Q: If the radius of the Earth is $$6.371 \times 10^6$\ \mathrm{m}$$, what is the distance from the center of the Earth to a point $$100\ \mathrm{km}$$ above the surface?

$$6.471 \times 10^6$\ \mathrm{m}$$

Q: A $$1000\ \mathrm{kg}$$ satellite is in a circular orbit $$300\ \mathrm{km}$$ above Earth's surface. Given $$m_E = 5.972 \times 10$$^{24}$$\ \mathrm{kg}$$ and $$r_E = 6.371 \times 10^6$\ \mathrm{m}$$, what is the radius $$r of $$the orbit?

$$6.671 \times 10^6$\ \mathrm{m}$$

Question 1

Which of the following best explains why the acceleration due to gravity ($$g) at $$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 from a height of $$100\ \mathrm{km}$$ above Earth's surface. What is the correct formula to calculate the gravitational force acting on the boulder at this height?

Accepted Answer

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

Question 3

If the radius of the Earth is $$6.371 	imes 10^6$\ \mathrm{m}$$, what is the distance from the center of the Earth to a point $$100\ \mathrm{km}$$ above the surface?

Accepted Answer

$$6.471 	imes 10^6$\ \mathrm{m}$$

Question 4

Which of the following statements about gravitational fields is correct?

Accepted Answer

A gravitational field emanates from a single mass and gets stronger as you get closer to the source.

Question 5

Given the universal gravitation equation $$F_g = G \dfrac{m_1$ m_2$}{r^2$}$$, what happens to the force if the distance $$r$$ between the two masses is doubled?

Accepted Answer

The force becomes one-fourth as large.

Question 6

Which equation correctly gives the gravitational field $$g at a $$distance $$r$$ from a mass $$M$$?

Accepted Answer

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

Question 7

A satellite orbits Earth at a height where $$g is $$not $$9.8\ \mathrm{m/s^2$}. $$Which equation should be used to determine the satellite's orbital speed for a circular orbit?

Accepted Answer

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

Question 8

Why is the gravitational potential energy $$U_g = -\dfrac{G m_1$ m_2$}{r}$$ negative?

Accepted Answer

Because gravitational potential energy is defined to be zero at infinite separation, and objects must lose energy to come together.

Question 9

If an object moves from a distance $$r_1 to$$ $$r_2$$ from a planet, what is the change in gravitational potential energy?

Accepted Answer

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

Question 10

A $$1000\ \mathrm{kg}$$ satellite is in a circular orbit $$300\ \mathrm{km}$$ above Earth's surface. Given $$m_E = 5.972 	imes 10$$^{24}$$\ \mathrm{kg}$$ and $$r_E = 6.371 	imes 10^6$\ \mathrm{m}$$, what is the radius $$r of $$the orbit?

Accepted Answer

$$6.671 	imes 10^6$\ \mathrm{m}$$

Question 11

If the gravitational potential energy of a system increases from $$-200\ \mathrm{J} to$$ $$-100\ \mathrm{J}$$, what can be said about the object's position relative to the source mass?

Accepted Answer

The object has moved farther from the source mass.

Question 12

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 13

A $$5\ \mathrm{kg}$$ object is placed in the gravitational field of a $$10^{24}$$\ \mathrm{kg}$$ planet at a distance of 2$$ 	imes $$10^6$$\ \mathrm{m}$$ from the planet's center. What is the gravitational field strength g$ at this location?

Accepted Answer

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

Question 14

If Superman throws a boulder too slowly from $$100\ \mathrm{km}$$ above Earth's surface, what will happen to the boulder?

Accepted Answer

It will fall and hit the Earth, following a projectile path.

Question 15

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 objects, while a field emanates from a single object and can act on any other mass placed within it.

Question 16

Which of the following is NOT a correct use of the 'big G' universal gravitation equation?

Accepted Answer

Calculating the weight of an object on Earth's surface using $$g = 9.8\ \mathrm{m/s^2$}.$$

Question 17

A $$2\ \mathrm{kg}$$ mass is moved from $$r_1 = 4$$ 	imes $$10^6$$\ \mathrm{m}$$ to r_2$ = 8 	imes 10^6$\ \mathrm{m}$$ from the center of a planet of mass $$6 	imes 10$$^{24}$$\ \mathrm{kg}. $$What is the change in gravitational potential energy?

Accepted Answer

$$\Delta U_g = -G \dfrac{6 	imes 10$$^{24}$$ 	imes 2}{8 	imes 10^6$} + G \dfrac{6 	imes 10$$^{24}$$ 	imes 2}{4 	imes 10^6$}$$

Question 18

Which of the following best explains why gravitational potential energy is always discussed in terms of changes ($$\Delta U_g) $$rather than absolute values?

Accepted Answer

Because only differences in potential energy affect the motion and energy transformations of objects.

Question 19

A $$1000\ \mathrm{kg}$$ satellite is in a circular orbit at a radius $$r$$ from Earth's center. If the satellite's speed is suddenly increased, what will happen to its orbit?

Accepted Answer

It will move into a higher, more elliptical orbit or may escape Earth's gravity if the speed is high enough.

Universal Gravitation and Gravitational Potential Energy

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