Chapter 6 SUMMARY Unit 2

Key Expectations

• analyze the factors affecting the motion of isolated

celestial objects and calculate the gravitational poten-

tial energy for each system (6.1, 6.2, 6.3)

• analyze isolated planetary and satellite motion, and

describe the motion in terms of the forms of energy and

energy transformations that occur (e.g., calculate the

energy required to propel a spacecraft from Earth’s sur-

face out of Earth’s gravitational field, and describe the

energy transformations that take place; calculate the

kinetic energy and gravitational potential energy of a

satellite in a stable orbit around a planet) (6.1, 6.2, 6.3)

Key Termsgravitational field

Kepler’s laws of planetary motion

escape speed

escape energy

binding energy

black hole

event horizon

singularity

Schwartzschild radius

Key Equations

• g 5 }G

r

M2} (6.1)

• v 5 !}G

r

M}§ (6.2)

• CS 5 }T

r 3

2} for the Sun (6.2)

• CS 5 }G

4

M

p2S

} for the Sun (6.2)

• C 5 }G

4p

M2

} 5 }T

r 3

2} in general (6.2)

• Eg 5 2}GM

r

m} (6.3)

• DEg 5 12}GMr2

m}2212}

GMr1

m}2 (6.3)

• v 5 !}2GrM}§ escape speed (6.3)

MAKE a summary

Draw an Earth-Moon system diagram. Add a geosynchro-

nous satellite (Figure 1) on the side of Earth opposite the

Moon. Beyond the geosynchronous satellite, add a space

probe, moving away from Earth, that has just enough energy

to escape Earth’s gravitational attraction. Show as many key

expectations, key terms, and key equations as possible on

your diagram.

Figure 1

Gravitation and Celestial Mechanics 297NEL

298 Chapter 6

Chapter 6 SELF QUIZ

Write numbers 1 to 10 in your notebook. Indicate beside

each number whether the corresponding statement is true

(T) or false (F). If it is false, write a corrected version.

1. At a particular location, the gravitational field around

a celestial body depends only on the mass of the body.

2. If both the radius and mass of a planet were to

double, the magnitude of the gravitational field

strength at its surface would become half as great.

3. The speed of a satellite in a stable circular orbit

around Earth is independent of the mass of the

satellite.

4. In the Sun’s frame of reference, the Moon’s orbit

around Earth appears as an epicycle.

5. In a typical high-school physics investigation, the

“Evidence” is to the “Analysis” as Kepler’s work was to

Tycho Brahe’s work.

6. In Figure 1, where the path distances d1 and d2 are

equal, the speeds along those path segments are equal.

7. When calculating Kepler’s third-law constant for

Earth, the value is larger for the Moon than for an

Earth-bound satellite because the Moon is much far-

ther away.

8. The gravitational potential energy of the Earth-Moon

system is inversely proportional to the square of the

distance between the centres of the two bodies.

9. As a space probe travels away from Earth, its change

in gravitational potential energy is positive, even

though its gravitational potential energy is negative.

10. As you are working on this problem, your escape

energy is greater than your binding energy.

Write numbers 11 to 26 in your notebook. Beside each

number, write the letter corresponding to the best choice.

For questions 11 to 19, refer to Figure 2.

11. The y-variable is the magnitude of the gravitational

field strength at a point above a planet’s surface; x is

the planet’s mass.

12. The y-variable is the magnitude of the gravitational

field strength at a point above a planet’s surface; x is

the distance to the centre of the planet.

13. The y-variable is the speed of a satellite in a stable cir-

cular orbit around a planet; x is the mass of the planet.

14. The y-variable is the speed of a satellite in a stable

circular orbit around a planet; x is the distance to the

centre of the planet.

15. The y-variable is the area swept out by a line joining a

planet to the Sun; x is the time interval during which

that line is swept out.

16. The y-variable is the average radius of a planet’s orbit;

x is the period of revolution of the planet’s motion

around the Sun.

Sun

direction of

motion of planet

d 2

d1

Figure 1

(a)

y

x

y

x

y

x

(b) (c)

(d) (e)

y

x

y

x

Figure 2

The first variable named in each of questions 11 to 19 corresponds

to the y-variable on one of these graphs; the second variable

named corresponds to the x-variable.

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Gravitation and Celestial Mechanics 299

Unit 2

17. The y-variable is the cube of the average radius of a

planet’s orbit; x is the square of the period of revolu-

tion of the planet’s motion around the Sun.

18. The y-variable is the kinetic energy of a space probe

that was given enough energy to escape Earth’s gravi-

tational field; x is the distance from Earth’s centre.

19. The y-variable is the gravitational potential energy of

a space probe that was given enough energy to escape

Earth’s gravitational field; x is the distance from

Earth’s centre.

20. The law that allows us to determine Earth’s mass is

(a) Kepler’s first law of planetary motion

(b) Kepler’s second law of planetary motion

(c) Kepler’s third law of planetary motion

(d) Newton’s law of universal gravitation

(e) Newton’s second law of motion

21. If the distance between a spacecraft and Saturn

increases by a factor of three, the magnitude of

Saturn’s gravitational field strength at the position of

the spacecraft

(a) decreases by a factor of Ï3w(b) increases by a factor of Ï3w(c) decreases by a factor of 9

(d) increases by a factor of 9

(e) decreases by a factor of 3

22. Satellite S1 is moving around Earth in a circular orbit

of radius four times as large as the radius of the orbit

of satellite S2. The speed of S1, v1, in terms of v2 equals

(a) 16v2

(b) v2

(c) 2v2

(d) 0.5v2

(e) none of these

23. If the mass of the Sun were to become half its current

value, with Earth maintaining its same orbit, the time

interval of one Earth year would

(a) remain the same

(b) decrease by a factor of Ï2w(c) increase by a factor of Ï2w(d) increase by a factor of 2

(e) decrease by a factor of 2

24. A satellite in geosynchronous orbit has a period of

revolution of

(a) 1.5 h

(b) 1.0 h

(c) 24 h

(d) 365.26 d

(e) none of these

25. Figure 3 shows the path of a comet around the Sun.

The speeds at the four positions shown are vA, vB, vC,

and vD. Which statement is true?

(a) vA > vB 5 vD > vC

(b) vA < vB 5 vD < vC

(c) vA > vB > vC > vD

(d) vA < vB < vC < vD

(e) none of these

26. A certain planet has Earth’s mass, but only one-

quarter its diameter. The escape speed from this

planet in terms of Earth’s escape speed vE is

(a) vE

(b) }

1

2}vE

(c) }

1

4}vE

(d) 4vE

(e) 2vE

Sun

comet’s

directionD

A C

B

Figure 3

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Chapter 6 REVIEW

300 Chapter 6 NEL

Understanding Concepts 1. If a rocket is given a great enough speed to escape

from Earth, could it also escape from the Sun and,

hence, the solar system? What happens to the artificial

Earth satellites that are sent to explore the space

around distant planets, such as Neptune?

2. Assuming that a rocket is aimed above the horizon,

does it matter which way it is aimed for it to escape

from Earth? (Neglect air resistance.)

3. Determine the elevation in kilometres above the sur-

face of Uranus where the gravitational field strength

has a magnitude of 1.0 N/kg.

4. Ganymede, one of Jupiter’s moons discovered by

Galileo in 1610, has a mass of 1.48 3 1023 kg. What is

the magnitude of Ganymede’s gravitational field

strength at a point in space 5.55 3 103 km from its

centre?

5. Determine the total gravitational field strength (mag-

nitude and direction) of the Earth and Moon at the

location of the spacecraft in Figure 1.

6. Mercury has both a surface gravitational field

strength and a diameter 0.38 times the corresponding

Earth values. Determine Mercury’s mass.

7. A satellite in a circular orbit around Earth has a

speed of 7.15 3 103 m/s. Determine, in terms of

Earth’s radius,

(a) the distance the satellite is from Earth’s centre

(b) the altitude of the satellite

8. Tethys, one of Saturn’s moons, travels in a circular

orbit at a speed of 1.1 3 104 m/s. Calculate

(a) the orbital radius in kilometres

(b) the orbital period in Earth days

9. Using the mass of the Sun and the period of revolution

of Venus around the Sun, determine the average Sun-

Venus distance.

10. A 4.60-kg rocket is launched directly upward from

Earth at 9.00 km/s.

(a) What altitude above Earth’s surface does the

rocket reach?

(b) What is the rocket’s binding energy at that

altitude?

11. Titan, a moon of Saturn discovered by Christian

Huygens in 1655, has a mass of 1.35 3 1023 kg and a

radius of 2.58 3 103 km. For a 2.34 3 103-kg rocket,

determine

(a) the escape speed from Titan’s surface

(b) the escape energy of the rocket

12. A rocket ship of mass 1.00 3 104 kg is located

1.00 3 1010 m from Earth’s centre.

(a) Determine its gravitational potential energy at

this point, considering only Earth.

(b) How much kinetic energy must it have at this

location to be capable of escaping from Earth’s

gravitational field?

(c) What is its escape speed from Earth at this

position?

13. Calculate the gravitational potential energy of the

Sun-Earth system.

14. Determine the escape speeds from

(a) Mercury

(b) Earth’s Moon

15. A neutron star results from the death of a star about

10 times as massive as the Sun. Composed of tightly

packed neutrons, it is small and extremely dense.

(a) Determine the escape speed from a neutron star

of diameter 17 km and mass 3.4 3 1030 kg.

(b) Express your answer as a percentage of the speed

of light.

16. A solar-system planet has a diameter of 5.06 3 104 km

and an escape speed of 24 km/s.

(a) Determine the mass of the planet.

(b) Name the planet.

17. A proton of mass 1.67 3 10227 kg is travelling away

from the Sun. At a point in space 1.4 3 109 m from

the Sun’s centre, the proton’s speed is 3.5 3 105 m/s.

(a) Determine the proton’s speed when it is 2.8 3

109 m from the Sun’s centre.

(b) Will the proton escape from the Sun? Explain

why or why not.

18. Explain this statement: “A black hole is blacker than a

piece of black paper.”

19. Determine the Schwartzschild radius of a black hole

equal to the mass of the entire Milky Way galaxy

(1.1 3 1011 times the mass of the Sun).

3.07 × 105 km

EarthMoon

90.0˚

spacecraft

2.30 × 105 km

Figure 1

Gravitation and Celestial Mechanics 301NEL

Unit 2

Applying Inquiry Skills 20. Table 1 provides data concerning some of the moons

of Uranus.

(a) Copy the table into your notebook. Determine

Kepler’s third-law constant CU for Uranus using

the data for the first four moons.

(b) Find the average of the CU values of your

calculations in (a).

(c) Use another method to determine CU. Do the

values agree?

(d) Complete the missing information for the last

four moons listed.

(e) Explain why some of the moons were discovered

so much earlier than others.

21. It is beneficial to develop skill in analyzing a situation to

determine if the given information or the answer to a

question makes sense. Consider the following problem:

Determine the radius of the orbit of a satellite travelling

around Earth with a period of revolution of 65 min.

(a) Do you think this problem makes sense? Why or

why not?

(b) Calculate a numerical answer to the problem.

(c) Does the numerical answer make sense? Why or

why not?

(d) Why would this skill be valuable to a research

physicist?

22. Figure 2 shows the energy relationships for a rocket

launched from Earth’s surface.

(a) Determine the rocket’s mass.

(b) What is the escape energy of the rocket (to three

significant digits)?

(c) Determine the launch speed given to the rocket.

(d) What will the rocket’s speed be at a very large

distance from Earth.

Making Connections 23. When the Apollo 13 spacecraft was about halfway to

the Moon, it developed problems in the oxygen system.

Rather than turning the craft around and returning

directly to Earth, mission control decided that the craft

should proceed to the Moon before returning to Earth.

(a) Explain the physics principles involved in this

decision.

(b) Describe at least one major risk of this decision.

Extension 24. Two remote planets consist of identical material, but

one has a radius twice as large as the other. If the short-

est possible period for a low-altitude satellite orbiting

the smaller planet is 40 min, what is the shortest pos-

sible period for a similar low-altitude satellite orbiting

the larger one? Give your answer in minutes.

25. A certain double star consists of two identical stars, each

of mass 3.0 3 1030 kg, separated by a distance of 2.0 3

1011 m between their centres. How long does it take to

complete one cycle? Give your answer in seconds.

26. We owe our lives to the energy reaching us from the

Sun. At a particular planet, the solar energy flux E

(the amount of energy from the Sun arriving per

square metre per second) depends on the distance

from the Sun to the planet. If T is the period of that

planet in its journey around the Sun, that is, the

length of its year, calculate how E depends on T.

Table 1 Data of Several Moons of the Planet Uranus for

Question 20

Moon Discovery raverage T (Earth CU

(km) days) (m3/s2)

Ophelia Voyager 2 (1986) 5.38 3 104 0.375 ?

Desdemona Voyager 2 (1986) 6.27 3 104 0.475 ?

Juliet Voyager 2 (1986) 6.44 3 104 0.492 ?

Portia Voyager 2 (1986) 6.61 3 104 0.512 ?

Rosalind Voyager 2 (1986) 6.99 3 104 ? ?

Belinda Voyager 2 (1986) ? 0.621 ?

Titania Herschel (1787) 4.36 3 105 ? ?

Oberon Herschel (1787) ? 13.46 ?

12

8

−8

−6

E (

310

10 J

)

−10

10

−12

−4

−2

0

2

4

6

2rE 3rE 4rE 5rErE

kinetic energy

gravitational

potential energy

Separation Distance

Figure 2

Sir Isaac Newton Contest Question

Sir Isaac Newton Contest Question

Sir Isaac Newton Contest Question

Chapter 7 SUMMARY

376 Chapter 7 NEL

Key Expectations

• state Coulomb’s law and Newton’s law of universal

gravitation, and analyze and compare them in qualita-

tive terms (7.2)

• apply Coulomb’s law and Newton’s law of universal

gravitation quantitatively in specific contexts (7.2)

• define and describe the concepts and units related to

electric and gravitational fields (e.g., electric and grav-

itational potential energy, electric field, gravitational

field strength) (7.2, 7.3, 7.4, 7.5, 7.6)

• determine the net force on, and the resulting motion

of, objects and charged particles by collecting, ana-

lyzing, and interpreting quantitative data from experi-

ments or computer simulations involving electric and

gravitational fields (e.g., calculate the charge on an

electron, using experimentally collected data; conduct

an experiment to verify Coulomb’s law and analyze

discrepancies between theoretical and empirical

values) (7.2, 7.5, 7.6)

• describe and explain, in qualitative terms, the electric

field that exists inside and on the surface of a charged

conductor (e.g., inside and around a coaxial cable)

(7.3)

• explain how the concept of a field developed into a

general scientific model, and describe how it affected

scientific thinking (e.g., explain how field theory

helped scientists understand, on a macro scale, the

motion of celestial bodies and, on a micro scale, the

motion of particles in electric fields) (7.3)

• analyze and explain the properties of electric fields and

demonstrate how an understanding of these properties

can be applied to control or alter the electric field

around a conductor (e.g., demonstrate how shielding

on electronic equipment or on connecting conductors

[coaxial cables] affects electric fields) (7.3)

• analyze in quantitative terms, and illustrate using field

and vector diagrams, the electric field and the electric

forces produced by a single point charge, two point

charges, and two oppositely charged parallel plates

(e.g., analyze, using vector diagrams, the electric force

required to balance the gravitational force on an oil

drop or on latex spheres between parallel plates)

(7.3, 7.5)

• compare the properties of electric and gravitational

fields by describing and illustrating the source and

direction of the field in each case (7.3, 7.6)

• apply quantitatively the concept of electric potential

energy in a variety of contexts, and compare the char-

acteristics of electric potential energy with those of

gravitational potential energy (7.4, 7.6)

Key Termsinduced charge separation

law of conservation of charge

Coulomb’s law

coulomb

field theory

field of force

electric field

electric potential

electric potential difference

electric potential energy

Key Equations

• FE 5 }

kq

r

12

q2} (7.2)

• k 5 9.0 3 109 N?m2/C2 Coulomb’s law (7.2)

• « 5 }

k

r

q

2

1} (7.3)

• EE 5 }

kq

r

1q2} (7.4)

• V 5 }

kq

r

1} (7.4)

• ∆E 5 q∆V for charged plates « 5 }∆rV} (7.4)

• e 5 1.602 3 10219 C elementary charge (7.5)

• q 5 Ne (7.5)

MAKE a summary

There are many different concepts and equations in this

chapter that are closely related to each other. List all the

equations in this chapter and show how they are related.

Identify which quantities in your equations are vectors,

which of your equations apply to point charges, and which

equations apply to parallel plates. Give an application for

each equation, and discuss any principles or laws from other

chapters that are related to them.

Chapter 7 SELF QUIZ

Electric Charges and Electric Fields 377NEL

Write numbers 1 to 6 in your notebook. Indicate beside

each number whether the corresponding statement is true

(T) or false (F). If it is false, write a corrected version.

1. If a charge q exerts a force of attraction of magnitude

F on a charge –2q, then the charge –2q exerts a force

of attraction of magnitude 2F on the charge q.

2. The only difference between electric and gravitational

forces is that the electric force is larger.

3. The electric field at the surface of a conductor in

static equilibrium is perpendicular to the surface of

the conductor.

4. Electric field lines indicate the path that charged par-

ticles will follow near another charged object.

5. It is safe to stay in your car during a lightning storm

because the tires act as insulators.

6. The acceleration experienced by two small charges as

they start from rest and move apart is inversely pro-

portional to the square of the distance between them.

Write numbers 7 to 13 in your notebook. Beside each

number, write the letter corresponding to the best choice.

7. When comparing the force of attraction between an

electron and a proton due to the electric force and

gravity, it can be concluded that

(a) the gravitational force is a lot stronger

(b) the electric force is a lot stronger

(c) the two types of forces are the same

(d) they cannot be compared

(e) the electric force is slightly stronger

8. The electric force on each of two small charged

spheres due to the other sphere has a magnitude of F.

The charge on one sphere is doubled, and the distance

between the centres of the spheres is tripled. The mag-

nitude of the force on each small charged sphere is

(a) 2F (c) }

2

3

F} (e) }

2

9

F}

(b) }

F

3} (d) }

F

9}

9. The magnitude of the electric field due to a small

charged object is 12 N/C at a distance of 3.0 m from

the charge. The field 6.0 m away from the charge is

(a) 36 N/C (c) 6.0 N/C (e) 3.0 N/C

(b) 12 N/C (d) 4.0 N/C

10. Which diagram in Figure 1 represents the net electric

field between two charged parallel plates if a neutral

conducting sphere is placed between the plates?

(a) (b) (c) (d) (e) none of these

Unit 3

11. A neutral charged conductor is placed near a posi-

tively charged object. The electric field inside the

neutral conductor is

(a) perpendicular to the surface

(b) zero

(c) directed toward the negative charge

(d) stronger than the electric field at the surface of

the conductor

(e) none of these

12. A mass has a charge on it. Another small mass with a

positive charge is moved away from the first mass,

which remains at rest. As the distance increases, what

happens to the gravitational potential energy Eg and

the electric potential energy EE?

(a) Eg decreases and EE decreases

(b) EE either decreases or increases, depending on the

unknown sign of charge, and Eg decreases

(c) Eg decreases and EE increases

(d) EE decreases or increases, depending on the

unknown sign of charge, and Eg increases

(e) Eg increases and EE decreases

13. Two isolated electrons starting from rest move apart.

Which of the following statements is true as the dis-

tance between the electrons increases?

(a) The velocity increases and the acceleration is

constant.

(b) The velocity increases and the acceleration

decreases.

(c) The velocity decreases and the acceleration is

constant.

(d) The velocity increases and the acceleration

increases.

(e) The velocity is constant and the acceleration is

constant.

+ + + + + + + +

− − − − − − − − − − − − − − −

− − − − − − − −

+ + + + + + + ++ + + + + + +

(a)

+ + + + + +

− − − − − −

(b)

+ + + + + +

− − − − − −

(c) (d)

Figure 1

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Chapter 7 REVIEW

378 Chapter 7 NEL

Understanding Concepts1. One of the children in Figure 1 is touching an elec-

trostatic generator.

(a) Why does the hair of the child touching the elec-

trostatic generator stand on end?

(b) Why does the hair of the other child likewise

stand on end?

(c) Are the children grounded? Explain your answer.

2. In a chart, compare similarities and differences

between Newton’s law of universal gravitation and

Coulomb’s law.

3. Coulomb’s law may be used to calculate the force

between charges only under certain conditions. State

the conditions, and explain why they are imposed.

4. Two small, oppositely charged conducting spheres

experience a mutual electric force of attraction of

magnitude 1.6 3 1022 N. What does this magnitude

become if each sphere is touched with its identical,

neutral mate, the initially neutral spheres are taken

far away, and the separation of the two initially

charged spheres is doubled?

5. What is the distance between two protons experi-

encing a mutually repelling force of magnitude

4.0 3 10–11 N?

6. One model of the structure of the hydrogen atom

consists of a stationary proton with an electron

moving in a circular path around it. The orbital path

has a radius of 5.3 3 10211 m. The masses of a

proton and an electron are 1.67 3 10227 kg and

9.1 3 10231 kg, respectively.

(a) Calculate the electrostatic force between the elec-

tron and the proton.

(b) Calculate the gravitational force between them.

(c) Which force is mainly responsible for the elec-

tron’s circular motion?

(d) Calculate the speed and period of the electron in

its orbit around the proton.

7. Two point charges, +4.0 3 1025 C and –1.8 3 1025 C,

are placed 24 cm apart. What is the force on a third

small charge, of magnitude –2.5 3 1026 C, if it is

placed on the line joining the other two,

(a) 12 cm outside the originally given pair of

charges, on the side of the negative charge?

(b) 12 cm outside the originally given pair of

charges, on the side of the positive charge?

(c) midway between the originally given pair of

charges?

8. Explain why we use a “small” test charge to detect and

measure an electric field.

9. If a stationary charged test particle is free to move in

an electric field, in what direction will it begin to

travel?

10. Why is it safer to stay inside an automobile during a

lightning storm? (Hint: It is not due to the insulating

rubber tires.)

11. Three small, negatively charged spheres are located at

the vertices of an equilateral triangle. The magnitudes

of the charges are equal. Sketch the electric field in

the region around this charge distribution, including

the space inside the triangle.

12. A small test charge of +1.0 mC experiences an electric

force of 6.0 3 1026 N to the right.

(a) What is the electric field strength at that point?

(b) What force would be exerted on a charge of

–7.2 3 1024 C located at the same point, in place

of the test charge?

13. What are the magnitude and direction of the electric

field strength 1.5 m to the right of a positive point

charge of magnitude 8.0 3 1023 C?

14. What are the magnitude and direction of the electric

field strength at point Z in Figure 2?

Figure 1

Two children holding hands; one is touching an electro-

static generator.

q1 = 22.0 3 10–5 C q2 = 8.0 3 10–6 C

X Y Z

+−

60.0 cm30.0 cm

Figure 2

Electric Charges and Electric Fields 379NEL

15. A ping-pong ball of mass 3.0 3 1024 kg hangs from a

light thread 1.0 m long, between two vertical parallel

plates 10.0 cm apart (Figure 3). When the potential

difference across the plates is 420 V, the ball comes

to equilibrium 1.0 cm to one side of its original

position.

(a) Calculate the electric field strength between the

plates.

(b) Calculate the tension in the thread.

(c) Calculate the magnitude of the electric force

deflecting the ball.

(d) Calculate the charge on the ball.

16. If two points have the same electric potential, is it

true that no work is required to move a test charge

from one point to the other? Does that mean that no

force is required, as well?

17. How much work is required to move a charged par-

ticle through an electric field if it moves along a path

that is always perpendicular to an electric field line?

How would the potential change along such a path?

18. A charge of 1.2 3 1023 C is fixed at each corner of a

rectangle 30.0 cm wide and 40.0 cm long. What are

the magnitude and direction of the electric force on

each charge? What are the electric field and the elec-

tric potential at the centre?

19. Calculate the electric potential 0.50 m from a

4.5 3 1024 C point charge.

20. A 1.0 3 1026 C test charge is 40.0 cm from a

3.2 3 1023 C charged sphere. How much work was

required to move it there from a point 1.0 3 102 cm

away from the sphere?

21. How much kinetic energy is gained by an electron

that is allowed to move freely through a potential dif-

ference of 2.5 3 104 V?

Unit 3

22. How much work must be done to bring two protons,

an infinite distance apart, to within 1.0 3 10215 m of

each other, a distance comparable to the width of an

atomic nucleus? (The work required, while small, is

enormous in relation to the typical kinetic energies of

particles in a school lab. This shows why particle

accelerators are needed.)

23. What is the magnitude of the electric field between

two large parallel plates 2.0 cm apart if a potential

difference of 450 V is maintained between them?

24. What potential difference between two parallel plates,

at a separation of 8.0 cm, will produce an electric

field strength of magnitude 2.5 3 103 N/C?

25. Most experiments in atomic physics are performed in

a vacuum. Discuss the appropriateness of performing

the Millikan oil drop experiment in a vacuum.

26. Assume that a single, isolated electron is fixed at

ground level. How far above it, vertically, would

another electron have to be so that its mass would be

supported against gravitation by the force of electro-

static repulsion between them?

27. An oil droplet of mass 2.6 3 10215 kg, suspended

between two parallel plates 0.50 cm apart, remains

stationary when the potential difference between the

plates is 270 V. What is the charge on the oil droplet?

How many excess or deficit electrons does it have?

28. A metallic table tennis ball of mass 0.10 g has a charge

of 5.0 3 1026 C. What potential difference, across a

large parallel plate apparatus of separation 25 cm,

would be required to keep the ball stationary?

29. Calculate the electric potential and the magnitude of

the electric field at a point 0.40 m from a small sphere

with an excess of 1.0 31012 electrons.

30. An electron is released from rest at the negative plate

in a parallel plate apparatus kept under vacuum and

maintained at a potential difference of 5.0 3 102 V.

With what speed does the electron collide with the

positive plate?

31. What potential difference would accelerate a helium

nucleus from rest to a kinetic energy of 1.9 3 10215 J?

(For a helium nucleus, q = +2e.)

32. An electron with a speed of 5.0 3 106 m/s is injected

into a parallel plate apparatus, in a vacuum, through

a hole in the positive plate. The electron collides with

the negative plate at 1.0 3 106 m/s. What is the

potential difference between the plates?

1.0 cm

10.0 cm

1.0 m

Figure 3

380 Chapter 7 NEL

33. Four parallel plates are connected in a vacuum as in

Figure 4. An electron, essentially at rest, drifts into

the hole in plate X and is accelerated to the right. The

vertical motion of the electron continues to be negli-

gible. The electron passes through holes W and Y,

then continues moving toward plate Z. Using the

information given in the diagram, calculate

(a) the speed of the electron at hole W

(b) the distance from plate Z to the point at which

the electron changes direction

(c) the speed of the electron when it arrives back at

plate X

34. Two a particles, separated by an enormous distance,

approach each other. Each has an initial speed of

3.0 3 106 m/s. Calculate their minimum separation,

assuming no deflection from their original path.

35. An electron enters a parallel plate apparatus 10.0 cm

long and 2.0 cm wide, moving horizontally at

8.0 3 107 m/s, as in Figure 5. The potential difference

between the plates is 6.0 3 102 V. Calculate

(a) the vertical deflection of the electron from its

original path

(b) the velocity with which the electron leaves the

parallel plate apparatus

Applying Inquiry Skills36. A versorium is a device that detects the presence of an

electric charge on an object. The device consists of any

convenient material (e.g., a straw or a long strip of

folded paper) balanced on a needle or tack with some

sort of base, such as modelling clay. The straw will

rotate if a charged object is brought close to one end.

Build your own versorium. Charge several objects and

try your device. Also try it on an operating television

screen. Examine the effect of turning the television off

and on while keeping your versorium near the screen.

Write a short report on your findings.

37. Design an experiment that can be used to test the

properties of conductors in electric fields. You may

use either or both of the following as is convenient: a

probe that can detect electric fields; a charged neutral

object attached to an insulating rod.

38. The electric field of Earth always points toward Earth.

The magnitude of the field strength varies locally

from as low as 100 N/C in fair weather to 20 000 N/C

in a thunderstorm. A field mill measures the local

electric field strength. In this device, the lower plate,

parallel to the ground, is connected to Earth through

an ammeter. The upper plate can be moved horizon-

tally, and it, too, is connected to Earth.

(a) When the mill is arranged as in Figure 6(a), what

kind of charge is on the surface of Earth and on

each plate? (Hint: Examine the field lines.)

(b) What will the ammeter show when you move the

upper plate rapidly over the lower plate, as in

Figure 6(b)? Explain your answer.

(c) What will the ammeter show when the upper

plate is quickly pushed away from the lower

plate? Explain your answer.

(d) What will the ammeter show if the upper plate is

attached to a motor and is rotated in a circle,

passing periodically over the lower plate?

(e) How is the ammeter reading related to the mag-

nitude of the electric field of Earth?

39. You place a circular conductor near a charged plate in

oil with suspended rayon fibres, as in Figure 7. The

configuration assumed by the fibres indicates the

geometry of the electric field. Explain what conclu-

sions this demonstration suggests regarding the

nature of electric fields (a) near the surfaces of con-

ductors and (b) inside conductors.

X Y ZW

3.0 3 102 V

−

4.0 cm 4.0 cm 4.0 cm

5.0 3 102 V Figure 4

6.0 3 102 V8.0 3 107 m/s

10.0 cm

2.0 cm

+

−−

Figure 5

(a) (b)

A A

Figure 6

A field mill is used to detect the magnitude of Earth’s electric field.

A

B

C

D

Answers 783NEL

7. 2.4 m8. (a) and (b) 0.349. (a) 3.5 3 105 J(c) 1.2 3 103 kg(d) 0.6110. (a) 22.0 3 102 J(b) 1.8 3 102 J(c) 2.0 3 102 JSection 4.5 Questions,

pp. 218–2195. 0.042 m6. 1.8 N7. 229 N8. 2.0 3 1022 m9. (a) 0.962 [down]; 3.33 m/s2[down] (b) 0.151 m 10. 6.37 m/s11. (a) 91 N/m (b) 0.40 J12. 2.0 3 101 N/m13. 0.38 m14. 0.14 m15. (b) 0.10 m (c) 1.0 3 103 N/m(d) 9.1 m/s17. 6.4 3 104 N/m18. 7.8 3 1022 m

Chapter 4 Self Quiz, p. 225 1. T 9. F 2. F 10. (c)3. F 11. (c)4. F 12. (e)5. T 13. (d)6. T 14. (e)7. T 15. (a)8. F 16. (d)Chapter 4 Review, pp. 226–229 9. (a) 249.1 J(b) 49.1 J10. 32°11. (a) 1.29 3 103 J(b) 1.29 3 103 J(c) 8.14 3 103 J12. 5.6 m13. 8.90 m/s14. (a) 2.5 3 1012 J(b) 3 3 103 people15. (a) 22.9 3 102 J(b) 2.9 3 102 J(c) 2.9 3 102 J16. (a) 9.2 m/s17. (a) 29 m/s (b) 29 m/s18. (a) 2.3 3 102 N; 1.3 3 102 N(b) 1.4 m/s (c) 2.0 3 102 J19. 1.0 3 104 m/s20. 8.40 m/s21. 42 J22. (a) 239 N/m (b) 35.9 N (c) 2.69 J; 10.8 J 23. 0.32 m24. 0.21 kg

Appendix D

25. (a) 0.053 J (b) 0.50 m/s (c) 0.33 m/s (d) 0.053 J32. (a) 19.8 m/s(b) 20.4 m/s34. (a) 1.12 mg(b) 1.12 mgDy35. 0.079 m36. 0.019 J37. 2.0 m38. 8.4 m/s39. 12 unitsChapter 5Section 5.1 Questions, p. 2383. (a) 77 N?s [E] (b) 1.1 N?s [forward] (c) 3.5 3 102 N?s [down] (d) about 0.12 N?s [S]4. 2.4 m/s [W]5. 1.6 3 104 N [W]6. (a) 0.66 kg?m/s [left] (b) 0.66 N?s [left]7. (a) 1.1 kg?m/s [backward] (b) 1.1 N?s [backward] (c) 0.45 N [backward]8. 1.8 m/s [backward]9. 3.0 m/s [N]10. (a) 11 kg?m/s [up] (b) 1.7 3 103 N [up]Section 5.2 Questions,

pp. 244–2455. 1.9 m/s in the original direc-tion of cart’s velocity6. 5.8 m/s [N]7. 4.95 m/s [E]8. (a) 2.34 3 104 kg?m/s [W];2.34 3 104 kg?m/s [E](c) zero9. 82 kg10. 0 m/sSection 5.3 Questions, p. 2534. 3.1 m/s forward and 0.4 m/sbackward

5. }m2}

6. 11 m/s 7. (b) }(m m

1

vM)}

(d) h 5 }2g (mm21

v2M)2}

(e) v 5 1}(m 1m M)}2 Ï2ghw

(f) 6.6 3 102 m/sSection 5.4 Questions,

pp. 258–2592. 66° from the initial directionof the neutron’s velocity3. 55 kg4. 1.7 m/s [47° S of E]5. (a) 0.22 kg (b) 1.3 3 1024 J

Chapter 5 Self Quiz,

pp. 267–2681. F 9. T 17. (b)2. T 10. F 18. (c)3. F 11. (e) 19. (a)4. F 12. (d) 20. (d)5. T 13. (d) 21. (a)6. T 14. (d) 22. (d)7. F 15. (e)8. F 16. (d)Chapter 5 Review, pp. 269–2717. 8.1 3 102 kg?m/s;7.9 3 102 kg?m/s8. 25 m/s9. 3.2 3 105 N [E]10. (a) 1.7 N?s [horizontally] (b) 28 m/s [horizontally]11. 1.00 m/s12. 0.619 km/s13. 1.90 3 102 m/s [towardJupiter]15. 0.08 m/s [N] for the 253-g car;1.88 m/s [N] for the 232-g car16. (b) 3.0 m/s; 4.0 m/s17. 0.56118. 3.00 m/s [W]19. (a) 2.3 m/s (b) 2.5 m/s20. (a) 0.80 m/s (b) 7.8 N21. 3.4 3 103 km/h22. 2.0 m/s [22° S of W](See Table 1 below.)

31. (a) v91 5 }vl(mm1

11

2 mm22)

} ;v92 5 }(m1

2m1

vml 2)}

(b) v91 5 0; v92 5 vl(c) v91 5 vl; v92 5 2vl(d) v91 5 2vl; v92 5 }

2mm12vl

}

32. 3.4 3 102 mChapter 6Section 6.1 Questions, p. 2772. (a) 3.99 3 103 N [towardEarth’s centre](b) 1.77 m/s2 [toward Earth’scentre]3. 7.3 3 1022 N/kg [towardEarth’s centre]4. (a) 3.0 3 106 m(b) 2.8 3 103 N5. 11.2 N/kg6. (a) 0.61 m/s2 [toward Earth’scentre]

(b) 2.9 3 102 N [towardEarth’s centre]7. (a) 2.6 3 103 km(b) 0.24 N8. 0.75 rESection 6.2 Questions, p. 2844. 1.8 3 108 s5. 1.6 times6. 4.0 3 101 h7. 9.2 3 106 mSection 6.3 Questions, p. 2943. (a) 21.7 3 1010 J(b) 5.4 3 103 m/s4. 1.4 3 109 J5. (a) 21.18 3 1011 J(b) 5.88 3 1010 J(c) 25.88 3 1010 J(d) 7.74 3 103 m/s6. (a) 23.03 3 1010 J(b) 1.52 3 1010 J(c) 21.52 3 1010 J(d) 94%7. (a) 6.18 3 105 m/s(b) 4.37 3 104 m/s8. 1.68 3 103 m/s9. 5.22 MS11. (a) 8.86 mmChapter 6 Self Quiz,

pp. 298–2991. T 10. F 19. (e)2. T 11. (a) 20. (c)3. T 12. (d) 21. (c)4. T 13. (c) 22. (d)5. F 14. (d) 23. (c)6. F 15. (a) 24. (c)7. F 16. (c) 25. (a)8. F 17. (a) 26. (e)9. T 18. (d)Chapter 6 Review, pp. 300–3013. 5.1 3 104 km4. 0.318 N/kg5. 4.23 3 1023 N/kg [1.26° fromthe spacecraft-to-Earth line]6. 3.3 3 1023 kg7. (a) 1.22 rE(b) 0.22 rE8. (a) 3.1 3 105 km(b) 2.1 d9. 1.08 3 1011 m10. (a) 1.21 3 104 km(b) 9.92 3 107 J11. (a) 2.64 3 103 m/s(b) 8.17 3 109 J12. (a) 23.99 3 108 J(b) +3.99 3 108 J(c) 2.82 3 102 m/s13. 25.33 3 1033 J

Table 1 Data for Question 22 (Chapter 5 Review)

Component 1 2 3

Mass 2.0 kg 3.0 kg 4.0 kg

Final Velocity 1.5 m/s [N] 2.5 m/s [E] 2.0 m/s [22° S of W]

784 Appendix D NEL

14. (a) 4.23 km/s(b) 2.37 km/s15. (a) 2.3 3 108 m/s(b) 77% of the speed of light16. (a) 1.1 3 1026 kg17. (a) 1.7 3 105 m/s19. 3.2 3 1014 m20. (a) and (b) 1.48 3 1014 m3/s2(c) 1.49 3 1014 m3/s2, yes(d) 0.557 d, 1.48 3 1014 m3/s2;7.52 3 104 km,1.48 3 1014 m3/s2;8.67 d, 1.48 3 1014 m3/s2;5.84 3 105 km,1.48 3 1014 m3/s2; Seealso completed Table 1below.22. (a) 1.6 3 103 kg(b) 1.0 3 1011 J(c) 1.2 3 104 m/s(d) 5.0 3 103 m/s24. 40 min 25. 7.9 3 107 s26. E 5 kT 2}

43}

Unit 2 Self Quiz, pp. 304–306 1. F 11. F 21. (e)2. T 12. F 22. (d)3. F 13. T 23. (c)4. F 14. F 24. (a)5. T 15. (c) 25. (c)6. F 16. (c) 26. (a)7. F 17. (a) 27. (d)8. F 18. (d) 28. (d)9. F 19. (e)10. F 20. (c)29. (a) Galileo Galilei(b) Johannes Kepler(c) James Prescott Joule(d) Tycho Brahe(e) Robert Hooke(f) Karl Schwartzschild30. (a) work (b) force constant of a spring (c) impulse (d) force(e) thermal energy (f) mass of Earth31. completely inelastic collision;equals; completely inelasticcollision

32. zero 33. singularity; Schwartzschildradius34. (a) A(b) E35. (e), (g), (h), (j), (k), (d), (b),(a), (m)Unit 2 Review, pp. 307–3119. 11 m10. (a) 1.0 3 101 J(b) 2.0 3 101 J(c) 2.0 m/s [W]11. (a) 10.0 kg (b) 2.50 3 103 N [E] 12. 71 kg?m/s13. 0.60 m 14. (a) 1.00 3 1022 J(b) 8.00 3 1022 J(c) 0.671 m/s17. 31 N18. 3.8 kg19. (a) 2.7 J (b) 0.60 m/s [W] (c) 21.6 J (d) 2.2 3 102 N/m20. 0.20 m21. (a) 0.42 m/s [left] (b) 0.87 m/s [left] (c) 0.38 m/s [left]22. 2.8 s23. 1.6 kg

24. }23m}25. 11 m/s [37° S of E]26. (a) 9.1 m/s [26° N of W] (b) 31%27. 4.9 m/s [12° W of N]31. 8.06 m/s2

32. 0.69 g33. 5.95 3 1023 N/kg [toward thecentre of the Sun] 34. (a) 6.16 a (b) 1.62 3 104 m/s35. (a) 1.74 3 1014 m3/s2(b) 1.09 3 108 m(c) 8.42 3 104 km36. 1.90 3 1027 kg37. (a) 4.23 3 103 m/s(b) 2.12 3 103 m/s(c) 3.67 3 103 m/s(d) 2.39 3 10219 J

38. (a) 2.4 3 102 m41. (a) 2.8 3 102 N/m43. (a) 2.3 3 1022 J; 2.1 3 1022 J(b) 28.5 3 1023 N46. (a) 2.9 3 1041 kg(b) 1.5 3 1011 stars47. 0.26 m/s [right] for both balls48. (a) 0.80 m/s [N] (b) 0.64 J (c) 1.6 N [S] (d) 24.8 3 102 J49. 3.4 3 102 m50. (a) 744 N/m; 15.3 kg (c) 2.3 kg52. 2.4 3 102 NChapter 7Section 7.2 Questions,

pp. 335–3363. 4.5 3 1022 N4. (a) 2.67 3 10214 N(b) 3.6 3 104 N(d) 3.6 3 104 N,3.6 3 103 m/s2(e) 3.6 3 104 N, 3.6 3 103 m/s2

5. 1.3 3 1024 C6. 3.9 3 1026 C7. 0.20 N [right], 1.94 N [right],2.14 N [left]8. 2.2 N, 1.4 N9. on the line joining them,0.67 m from the 1.6 3 1025 C10. 55 N/m13. (a) 5.7 3 1013 CSection 7.4 Questions,

pp. 358–3591. 4.3 3 1029 C2. 20.407. 4.0 3 1025 m8. (a) 23.6 3 1022 J(b) 1.0 3 104 V, 3.3 3 104 V,2.8 3 103 V9. (a) 1.1 3 1026 C(b) 7.1 3 105 N/CSection 7.5 Questions, p. 3641. (a) 1.1 3 1014

(b) 0, 1.1 3 105 V(c) 1.2 N2. (b) 2.9 3 1083. (a) 1.9 3 10218 C(b) 124. 1.7 3 10215 C5. (a) 8.4°(b) 0.50 N8. (a) 4.5 3 105 C(c) 1.6 3 10218 kg

Section 7.6 Questions, p. 3711. (a) 2.1 3 107 m/s(d) 4.8 3 105 m/s2. (a) 1.0 3 10218 J(b) 1.9 3 106 m/s(c) 1.6 cm

3. (a) 4.5 3 1026 m4. 7.7 3 10212 J5. (a) 1.8 3 1023 m(b) 2.7 3 105 m/s(c) 5.1°Chapter 7 Self Quiz, p. 3771. F 6. T 11. (b)2. F 7. (b) 12. (b)3. T 8. (e) 13. (b)4. F 9. (e)5. F 10. (e)Chapter 7 Review, pp. 378–3814. 1.0 3 1023 N5. 2.4 3 1029 m6. (a) 8.2 3 1028 N(b) 3.6 3 10247 N(d) 2.2 3 106 m/s,1.5 3 10216 s7. (a) 21 N away from negativecharge(b) 59 N toward positivecharge(c) 91 N toward positivecharge12. (a) 6.0 N/C [right](b) 4.3 3 1023 N [left]13. 3.2 3 107 N/C [right]14. 5.8 3 105 N/C [right]15. (a) 4.2 3 103 N/C(b) 2.9 3 1023 N(c) 2.9 3 1025 N(d) 6.9 3 1029 C18. 2.1 3 105 N [55° up from theleft], 0, 1.7 3 108 V19. 8.1 3 106 V20. 43 J21. 4.0 3 10215 J22. 2.3 3 10213 J23. 2.3 3 104 N/C24. 2.0 3 102 V26. 5.1 m27. 4.7 3 10219 C, 63 electrons28. 49 V29. 23.6 3 103 V, 9.0 3 103 N/C[toward sphere]30. 1.3 3 107 m/s31. 5.9 3 103 V32. 68 V33. (a) 1.0 3 107 m/s(b) 1.6 cm, to the left(c) 0 m/s34. 1.6 3 10214 m35. (a) 0.41 cm(b) 8.0 3 107 m/s [4.7° upfrom the right]45. (a) 1.0 mm(b) 1.5 3 1023 mChapter 8Section 8.2 Questions,

pp. 402–4032. 1.5 3 10212 N [up]3. 8.4 3 1024 m

Table 1 Data of Several Moons of the Planet Uranus (for question 20

Chapter 6 Review)

Moon Discovery raverage (km) T (Earth days) CU (m3/s2)

Ophelia Voyager 2 (1986) 5.38 3 104 0.375 1.48 3 1014

Desdemona Voyager 2 (1986) 6.27 3 104 0.475 1.48 3 1014

Juliet Voyager 2 (1986) 6.44 3 104 0.492 1.48 3 1014

Portia Voyager 2 (1986) 6.61 3 104 0.512 1.48 3 1014

Rosalind Voyager 2 (1986) 6.99 3 104 0.556 1.48 3 1014

Belinda Voyager 2 (1986) 7.52 3 104 0.621 1.48 3 1014

Titania Herschel (1787) 4.36 3 105 8.66 1.48 3 1014

Oberon Herschel (1787) 5.85 3 105 13.46 1.48 3 1014