Q: Given two people, one with mass $$m_1 = 60$$\ \mathrm{kg}$$ and another with mass m_2$ = 70\ \mathrm{kg}$$, sitting $$r = 0.5\ \mathrm{m}$$ apart, what is the magnitude of the gravitational force between them? Use $$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2.$$

$$F = 1.12 \times 10$$^{-8}$$\ \mathrm{N}$$

Q: What is the value of the universal gravitational constant $$G$$?

$$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2$$

Question 1

Which of the following best describes Newton's Law of Universal Gravitation?

Accepted Answer

Every object in the Universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Question 2

Given two people, one with mass $$m_1 = 60$$\ \mathrm{kg}$$ and another with mass m_2$ = 70\ \mathrm{kg}$$, sitting $$r = 0.5\ \mathrm{m}$$ apart, what is the magnitude of the gravitational force between them? Use $$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2.$$

Accepted Answer

$$F = 1.12 	imes 10$$^{-8}$$\ \mathrm{N}$$

Question 3

Which statement about the gravitational force between the Earth and the Moon is correct?

Accepted Answer

The Earth and the Moon exert equal and opposite gravitational forces on each other.

Question 4

What is the value of the universal gravitational constant $$G$$?

Accepted Answer

$$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N}\cdot\mathrm{m}^2/\mathrm{kg}^2$$

Question 5

A satellite orbits the Earth at a height where the radius from the Earth's center is $$r = 2R_E$$, with $$R_E = 6.38 	imes 10^6$\ \mathrm{m}. If $$the mass of the Earth is $$M_E = 5.98 	imes 10$$^{24}$$\ \mathrm{kg}$$, what is the acceleration due to gravity at this altitude?

Accepted Answer

$$g = 2.45\ \mathrm{m}/\mathrm{s}^2$$

Question 6

Which of the following is true about the escape speed from Earth?

Accepted Answer

It is independent of the mass of the object trying to escape.

Question 7

A geosynchronous satellite orbits the Earth such that its period matches the Earth's rotation period. Which location must it be above?

Accepted Answer

A point above the Earth's equator

Question 8

Kepler's First Law states that planets move in:

Accepted Answer

Elliptical orbits with the Sun at one focus

Question 9

According to Kepler's Second Law, a planet moves fastest when:

Accepted Answer

It is closest to the Sun (perihelion)

Question 10

Kepler's Third Law relates the period $$T of a $$planet's orbit to the semi-major axis $$a by $$which equation?

Accepted Answer

$$T^2 = K$$ $$a^3$$

Question 11

If the acceleration due to gravity at the Earth's surface is $$g = 9.81\ \mathrm{m}/\mathrm{s}^2$$, what is the acceleration due to gravity at the top of Mt. Everest ($$h = 8.85 	imes 10^3$\ \mathrm{m}$$ above sea level)? Assume $$R_E = 6.38 	imes 10^6$\ \mathrm{m}.$$

Accepted Answer

$$g \approx 9.77\ \mathrm{m}/\mathrm{s}^2$$

Question 12

Which of the following is NOT a fundamental force recognized by modern physics?

Accepted Answer

Friction

Question 13

The principle of equivalence states that:

Accepted Answer

Gravitational mass and inertial mass are the same.

Question 14

What is the gravitational field $$g at a $$distance $$r$$ from a mass $$M$$?

Accepted Answer

$$g = \dfrac{GM}{r^2$}$$

Question 15

Which experiment first measured the universal gravitational constant $$G$$?

Accepted Answer

Cavendish's torsion balance experiment

Question 16

A black hole is formed when:

Accepted Answer

The gravitational field is strong enough that light cannot escape.

Question 17

Which of the following best explains why astronauts in orbit experience 'weightlessness'?

Accepted Answer

They are in free fall, so there is no normal force acting on them.

Question 18

If the Earth's radius is $$R_E$$ and its mass is $$M_E$$, what is the formula for the acceleration due to gravity at the surface?

Accepted Answer

$$g = \dfrac{GM_E}{R_E^2$}$$

Question 19

Which of the following is a consequence of the inverse-square law of gravitation?

Accepted Answer

Doubling the distance between two masses reduces the gravitational force by a factor of four.

Question 20

Which orbital parameter determines how much an orbit deviates from a perfect circle?

Accepted Answer

Eccentricity

Gravitation and Newton's Synthesis: Study Notes

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