Gravitation: Universal Law, Free Fall & Orbits: 20 flashcards
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1. State Newton's law of universal gravitation in words.
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Every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
2. Write the formula for Newton's law of gravitation.
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$$F = G\frac{m_1 m_2}{r^2}$$
3. What is the value of the universal gravitational constant $G$?
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$G = 6.67 \times 10^{-11}\ \text{N m}^2/\text{kg}^2$
4. What is the approximate value of $g$ at Earth's surface?
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$g \approx 9.8\ \text{m/s}^2$
5. How are $g$, $G$, $M$ and $R$ related?
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$$g = \frac{GM}{R^2}$$
6. What happens to the gravitational force if the distance between two masses is doubled?
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The force becomes one-quarter of its original value.
7. What happens to the gravitational force if one of the masses is tripled?
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The force triples.
8. Define mass and state its SI unit.
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Mass is the amount of matter in a body; its SI unit is the kilogram (kg). It is constant everywhere.
9. Define weight and state its SI unit.
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Weight is the gravitational force on a mass; its SI unit is the newton (N). It depends on $g$.
10. Why do astronauts float in an orbiting spacecraft?
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They and the spacecraft are in free fall together, so they experience apparent weightlessness — gravity is not zero.
11. What is orbital velocity for a low Earth orbit?
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About $7.9\ \text{km/s}$
12. What is escape velocity from Earth?
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About $11.2\ \text{km/s}$
13. State Kepler's third law.
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$T^2 \propto a^3$ — the square of the orbital period is proportional to the cube of the semi-major axis.
14. Why does the Moon not crash into Earth?
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It has enough sideways (tangential) velocity that as it falls toward Earth, it keeps missing — it is in orbit.
15. Distinguish $G$ and $g$.
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$G$ is the universal gravitational constant, same everywhere; $g$ is the local acceleration due to gravity, which varies with planet, altitude and latitude.
16. Why does a feather fall slower than a hammer on Earth but at the same rate on the Moon?
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On Earth, air resistance slows the feather; on the Moon there is no atmosphere, so both fall with the same acceleration due to gravity.
17. What causes tides on Earth?
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The difference in the Moon's gravitational pull across Earth's diameter — stronger on the near side, weaker on the far side.
18. Does gravity need a medium to act?
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No — gravity acts through vacuum; it does not require air or any medium.
19. How does $g$ change with altitude?
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$g$ decreases as altitude increases, because the distance from Earth's centre increases.
20. For a body on Earth's surface, from where is $r$ measured in Newton's law?
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From Earth's centre, not its surface.
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