from the H-R diagram. (3 marks)

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i. → Curve A represents star `W`.

→ `W` is hotter so will emit more energy overall, and peak frequency will be higher.

ii. Differences displayed in H-R graph:

→ Star `W` lies in the main sequence and is therefore fusing hydrogen to helium, most likely via CNO cycle as it is a large dense star.

→ Star `Z` is past main sequence and is therefore fusing larger elements.

→ Since star `Z` is cooler than `W` (refer to its H-R diagram location ) but has similar luminosity, we can deduce it is much larger than `W`.