Q: A $$1000\ \mathrm{kg}$$ satellite is in a circular orbit $$300\ \mathrm{km}$$ above Earth's surface. Given Earth's mass $$M_E = 5.972 \times 10$$^{24}$$\ \mathrm{kg}$$ and radius $$R_E = 6.371 \times 10^6$\ \mathrm{m}$$, what is the gravitational force acting on the satellite?

$$F_g = G \dfrac{M_E m_{sat}}{(R_E + 3.00 \times 10^5$)^2$$}$

Q: A $$5\ \mathrm{kg}$$ object is placed $$2\ \mathrm{m}$$ from a $$10\ \mathrm{kg}$$ object. What is the magnitude of the gravitational force between them? ($$G = 6.67 \times 10$$^{-11}$$\ \mathrm{Nm^2$/kg^2$$}$)

$$F_g = 6.67 \times 10$$^{-11}$$ \dfrac{5 \times 10}{2^2$}$$

Question 1

Which of the following best explains why the gravitational acceleration $$g at $$the surface of the Moon is less than $$9.8\ \mathrm{m/s^2$}$$?

Accepted Answer

The Moon has a smaller mass and radius compared to Earth, resulting in a weaker gravitational field at its surface.

Question 2

A $$2520\ \mathrm{kg}$$ boulder is thrown by Superman from $$100\ \mathrm{km}$$ above Earth's surface. What is the correct formula to calculate the weight of the boulder at that height?

Accepted Answer

$$F_g = G \dfrac{m_{E} m_{b}}{r^2$}$$, where $$r is $$the distance from Earth's center to the boulder.

Question 3

If the gravitational potential energy $$U_g$$ between two objects is given by $$U_g = -G \dfrac{m_1$ m_2$}{r}$$, what does the negative sign indicate?

Accepted Answer

The gravitational force is always attractive, and energy must be supplied to separate the objects to infinity.

Question 4

Which of the following statements about gravitational fields is correct?

Accepted Answer

Every object with mass produces a gravitational field that gets stronger as you get closer to the object.

Question 5

A satellite orbits Earth at a distance $$r$$ from Earth's center. Which equation gives the gravitational field $$g at $$that location?

Accepted Answer

$$g = G \dfrac{M_E}{r^2$}$$

Question 6

Superman wants to throw a boulder so that it orbits Earth at $$100\ \mathrm{km}$$ above the surface. Which equation should he use to find the required tangential velocity $$v_T$$ for a stable circular orbit?

Accepted Answer

$$v_T = \sqrt{\dfrac{G M_E}{r}}$$

Question 7

If an object is moved from a distance $$r_1 to$$ $$r_2$$ from the center of a planet, what is the change in gravitational potential energy $$\Delta U_g$$?

Accepted Answer

$$\Delta U_g = -G \dfrac{M m}{r_2$} + G \dfrac{M m}{r_1$}$$

Question 8

Why must the 'big G' universal gravitation equation be used instead of $$F = mg$$ when calculating the gravitational force on an object far from Earth's surface?

Accepted Answer

Because $$g is $$only approximately constant near Earth's surface and decreases with distance.

Question 9

A $$1000\ \mathrm{kg}$$ satellite is in a circular orbit $$300\ \mathrm{km}$$ above Earth's surface. Given Earth's mass $$M_E = 5.972 	imes 10$$^{24}$$\ \mathrm{kg}$$ and radius $$R_E = 6.371 	imes 10^6$\ \mathrm{m}$$, what is the gravitational force acting on the satellite?

Accepted Answer

$$F_g = G \dfrac{M_E m_{sat}}{(R_E + 3.00 	imes 10^5$)^2$$}$

Question 10

If the gravitational potential energy $$U_g of a $$system is zero when the two objects are infinitely far apart, what happens to $$U_g as $$the objects move closer together?

Accepted Answer

$$U_g$$ becomes more negative.

Question 11

A $$5\ \mathrm{kg}$$ object is placed $$2\ \mathrm{m}$$ from a $$10\ \mathrm{kg}$$ object. What is the magnitude of the gravitational force between them? ($$G = 6.67 	imes 10$$^{-11}$$\ \mathrm{Nm^2$/kg^2$$}$)

Accepted Answer

$$F_g = 6.67 	imes 10$$^{-11}$$ \dfrac{5 	imes 10}{2^2$}$$

Question 12

Which of the following best describes the difference between a force and a field in the context of gravity?

Accepted Answer

A force requires two interacting objects, while a field emanates from a single object and can exert a force on another object placed within it.

Question 13

If an object is lifted from the surface of Earth to a height where $$r is $$doubled (measured from Earth's center), how does the gravitational field $$g at $$that height compare to its value at the surface?

Accepted Answer

$$g is $$one-fourth its value at the surface.

Question 14

A $$1\ \mathrm{kg}$$ mass is placed in the gravitational field of a $$2 	imes 10$$^{24}$$\ \mathrm{kg}$$ planet at a distance of $$4 	imes 10^6$\ \mathrm{m}$$ from the planet's center. What is the gravitational field $$g at $$that location?

Accepted Answer

$$g = G \dfrac{2 	imes 10$$^{24}$$}{(4 	imes 10^6$)^2$$}$

Question 15

Which of the following is true about the gravitational force between two objects?

Accepted Answer

It is always attractive and acts along the line joining the centers of mass of the two objects.

Question 16

A $$1000\ \mathrm{kg}$$ satellite is moved from a distance of $$7 	imes 10^6$\ \mathrm{m} to$$ $$8 	imes 10^6$\ \mathrm{m}$$ from Earth's center. What is the change in gravitational potential energy?

Accepted Answer

$$\Delta U_g = -G \dfrac{M_E m}{8 	imes 10^6$} + G \dfrac{M_E m}{7 	imes 10^6$}$$

Question 17

If the mass of one object is doubled and the distance between two objects is also doubled, how does the gravitational force between them change?

Accepted Answer

It becomes half as large.

Question 18

Which of the following best describes the relationship between gravitational potential energy and kinetic energy for a falling object near Earth?

Accepted Answer

As the object falls, its gravitational potential energy decreases (becomes more negative) and is transformed into kinetic energy.

Universal Gravitation and Gravitational Potential Energy

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