- Understand that for a point outside a uniform sphere, its mass may be treated as concentrated at its centre
- Recall and apply Newton’s law of gravitation (F = G dfrac{m_1 m_2}{r^2}) for two point masses
- Sketch and interpret force vs distance relationships for point masses
- Calculate gravitational forces and discuss the inverse-square nature of gravity
- Use terms “uniform sphere,” “point mass,” “centre of mass,” “inverse-square law” correctly
- Explain gravitational interactions clearly in academic English
- Interpret and describe formulae and graphs using precise terminology
- Discuss proportionality and dependency on distance in speaking and writing
| English Term | Russian | Kazakh |
|---|---|---|
| Point mass | Точечная масса | Нүктелік масса |
| Uniform sphere | Однородная сфера | Теңмасса сфера |
| Centre of sphere | Центр сферы | Сфера орталығы |
| Gravitational constant (G) | Гравитационная постоянная | Гравитациялық тұрақты |
| Inverse-square law | Закон обратных квадратов | Квадраттық кері заң |
| Gravitational force | Сила гравитации | Гравитациялық күш |
Point Mass
Definition: An object whose dimensions are negligible compared to distances involved
Use: Simplifies gravitational calculations
Uniform Sphere
Definition: Sphere with constant density throughout
Key Fact: External gravity behaves as if mass concentrated at centre
Inverse-Square Law
Definition: Physical quantity varies as (1/r^2) with distance
Example: Gravitational force decreases with square of separation
Newton’s Law
Formula: (F = G dfrac{m_1 m_2}{r^2})
Role: Calculates force between two masses
Point mass
An idealized object with all its mass concentrated at a single point for ease of calculation.
Russian: Идеализация, при которой вся масса сосредоточена в одной точке.Kazakh: Барлық масса бір нүктеге шоғырланған идеализация.
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Uniform sphere
A sphere of constant density; gravitational field outside equals that of a point mass at its centre.
Russian: Сфера с постоянной плотностью; поле вне такой сферы аналогично полю точечной массы.Kazakh: Тұрақты тығыздықты сфера; оның сыртындағы өріс нүктелік массаға ұқсас.
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Mass of Uniform Sphere as Point Mass
For any point outside a , the gravitational effect is identical to that of a located at the with the same total mass.
Newton’s Law of Gravitation
The magnitude of the force between two point masses (m_1) and (m_2) separated by distance (r) is:
(F = G dfrac{m_1 m_2}{r2}),
where (G) is the gravitational constant.
Fill in the Blanks
- A uniform sphere’s gravity acts as if mass is at its _______.
- Newton’s law: (F = G dfrac{m_1 m_2}{r^______}).
- Gravitational force varies inversely with the _______ of distance.
- (G) is called the gravitational _______.
Additional Video Resources:
• Newton’s Law of Gravitation Explained
• Gravity & Inverse-Square Law
Example 1: Point Mass Approximation
A uniform sphere of mass 2×103 kg and radius 0.5 m. Calculate gravitational force on a 1 kg mass 2 m from centre.
Example 2: Inverse-Square Effect
Two 5 kg masses separated by 0.1 m. Find (F) (use (G=6.67times10^{-11})).
Explore gravity between point masses:
Using an online quiz (e.g. Quizizz), challenge peers to calculate gravitational forces for given scenarios.
Solve these structured questions:
- Show why external field of uniform sphere equals that of point mass at centre.
- Calculate force between Earth (6×1024 kg) and 70 kg person at surface (R=6.4×106 m).
- Derive dependence of weight on altitude using inverse-square law.
- Compare gravitational force inside vs outside a uniform sphere.
- Critically evaluate errors if density is not uniform.
- Which assumption (point mass) simplifies gravitational calculations most?
- How does changing (r) affect (F)? Explain with examples.
- What practical limitations arise from non-uniform density?
- How can you apply Newton’s law in astrophysical contexts?