Download Inverse Square Laws

Name: ______________________________________________
Period: _______
Physics Unit II: Forces
Subunit C: Inverse-Square Laws
Equations
Variables, Constants, Units
Solar System Data
Name
Mass (kg)
Radius (m)
Distance from
Sun (m)
Sun
1.99 x 1030
696 x 106
----
Mercury
3.30 x 10
2.44 x 10
5.79 x 10
Venus
4.87 x 1024
6.05 x 106
1.08 x 1011
Earth
5.98 x 1024
6.37 x 106
1.50 x 1011
Mars
6.42 x 1023
3.40 x 106
2.28 x 1011
Jupiter
1.90 x 1027
71.5 x 106
7.78 x 1011
Saturn
5.69 x 1026
60.3 x 106
1.43 x 1012
Uranus
8.66 x 1025
25.6 x 106
2.87 x 1012
Neptune
1.03 x 1026
24.8 x 106
4.50 x 1012
Pluto
1.50 x 1022
1.15 x 106
5.91 x 1012
23
6
10
Earth’s Moon
Mass
7.40 x 1022 kg
Radius
1.75 x 106 m
Distance from Earth
3.80 x 108 m
Elementary Particles
Object
Mass (kg)
Electrical
Charge (C)
Proton
1.672 x 10-27
+1.602 x 10-19
Neutron
1.674 x 10-27
0
Electron
9.11 x 10-31
-1.602 x 10-19
Unit II: Forces
Subunit D: Inverse-Square Laws
Objectives
By the time we finish the labs and related materials in this unit, you should be able to:
1. Use Newton’s Law of Universal Gravitation to describe the relationships between the
Gravitational Force, Mass, and Distance between any two objects.
2. Use Newton’s Law of Universal Gravitation to calculate the gravitational force between
objects and gravitational field strength of a planet.
3. Using Newton’s Law of Universal Gravitation and previous equations, calculate gravitational
field strengths and orbital velocities.
4. Use Coulomb’s Law to describe the relationships between the Electrical Force, Mass, and
Distance between any two objects.
5. Use Coulomb’s Law to calculate the electrical force.
6. Explain the difference between the force between two like charges and the force between
two unlike charges.
7. List the ways that charge can be transferred, and differentiate between conductors and
insulators.
8. Draw graphs of inverse square functions.
9. Draw force diagrams for objects experiencing gravitational and electrical forces.
10. Draw field lines that show the direction of the force on a test mass or charge.
Unit II-D: Inverse-Square Laws
Worksheet 1
1. The universal part of Newton's law of universal gravitation means that
A) the amount of gravitational forces is the same for all objects.
B) the acceleration caused by gravity is the same for all objects.
C) the force of gravity acts between all objects.
2. According to Newton's gravitation law, the force of gravitational attraction between a planet
and an object located upon the planet's surface depends upon _____. Choose all that apply.
A) the radius of the planet
B) the mass of the planet
C) the mass of the object
D) the volume of the object
E) ... nonsense! None of these variables affect the force of gravity.
3. The more massive that an object is, the ______ (more, less) that the object will be attracted
to Earth.
4. The more massive the Earth is, the ______ (more, less) that another object will be attracted
to Earth.
5. The greater that Earth's radius is, the ______ (more, less) that another object will be attracted
to Earth.
6. In the mathematical form of Newton's law of universal gravitation, the symbol G stands for
A) gravity
B) the acceleration of gravity
C) the gravitational constant
7. Orbiting astronauts on the space shuttle do not have weight in space because
A) there is no gravity in space
B) there is no air resistance in space
C) there are no scales in space
D) the food is terrible and they work all the time
E) ... nonsense! The astronauts do have weight in space.
TRUE or FALSE:
8. _______ The value of G (in the equation above) is an enormously large number; that explains
why (at least in part) the force of gravitational attraction between the Sun and the very distant
Earth is such a large number.
8. _______ Two lab partners attract each other with a gravitational force. However, it is
impossible to calculate such a force since it is only an unproven theory.
10. _______The notion that any two objects attract each other gravitationally
is a theory. There is no empirical evidence for such a notion.
11. ______ Gravity is zero on the way to the moon. Astronauts are weightless in the shuttle.
Use Newton's gravitational law in a conceptual manner in order to fill in the following blanks.
12. Two objects gravitationally attract with a force of 18.0 N. If the distance between the two
objects' centers is doubled, then the new force of attraction is ______ N.
13. Two objects gravitationally attract with a force of 18.0 N. If the distance between the two
objects' centers is tripled, then the new force of attraction is ______ N.
14. Two objects gravitationally attract with a force of 18.0 N. If the distance between the two
objects' centers is halved, then the new force of attraction is ______ N.
15. Two objects gravitationally attract with a force of 18.0 N. If the distance between the two
objects' centers is decreased by a factor of three, then the new force of attraction is ______ N.
16. Two objects gravitationally attract with a force of 18.0 N. If the distance between their
centers is decreased by a factor of four, then the new force of attraction is ______ N.
17. Two objects gravitationally attract with a force of 18.0 N. If the mass of one of the objects is
doubled and the distance between their centers is doubled, then the new force of attraction is
______ N.
18. Two objects gravitationally attract with a force of 18.0 N. If the masses of both of the objects
are doubled and the distance between their centers is doubled, then the new force of attraction
is ______ N.
19. Two objects gravitationally attract with a force of 18.0 N. If the masses of both of the objects
are tripled and the distance between the two objects' centers is doubled, then the new force of
attraction is ______ N.
Unit II-D: Inverse-Square Laws
Worksheet 2
1. Calculate Earth’s gravitational force on a space shuttle with a mass of 9.48 x 104 kg:
A) at the Earth’s surface.
B) 6.37 x 106 m away from the Earth’s surface. How many times smaller is it here?
C) 1.274 x 107 m away from the Earth’s surface. How many times smaller is it here?
2. John claims that there is a strong attraction force between him and a fellow student, Jan. If
John’s mass is 75 kg, Jan’s is 60 kg, and they sit 0.5 m apart, how much gravitational force
attracts these two students?
3. A) Using Newton’s law of Universal Gravitation, find the force of attraction between you (say
you weigh about 150 lbs., which would give you a mass of 68 kg) and the Earth.
B) Now find the force of gravity on you using Fg = mg. How does this compare to your answer
from part A?
4. A) Find the gravitational force between the Earth and the Sun.
B) How much would the Earth “weigh” on the surface of the Sun? (remember r = total distance
from center to center!)
5. A) Find the gravitational force between the Earth and the moon.
B) How much would the moon “weigh” on the surface of the Earth?
6. Mercury is very close to the Sun, but is very small. Jupiter is far from the Sun, but is very
large. Calculate the Sun’s gravitational force on each to determine which is greater.
7. An astronaut stands on a newly discovered planet, whose mass is unknown. He pulls his
trusty bathroom scale out of his rover, and finds that he weighs 1200 N. From his orbit, he
approximated the radius of the new planet to be 12 x 106 m. If he has a mass of 100 kg when
fully suited, what is the mass of this new planet?
Unit II-D: Inverse-Square Laws
Worksheet 3
1. Calculate the strength of Earth’s gravitational field at its surface using Newton’s laws.
2. The asteroid Ceres has a mass of 7.0 x 1020 kg and a radius of 500 km. Find the gravitational
field strength at the surface of Ceres.
3. One planet whose radius is 1.2 x 107 m has a gravitational acceleration of 18 m/s2. What is
the mass of this planet?
4.Calculate the gravitational field strength at the surface of each object in the solar system listed
in the table below.
Solar System Data
Name
Mass (kg)
Radius (m)
Sun
1.99 x 1030
696 x 106
Mercury
3.30 x 1023
2.44 x 106
Gravitational Field Strength (N/kg or m/s2)
Venus
4.87 x 1024
6.05 x 106
Earth
5.97 x 1024
6.38 x 106
Mars
6.42 x 1023
3.40 x 106
Jupiter
1.90 x 1027
71.5 x 106
Saturn
5.69 x 1026
60.3 x 106
Uranus
8.66 x 1025
25.6 x 106
Neptune
1.03 x 1026
24.8 x 106
Pluto
1.50 x 1022
1.15 x 106
Unit II-D: Inverse-Square Laws
Worksheet 4
Vocabulary Matching.
A) Charge
B) Charging by conduction
C) Charging by induction
D) Conductors
E) Conservation of charge
F) Coulomb
G) Electrostatics
H) Elementary charge
I) Grounding
J) Insulators
K) Neutral
1. _______ Materials through which charges will not move easily.
2. _______ The study of electrical charges that can be collected and held in one place.
3. _______ Touching an object to Earth to eliminate excess charge.
4. _______ The magnitude of the charge of a single electron.
5. _______ Separating the charges in an object without touching the object.
6. _______ Materials such as metals that allow charges to move about easily.
7. _______ An object that has positive and negative charges exactly balanced.
8. _______ Giving a neutral body a charge by touching it with a charged body.
9. _______ The net electrical charge in an isolated system never changes.
10. _______ The standard metric unit of charge.
11. _______ The property of an object that causes electrical forces.
Multiple Choice.
12. An electrically neutral atom is an atom which
A) does not have any protons or electrons
B) has more neutrons than the sum of all its protons and electrons
C) has a balance of protons and electrons (the same number of each)
D) has a balance of neutrons and electrons (the same number of each)
E) has a balance of protons, electrons and neutrons (the same number of each)
13. An electrically charged atom (sometimes referred to as an ion) can be distinguished from an
electrically neutral atom in that the charged atom (ion)
A) does not have any neutrons
B) has lost one or more of its neutrons
C) either has a proton or an electron present somewhere within it
D) has a different number of neutrons than the sum of its electrons and protons
E) has an imbalance of protons and electrons (unequal numbers of these)
5.
TRUE or FALSE:
Conductors cannot be charged by frictional rubbing.
Explain your answer.
6.
A balloon is charged by rubbing it with animal fur. It is then pressed against a
wooden cabinet. The balloon and cabinet attract, seeming to defy the force of
gravity. This attraction is best explained by ____.
a. induction charging of the wood
b. frictional charging of the wood
c. polarization of wood molecules
d. polarization of balloon molecules
14. A balloon is charged by rubbing it with animal fur. It is then pressed against a
wooden cabinet. The balloon and cabinet attract, seeming
to defy the force of gravity.
7. The above effect (in question # 6) is most often noticed of ____.
a. conductors
b. insulators
c. charged objects
This attraction is best explained by
A) induction charging of the wood
C) polarization of wood molecules
Physics Classroom, 2009 of balloon molecules
B) frictional charging of the wood
D)© The
polarization
Page 7
15. Complete the following statements to illustrate your understanding of the three types of
charge interactions:
A) Oppositely-charged objects __________________________
B) Like-charged objects ____________________________
C) A charged object and a neutral object
________________________________
Staticwill
Electricity
8. A negatively
balloon is brought
near a neutral
conducting
16. A negatively charged balloon is brought
nearcharged
a neutral
conducting
sphere
sphere as shown in the diagram at the right. The presence of the
as shown in the diagram at the right. Thecharged
presence
of
the
charged
balloon
will
balloon will cause something to happen in the sphere.
Static Electricity Which of the following would you expect to occur?
N ame: Select all that
cause something to happen in the Nsphere.
Which of the following would you
apply.
Static Electricity
ame:
a. Electrons in the sphere will move to the balloon.
expect to occur? Select all that apply.
b. Protons
in the sphere
will move to and
the balloon.
I nsulators,
Conductors
Polarization
c. Electrons in the sphere will move to the left side.
A) Electrons inI the
sphere
will
move
to
the
balloon.
the sphere
will move
to the
right Classroom:
side.
Lesson 1d.of Electrons
the Staticin
Electricity
chapter
at The
Physics
nsulators, ConductorsRead
andfrom
Polarization
Protons in the sphere will move to the left side.
http://www.physicsclassroom.com/Class/estatics/u8l1d.html
B) from
Protons
spherechapter
willatmove
toClassroom:
the e.f.balloon.
Read
Lesson 1 ofin
the the
Static Electricity
The Physics
Protons in the sphere will move to the right side.
http://www.physicsclassroom.com/Class/estatics/u8l1e.html
C) Electronshttp://www.physicsclassroom.com/Class/estatics/u8l1d.html
in the sphere will Mmove
to9.the
left
side.
The process
of inducing
the movement
of charge
OP Connection:
Static Electricity:
preface
to sublevels
5 - 7 within the sphere (referring to question # 8) causes
http://www.physicsclassroom.com/Class/estatics/u8l1e.html
positive
and side.
negative charge to be separated. This is known as ____.
D)
Electrons
in
the
sphere
will
move
to
the
right
M OP Connection:
Static Electricity: preface to sublevels
5-7
a. grounding
b. charging
c. polarization
d. induction
1. Insulators
are different
than conductors
in that insulators ____.
E) Protons in the sphere will move
tonotthe
left
side.
a. do
contain
electrons
or protons
b. do not contain any charge
1. Insulators are different than conductors in that insulatorsc.____.
Charged
rods are placed
a neutral
conducting
sphere,
have a 10.
weaker
affinityrubber
for electrons
d. near
do not
allow charge
to freely
movecausing a redistribution of charge
do not containin
electrons
protons
b. domove
not contain
charge
on
the spheres.
F)a.Protons
the orsphere
will
toanythe
right
side.Which of the diagrams below depict the proper distribution of charge on the
c. have a weaker affinity for electrons
2.
d. do not
chargethrough
to freely
moveList
spheres?
all thatcan
apply.
2. allow
Materials
which
electrons
move readily are classified as _____.
a. conductors
b. insulators
c. semi-conductors
Materials through which electrons can move readily are classified as _____.
a. conductors
b. insulators
c. 3.
semi-conductors
The diagram at the right shows a metal sphere attached to the top of an insulating stand. The metal
sphere contains an excess of electrons and is thus charged. A student holds various objects in her
The diagram at the right shows a metal sphere attached to
the and
top of
an insulating
stand.
metalWhich of the following objects below would allow charge
hand
touches
the object
to theThe
sphere.
sphere contains an excess of electrons and is thus charged.
A student
holds
in the
her object to the sphere?
to throw
it when
thevarious
studentobjects
touches
11. In the
above situation (question # 10), the conducting sphere is ____. List all that apply.
hand and touches the object to the sphere. Which of the a.
following
a plasticobjects
straw below would allow charge b. a piece of paper
a.
charged
b.
polarized
c. uncharged (neutral)
to throw it when the student touches the object to the sphere?
c. a steel house key
d. a metal paper clip
a. a plastic straw
b. a piece e.
of paper
a strip of aluminum foil
c. a steel house key
d. a metal paper clip12. A physics teacher fills a buret with water and opens the valve,
producing a steady stream of water falling vertically to the sink.
e. a strip of aluminum foil
4. Consider these two spheres. They have both
Then the teacher rubs a rubber balloon with animal fur and holds
been charged. In one case the charge is isolated
The stream is observed to deflect from its usual
4. Consider these two spheres. They have both it near theinstream.
three distinct locations; in the other case, the
towards the balloon. Explain what is causing the
been charged. In one case the charge is isolatedvertical flow
excess charge is even distributed about the
of the water stream.
in three distinct locations; in the other case, thedeflectionsurface
of the sphere. Which one of these spheres
excess charge is even distributed about the
is made of an insulating material and which is
surface of the sphere. Which one of these spheres
made of a conducting material? Label which is
is made of an insulating material and which is
which and support your answer with an
made of a conducting material? Label which is
explanation.
which and support your answer with an
explanation.
17. Consider these two spheres. They have both been charged. In one case the charge is
3.isolated in three distinct locations; in the other case, the excess charge is evenly distributed
about the surface of the sphere. Which one of these spheres is made of an insulating material
and which is made of a conducting material? Label which is which and support your answer with
an explanation.
13. A physics teacher charges a balloon negatively
by rubbing it with animal fur. The balloon is
TRUE or FALSE:
then placed next to a wooden cabinet and
adheres
to the
whatrubbing.
is
Conductors
cannot
be cabinet.
charged Explain
by frictional
TRUE or FALSE:
happening at the particle level to cause such a
Explain your answer.
Conductors cannot be charged by frictional rubbing.
gravity-defying phenomenon. Add to the blownup view of the diagram to assist in your
Explain your answer.
explanation.
5.
5.
6.
6. A balloon is charged by rubbing it with animal fur. It is then pressed against a
wooden cabinet. The balloon and cabinet attract, seeming to defy the force of
A balloon is charged by rubbing it with animal fur. It is gravity.
then pressed
a is best explained by ____.
Thisagainst
attraction
wooden cabinet. The balloon and cabinet attract, seeming
defy the charging
force of of the wood
a. to
induction
b. frictional charging of the wood
gravity. This attraction is best explained by ____.
c. polarization of wood molecules
d. polarization of balloon molecules
a. induction charging of the wood
b. frictional charging of the wood
c. polarization of wood molecules
d. polarization
balloon
molecules
7. ofThe
above
question
# 6) is most
©effect
The (in
Physics
Classroom,
2009often noticed of ____.
a. conductors
b. insulators
c. charged objects
The above effect (in question # 6) is most often noticed of ____.
a. conductors
b. insulators
c. charged objects
18. Considering the previous question, why is your car a SAFE place to be during a
thunderstorm? (and don’t give me the rubber wheels excuse!!!)
7.
© The Physics Classroom, 2009
© The Physics Classroom, 2009
Page 8
Page 7
Page 7
Unit II-D: Inverse-Square Laws
Worksheet 5
Alteration in the Quantity of Charge
1. Two charged objects have a repulsive force of .080 N. If the charge of one of the objects is
doubled, then what is the new force?
2. Two charged objects have a repulsive force of .080 N. If the charge of both of the objects is
doubled, then what is the new force?
Alteration in the Distance between Charged Objects
3. Two charged objects have a repulsive force of .080 N. If the distance separating the objects
is doubled, then what is the new force?
4. Two charged objects have a repulsive force of .080 N. If the distance separating the objects
is halved, then what is the new force?
Alteration in both the Quantity of Charge and the Distance
5. Two charged objects have a repulsive force of .080 N. If the charge of one of the objects is
doubled, and the distance separating the objects is doubled, then what is the new force?
6. Two charged objects have a repulsive force of .080 N. If the charge of both of the objects is
doubled and the distance separating the objects is doubled, then what is the new force?
7. Two charged objects have an attractive force of .080 N. If the charge of one of the objects is
halved and the distance separating the objects is doubled, then what is the new force?
8. A balloon with a charge of 4.0 x 10-5 C is held a distance of 0.10 m from a second balloon
having the same charge. Calculate the magnitude of the repulsive force.
9. Calculate the electrical force (in Newtons) exerted between a 0.022 kg balloon with a charge
of -2.6 μC and a wool sweater with a charge of +3.8 μC; the separation distance is 0.75 m.
(NOTE: a μC or microCoulomb is a unit of charge; 10-6 C)
10. Suppose that two equally charged spheres attract each other with a force of -0.492 N ("-"
means attractive) when placed a distance of 0.03 m from each other. Determine the charge of
the spheres.
Unit II-D: Inverse-Square Laws
Worksheet 6
1. A +5.0 μC charge and a -6.0 μC charge experience an attractive force of -0.72 N. Determine
their separation distance.
2. The electron and proton of a hydrogen atom are separated on the average by a distance
of about 5.3 x 10-6 m. Find the magnitudes of the electric force and the gravitational
force that each particle exerts on the other.
3. A positive charge of 3.6 x 10-5 C and a negative charge of -2.4 x 10-5 C are 0.034 m apart.
What is the electric force between the two particles? Is it attractive or repulsive?
4. What is the electrostatic force between a pair of balloons, each having -5.0 x 10-6 C of charge,
when they are 0.3 m apart? Is the force attractive or repulsive?
5. Two charges of +4.2 x 10-8 C are separated by 0.46 m. What is the magnitude of the
electrical force acting on each object? Is the force attractive or repulsive?
6. Two objects exert a force of 4.2 N on each other. The distance between the objects is 0.36 m.
The charge on one object is 2.8 x 10-9 C. What is the charge on the second object?
7. A negative charge of 2.0 x 10-4 C and a positive charge of 8.0 x 10-4 C are separated by 0.2 m.
What force exists between the charges? Is this force of repulsive or attractive?
8. Two positive charges are located 2 cm apart. Charge qA is +2 x 10-9 C and charge qB is
+3 x 10-9 C. Calculate the electrical force between them. Is the force attractive or repulsive?
9. A +4.5 x 10-6 C charge is located 3.2 m from a -2.8 x 10-6 C. Find the magnitude of the
electrostatic force by one charge on the other.
Unit II-D: Inverse-Square Laws
Worksheet 7
Multiple Choice.
1. The _____ of a charged object exerts force on other objects.
A) charge
B) electric field
C) voltage
D) mass
2. The direction and strength of a field are depicted by
A) spokes
B) field lines
C) vector lines
D) tangents
3. Only ____ electric potential can be measured.
A) points of
B) absolute values of C) differences in
D) attractions between
4. The strength of the force on a mass in a gravitational field depends on
A) the direction of the field.
C) the magnitude of the field.
B) the size of the mass
D) both B and C.
5. The strength of the force on a charge in an electric field depends on
A) the direction of the field.
C) the magnitude of the field.
B) the size of the charge
D) both B and C.
6. As a field becomes stronger, the field lines should be drawn
A) thicker.
B) thinner.
C) closer together.
D) farther apart.
7. Consider the electric field lines shown in the diagram below. From
diagram, it is apparent that object A is ____ and object B is ____.
A) +, +
B) -, C) +, D) -, +
the
Short Answer.
8. Describe two ways in which gravitational forces are like electrical forces.
9. Describe one major difference between gravitational and electrical forces.
10. Both gravitational and electrical forces act over distances. Which force is greater over the
distance between the Earth and the Sun? Which force is greater over the distance between two
oxygen atoms in a water molecule?
11. Several electric field line patterns are
diagrams. Which of these patterns are
Explain what is wrong with all incorrect
shown in the
incorrect?
diagrams.
12. Consider the electric field lines drawn at the left for a configuration of two
charges. Several locations are labeled on the diagram. Rank these locations in
order of the electric field strength - from smallest to largest.
Smallest 1. ____ 2. ____ 3. ____ 4. ____ 5. ____ Largest
13. For the diagram at right, use your
of electric field lines to identify the
objects in the following configurations.
understanding
charges on the
Static Electricity
14. Draw the electric field lines for the following configurations of charges in the diagram below.
Place arrows
upon your
electric
field
lines. <
Ranking:
<
<
Ranking:
<
4.
Draw the electric field lines for the following configurations of charges. Place arrows upon your
electric field lines.
© The Physics Classroom, 2009
Page 18
Unit II-D: Inverse-Square Laws
Review Worksheet
1. What happens to the force between two objects when
A) the mass of one object is doubled?
B) both charges are halved?
C) the distance between them is tripled?
D) both masses are doubled and the distance between them is doubled?
2. Which way do field lines point around
A) a small mass?
B) a large mass?
C) a positive charge?
D) a negative charge?
3. How is the gravitational force related to the mass of an object? How is the electrical force
related to the charge of an object?
4. How are the long-range forces such as the gravitational force and the electrical force related
to the distance between objects?
Sample Problems. Show your work!
5. What is the force of attraction between two pencils, each with a mass of 0.020 kg that are
0.05 m apart?
6. A newly discovered planet whose radius is 8.2 x 106 m has a gravitational acceleration of 14
m/s2. What is the mass of this planet?
7. The International Space Station is in an approximately circular orbit at an average altitude of
400 km above the Earth.
A) Find the acceleration due to gravity on the ISS at this altitude.
B) The ISS is reported to have a mass of about 370 metric tons (1 metric ton = 1000 kg). Find
the “weight” of the ISS at this altitude.
8. What is the electrostatic force between a pair of electrons when they are 0.01 m apart? Is the
force attractive or repulsive?
9. Two charged objects are 0.4 m apart. The charge on one object is 2.8 x 10-9 C and the
charge on the second object is 5.2 x 10-6 C. What is the force between the charges?
10. Use the diagram below to answer the following questions about charge QA and QB.
A) Charge QA is _________ (positive / negative).
B) Charge QB is _________ (positive / negative).
C) Which charge is stronger, QA or QB? ________