Q: A lion of mass $$175\ \mathrm{kg} is$$ $$3\ \mathrm{m}$$ away from a gazelle of mass $$40\ \mathrm{kg}. $$What is the magnitude of the gravitational force the lion exerts on the gazelle? (Use $$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N\,m^2$/kg^2$$}$)

$$1.56 \times 10$$^{-8}$$\ \mathrm{N}$$

Q: If the weight of the gazelle is $$392\ \mathrm{N}$$, how close would the lion need to be for the gravitational force between them to equal the gazelle's weight? ($$m_{lion} = 175\ \mathrm{kg}$$, $$m_{gazelle} = 40\ \mathrm{kg}$$, $$g = 9.8\ \mathrm{m/s^2$}$$, $$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N\,m^2$/kg^2$$}$)

$$3.45 \times 10$$^{-4}$$\ \mathrm{m}$$

Q: Given the mass of the Earth $$M_e = 5.98 \times 10$$^{24}$$\ \mathrm{kg}$$ and the universal gravitational constant $$G = 6.67 \times 10$$^{-11}$$\ \mathrm{N\,m^2$/kg^2$$}$$, what is the radius of a geosynchronous orbit? (Period T = 24$$\ \mathrm{h}$)

$$4.2 \times 10^7$\ \mathrm{m}$$

Question 1

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

Accepted Answer

The gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers: $$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 2

A lion of mass $$175\ \mathrm{kg} is$$ $$3\ \mathrm{m}$$ away from a gazelle of mass $$40\ \mathrm{kg}. $$What is the magnitude of the gravitational force the lion exerts on the gazelle? (Use $$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N\,m^2$/kg^2$$}$)

Accepted Answer

$$1.56 	imes 10$$^{-8}$$\ \mathrm{N}$$

Question 3

If the weight of the gazelle is $$392\ \mathrm{N}$$, how close would the lion need to be for the gravitational force between them to equal the gazelle's weight? ($$m_{lion} = 175\ \mathrm{kg}$$, $$m_{gazelle} = 40\ \mathrm{kg}$$, $$g = 9.8\ \mathrm{m/s^2$}$$, $$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N\,m^2$/kg^2$$}$)

Accepted Answer

$$3.45 	imes 10$$^{-4}$$\ \mathrm{m}$$

Question 4

Which of the following statements about geosynchronous satellites is correct?

Accepted Answer

A geosynchronous satellite orbits the Earth with a period equal to one sidereal day, remaining above the same point on the equator.

Question 5

Given the mass of the Earth $$M_e = 5.98 	imes 10$$^{24}$$\ \mathrm{kg}$$ and the universal gravitational constant $$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{N\,m^2$/kg^2$$}$$, what is the radius of a geosynchronous orbit? (Period T = 24$$\ \mathrm{h}$)

Accepted Answer

$$4.2 	imes 10^7$\ \mathrm{m}$$

Question 6

What is the tangential speed of a satellite in a circular orbit of radius $$r$$ around the Earth? ($$M_e is $$Earth's mass, $$G is $$the gravitational constant)

Accepted Answer

$$v = \sqrt{\frac{G M_e}{r}}$$

Question 7

According to Kepler's Third Law, the square of the period of a planet's orbit is proportional to:

Accepted Answer

The cube of the semi-major axis of its orbit: $$T^2$$ \propto $$a^3$$

Question 8

Mars’s orbit has a diameter 1.52 times that of Earth’s orbit. If Earth’s orbital period is 1 year, what is Mars’s orbital period?

Accepted Answer

$$1.87\ \mathrm{years}$$

Question 9

A person stands on a scale in an elevator accelerating upward at $$\frac{1}{2}g. If $$the person’s mass is $$m$$, what does the scale read?

Accepted Answer

$$\frac{3}{2}mg$$

Question 10

Which of the following best describes the direction of the gravitational force between two objects?

Accepted Answer

The force is always attractive and directed along the line joining the centers of the two objects.

Question 11

If the distance between two objects is doubled, how does the gravitational force between them change?

Accepted Answer

It becomes one-fourth as large.

Question 12

Which experiment is historically associated with the measurement of the universal gravitational constant $$G$$?

Accepted Answer

Cavendish experiment using a torsion balance

Question 13

A satellite is in a circular orbit around Earth. If its speed is less than the required orbital speed for its altitude, what will happen to its orbit?

Accepted Answer

It will move into an elliptical orbit with the perigee at its current position.

Question 14

Which of the following is NOT a statement of Kepler’s Laws of Planetary Motion?

Accepted Answer

The force between a planet and the Sun is inversely proportional to the square of the distance between them.

Question 15

If the mass of the Earth were doubled, but its radius remained the same, what would happen to the acceleration due to gravity at the surface?

Accepted Answer

It would double.

Question 16

Which of the following best explains why astronauts in the International Space Station appear weightless?

Accepted Answer

They are in continuous free fall around the Earth, experiencing apparent weightlessness.

Question 17

A planet orbits the Sun in an ellipse. According to Kepler’s Second Law, when is the planet moving fastest?

Accepted Answer

When it is closest to the Sun (at perihelion).

Gravitation and Planetary Motion: Study Notes for PHYS 120

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