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Zwei fiktive Heliumkerne

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Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.

That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:

Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise

Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise

Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise

Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise

Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/zwei-fiktive-heliumkerne/

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The following quantities appear in the problem: Masse \(m\) / elektrische Ladung \(q, Q\) / Kraft \(F\) / Strecke \(s\) / Radius \(r\) /

The following formulas must be used to solve the exercise: \(F = \frac{1}{4\pi\epsilon_0}\cdot \frac{q_1q_2}{r^2} \quad \) \(F = G \dfrac{m_1m_2}{r^2} \quad \)

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Exercise:
Heliumkerne sind zweifach positiv geladen da Sie aus zwei Protonen und zwei Neutronen bestehen. Nehmen Sie an Sie könnten nun zwei Heliumkerne nehmen und diese beliebig schwerer machen. Wie gross müsste die Masse jedes fiktiven "Heliumkerns" sein um die Abstossung aufgrund ihrer gleichnamigen Ladung bei jedem beliebigen Abstand auszugleichen?

Solution:
Geg q e Q GesMasse eines fiktiven "Heliumkerns"msikg Hierbei müsste die Gravitationskraft die Coulombkraft ausgleichen: fracGm^r^ fracq^piepsilon_ r^ Gm^ fracq^piepsilon_ m sqrtfracq^piepsilon_ G sqrtfracQ^pincepsncG M m sqrtfracq^piepsilon_ G M

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Gravitationsgesetz und Coulomb-Kraft by TeXercises

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Branches	Electrostatics
Tags	coulomb, gravitation, physics, proton
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Difficulty	(2, default)
Points	5 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	aej
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