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Grade 12
Unit 10
SCIENCE 1210
KINEMATICS – NUCLEAR ENERGY
CONTENTS
I. MECHANICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
KINEMATICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ENERGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
6
9
II. WAVE MOTION . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
WAVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LIGHT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SOUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
15
21
III. ELECTRICITY AND MAGNETISM . . . . . . . . . .
26
SOURCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
FIELDS AND FORCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CIRCUITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
28
33
IV. MODERN PHYSICS . . . . . . . . . . . . . . . . . . . . . . .
41
THE PLANETARY ATOM . . . . . . . . . . . . . . . . . . . . . . . . . . . .
EMISSION SPECTRA AND QUANTIZED ENERGY . . . . . . . . . . .
THE BOHR ATOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
DUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
NUCLEAR ENERGIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
42
46
49
51
Authors:
Mary Grace Ferreira, M.N.S.
Lee H. Dunning, M.S.T., M.S.Ed.
Editor:
Alan Christopherson, M.S.
Illustrations:
John Mitchell
Alpha Omega Graphics
804 N. 2nd Ave. E., Rock Rapids, IA 51246-1759
© MM by Alpha Omega Publications, Inc. All rights reserved.
LIFEPAC is a registered trademark of Alpha Omega Publications, Inc.
All trademarks and/or service marks referenced in this material are the property of their respective owners. Alpha Omega Publications, Inc.
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KINEMATICS – NUCLEAR ENERGY
Physical phenomena may be grouped into four
categories: mechanics, wave motion, electricity and
magnetism, and atomic and nuclear physics.
Mechanics is the study of motion, force,
momentum, work, power, and energy; wave motion
is the study of wave behavior as it explains
phenomena associated with light; electricity and
magnetism deal with those two related phenomena;
and atomic and nuclear physics, frequently referred
to as modern physics, is the most imaginative of the
four branches if only because imagination was
copiously applied during its development. It is the
most comprehensive of the four, applying principles
from the other three, and introducing several
unique insights.
Physics, like other true sciences, is a description
and interpretation of natural phenomena.
Advancing technology has made description more
accurate; new interpretation has had to follow. Two
cases in which interpretations have been adjusted
to new descriptions are the models for light and for
the atom. Three hundred years ago the wave model
of light was postulated. That model still holds; but
experiments of the twentieth century have revealed
that light also behaves like a stream of particles.
Somehow, light is both a wave and a particle.
In the second case, our perception of the atom
has changed from an invisible solid sphere to an
incredibly complex solar system, an analogy of
which does not exist on the macroscopic level.
OBJECTIVES
Read these objectives. The objectives tell you what you will be able to do when you have
successfully completed this LIFEPAC®.
When you have finished this LIFEPAC, you should be able to:
1.
Define and apply displacement, velocity, and acceleration.
2.
Explain and apply Newton’s laws of motion.
3.
Define and apply momentum and impulse.
4.
Explain and apply Kepler’s laws of planetary motion.
5.
Define and apply energy, work, power, and efficiency.
6.
Describe transverse and longitudinal waves.
7.
Calculate velocity problems for sound and light.
8.
Calculate index of refraction problems for light.
9.
Draw lens and mirror diagrams.
10.
Calculate lens and mirror problems.
11.
Describe refraction, diffraction, interference, and polarization.
12.
Identify the phenomena that support the particle model and the wave model of light.
13.
Identify natural sources of electricity and magnetism.
14.
Describe force fields that surround electric charges and magnetic poles.
15.
Apply Ohm’s law to series and parallel circuits.
16.
Describe the development of the atomic model.
17.
Associate major contributors to the atomic model with their contributions.
18.
Describe emission and absorption spectra as they relate to the quantum atom.
19.
Describe the matter-energy duality.
20.
Define isotope and half-life.
21.
Explain nuclear reactions.
1
Survey the LIFEPAC. Ask yourself some questions about this study. Write your questions here.
2
I. MECHANICS
The study of mechanics covers a broad area
that includes kinematics, dynamics, and energy. In
this review of mechanics, the emphasis will be on
the use of equations to solve problems and to
understand the relationships of distance, time,
velocity, acceleration, force, momentum, energy,
and power.
SECTION OBJECTIVES
Review these objectives. When you have completed this section, you should be able to:
1.
Define and apply displacement, velocity, and acceleration.
2.
Explain and apply Newton’s laws of motion.
3.
Define and apply momentum and impulse.
4.
Explain and apply Kepler’s laws of planetary motion.
5.
Define and apply energy, work, power and efficiency.
KINEMATICS
10 -6 meters
10 -10 meters
You may wish to review LIFEPAC 1201: the
vocabulary words, the difference between
fundamental and derived units, and scalars and
vectors.
Kinematics is the study of motion apart from
the cause of that motion. The aspects of motion are
displacement, velocity, and acceleration.
Velocity. Velocity is the rate at which
displacement changes with respect to time. If a
greater displacement occurs in a given period of
time or if the same displacement occurs in a
shorter period of time, the velocity increases. The
reverse cases produce a decrease in velocity.
The symbol that conventionally represents
change is the Greek letter ∆ (delta). A change in
displacement is ∆d, and a change in displacement
divided by the time interval required for that
change is the definition of velocity:
Displacement. Displacement is the distance
from a defined starting point to a second point
along a straight line. Implicit in this definition is
the specific direction from the starting point to the
second point: displacement is a vector quantity.
starting
point
second
point
A
B
= 1 micron (µ)
o
= 1 angstrom ( A )
v=
∆d
/∆t
Velocity is the slope of a displacement-time
graph:
AB
The vector from the second point back to the starting
point is a negative of the vector previously cited.
B
A
B
A
BA = -AB
q
The magnitude of displacement is distance, the
length of the straight line connecting the two
points, without regard for the direction of travel.
The standard metric unit of distance and
displacement is the meter. The meter has
convenient subdivisions and multiples.
d
p
1,000 meters (m) = 1 kilometer (km)
= 1 centimeter (cm)
10 -2 meters
-3
= 1 millimeter (mm)
10 meters
t
3
Curve A represents constant velocity because the
slope ∆d/∆t is uniform. Curve B represents
increasing velocity because the slope at Point q is
greater than the slope at Point p.
When velocity vectors on a circular path are taken
infinitely close together, the centripetal (“centerseeking”) acceleration vector points to the center of
the circle.
The magnitude of centripetal acceleration is
proportional not to velocity but to velocity squared,
Acceleration. The rate of change in velocity
with respect to time is acceleration. A greater
velocity change in a given period of time or the
same velocity change in a shorter period of time
produces an increase in acceleration. The reverse
cases produce a decrease in acceleration.
a=
a ⬀ v2,
and is inversely proportional to the radius of the
curve,
∆v
/∆t
a ⬀ 1/R
Acceleration is the slope of a velocity-time
graph:
Combining these two formulas, the result is
2
a ⬀ v /R
B
tangent to
When a car turns a corner, the car is harder to
control; and the centripetal acceleration is
increased if the speed is increased or if speed is
maintained on a curve with a smaller radius.
Rollovers occur at high speeds on sharp turns.
As the velocity changes, the acceleration
changes in ratios of 2:4, 3:9, 4:16, 5:25, and so on.
Notice that the change in acceleration is as the
square of the velocity. The radius of the curve,
however, affects the centripetal acceleration in this
manner 1/3:3, l/2:2, 2:1/2, 4:l/4. Therefore, if the car
turns in a larger arc (double the radius) and doubles
the speed, the acceleration is decreased by half
because of the greater arc; but the acceleration is
increased by a factor of four because of the greater
speed. Therefore, the centripetal acceleration has
increased by a factor of two (1/2 • 4 = 2).
The last item in this section is the acceleration
due to gravity. To simplify the study, assume that
the initial velocity of an object in free fall is zero,
that frictional effects are negligible, and that the
acceleration is constant. A general statement of
displacement produced by acceleration is
tangent to
d = 1/2 at2
A
v
t
Curve A represents constant acceleration because
the slope ∆v/∆t is uniform. Curve B represents
increasing acceleration.
Velocity is a vector quantity. If the magnitude
of the velocity (the speed) remains constant but its
direction changes, this change in velocity, by
definition, constitutes acceleration. Motion of an
object in a circular path is centripetal acceleration.
V1
∆V
V2
When the acceleration is a result of gravity, the
equation is conventionally rewritten
d = 1/2 gt2
-V
parallel to,
and equal to,
The former equation is valid for any object
undergoing acceleration. Acceleration resulting
from gravitational attraction is called acceleration
V1
4
due to gravity. In either case the displacement is
proportional to acceleration and to the square of
time. Therefore, in a given time, tripling the
✍
1.1
acceleration triples the distance covered. However,
if the time factor is tripled, the displacement is
nine times greater.
Complete these sentences.
.
decreased) by a factor of b.
1.2
(increased,
If displacement per unit time is tripled, the velocity is a.
(positive,
If the velocity decreases, the acceleration has a
negative) value.
1.3
If the velocity is halved, the acceleration is a.
(halved, quartered,
(negative, positive) value.
doubled, quadrupled) and has a b.
1.4
An object is traveling in a circular motion at constant speed. If the speed is doubled, the
centripetal acceleration is changed by a factor of
(one-half,
one-fourth, two, four).
1.5
A car turns a corner at 15 kph. If the car were to turn in a shorter radius, the centripetal
(increase, decrease). If the radius of the
acceleration will a.
arc is decreased to one-half, the centripetal acceleration is changed to b.
(one-half, one-fourth, two times, four times) its original value.
1.6
An object falls toward the surface of the earth, traveling 120 feet in a given period of time.
The gravitational acceleration of the moon is one-sixth that of the earth; therefore, the object
would fall a a.
(greater, shorter) distance in the same period
of time as it falls toward the surface of the moon. Specifically, it would fall b.
✍
feet.
Solve these problems.
1.7
If a car previously traveled at 15 mph but now covers the same distance in half the time,
calculate its velocity.
1.8
If an object moved at 30 m/sec and at a later time covers half the distance in the same time,
calculate its new speed.
1.9
A car turns a corner that has a radius of 5 m and experiences a centripetal acceleration of 20
m
/sec . If the radius of turn were increased to 10 m, calculate the centripetal acceleration.
2
5
1.10
A stone whirled on a string experiences a centripetal acceleration of 10 m/sec . If the string were
shortened to half its length (one-half the radius) and the speed were doubled, calculate the
centripetal acceleration.
1.11
A car undergoing uniform acceleration travels 100 meters from a standing start in a given
period of time. If the time were increased by a factor of four, calculate the displacement.
2
DYNAMICS
You may wish to review LIFEPAC 1202: the
vocabulary words and the concepts of force,
conservation of momentum, gravitational force
fields, Newton’s laws of motion, and Kepler’s laws
of planetary motion.
Dynamics is the study of forces and of their
effects on objects. Through brilliant intuition and
with no experimental confirmation, Newton
declared that force tends to produce proportional
acceleration: no force, no acceleration; small force,
small acceleration; and so on. The ubiquitous force
is gravity. It is, conveniently, a uniform
acceleration. Springs and rubber bands do not
exert uniform forces and are, therefore, not as
useful for study on this elementary level.
Force is simply a push or a pull. Force is
proportional to mass and to acceleration,
Force. An object in the state of rest or in the
state of uniform linear motion continues in that
state unless a net (unbalanced) external force acts
on it. A car moving in a straight line at constant
speed does so only because the friction in the drive
train, the tires, and the wind resistance are
balanced by the action of the engine. Removing
your foot from the gas pedal produces a reduction
in the velocity; therefore, external forces must be
present. Except for the pull of gravity, the planets
would move in straight lines; instead, they orbit in
elliptical paths around the sun.
A more massive car has more momentum than a
smaller car traveling at the same speed. If several
objects have the same mass, the object with the
greatest speed has the most momentum.
Momentum is a property of all moving objects.
A change in momentum (∆mv), either from zero or
from a finite value, is produced when the object
undergoes acceleration:
F = ma
Mass and acceleration are inversely proportional
to each other. As mass increases, the acceleration
produced by a force decreases.
Momentum. Momentum is the product of
mass and velocity and is, therefore, proportional to
both mass and velocity. Mass and velocity are
inversely proportional to each other.
momentum ⬀ m
momentum ⬀ v
v ⬀ 1/m
F = ma
F = m ∆v/∆t
F∆t = m∆v
6
The left side of the equation, simplified to F•t, is
called impulse. An impulse—a force acting during
some time interval—causes a change in
momentum. Both momentum and impulse are
vector quantities.
F=(mman) (g)
The weight of a man 8,000 miles above the
surface of the earth (12,000 miles from its center,
equal to three earth radii) is one-ninth his weight
on the surface. If an object weighs 10 pounds at 5
radii, then on the surface of the earth (1/5 of 5 radii),
the object will weigh more by a factor of the inverse
of (1/5)2: The object will weigh 25 times more, or 250
lbs. The weight of an object is a measure of
gravitational force.
The centripetal force that causes planets to
orbit the sun is gravitational attraction. Kepler
tried unsuccessfully to measure that force. Newton,
through the use of calculus, finally derived it.
Kepler, however, did determine that planets moved
not in circles but in elliptical orbits, that planets
sweep out equal areas in equal times, and that the
period of revolution (“year”) squared by the
distance cubed is a constant for all planets.
Another way of stating this last discovery is
Gravity. When the force under consideration
is the gravitational attraction close to the surface
of the earth, the symbol a is changed to g:
F= mg;
g is 9.8 m/sec or 32 ft/sec . The force of gravity obeys the
inverse square law:
2
2
F=G
m1•m2
d2
G is the universal gravitational constant:
(6.67•10-11 N m /kg ), m1 and m2 are the masses of the
two objects, and d is the separation of the two
objects measured from the centers of mass. At
4,000 miles from the center of the earth (the
surface), a man experiences a force:
•
F=G
2
2
TA2 = TB2 = … = TX2 = K,
RB3
RX3
RA3
mearth mman
(radius of earth)2
where TA is the time Planet A takes to orbit the sun
and RA is the average distance of that planet from
the sun. TB and RB are the time and distance for
Planet B.
F = (G m /R ) mman
e
2
The value of the factors in parentheses is g,
9.8 m/sec or 32 ft/sec .
2
✍
1.12
✍
2
Choose the correct answer.
A car that experiences no frictional force is started and caused to move. For the car to
continue in that motion, the gas pedal would have to be used
.
a. at all times
c. infrequently
b. intermittently
d. not at all
Answer these questions and solve these problems.
1.13
A space craft is traveling in space far from any planets or stars. How much force is required
to maintain the space craft’s speed?
1.14
An object experiences an impulse, moves and attains a momentum of 200
is 50 kg, what is its velocity?
7
/sec. If its mass
kg•m
1.15
If the mass in the preceding problem were changed to 100 kg, what would be its velocity?
1.16
Two boys on skates push off from each other. The 40-kg boy moves to the left at 10 m/sec .
If the other boy moves to the right at 8 m/sec, what is his mass?
1.17
If a force of 60 N is exerted on a 15-kg object, calculate the acceleration that the object undergoes.
1.18
A force exerted on an object produces an acceleration.
a. If the mass is doubled, the acceleration is
.
.
b. If the mass is reduced by one-third, the acceleration is
c. If the mass remains the same and the acceleration is doubled, the force must be
.
1.19
What is the weight of a 3-kg object on the surface of the earth?
1.20
Jupiter’s gravitational field at the surface is approximately three times that of the earth.
A person weighing 120 lbs. on the earth’s surface would weigh how much on Jupiter?
1.21
An object weighs 3 lbs. at 10 earth radii from its center. What is the object’s weight on the
earth’s surface?
3
∆tB
2
AREA
B
SUN
AREA
A
4
1.22
1
∆tA
Referring to the sketch of a planet around the sun, Area A is three times that of Area B.
Compare the times required for the planet to travel from Point 1 to Point 2 and from Point 3
.
to Point 4 and choose the correct answer:
a. ∆tA is equal to ∆tB.
d. ∆tA is nine times ∆tB.
b. ∆tA is three times ∆tB.
e. ∆tB is nine times ∆tA.
c. ∆tB is three times ∆tA.
8
1.23
Planet A takes one year to go around the sun at a distance of one A. U. (astronomical unit).
Planet B is three A.U. from the sun. How many years does Planet B take to orbit? Choose
the closest answer.
a. 3 years
c. 7 years
b. 5 years
d. 9 years
ENERGY
PE = (mg)•h
or
PE = weight•height
You may wish to review LIFEPAC 1203: the
vocabulary words and the concepts of conservation
of energy, kinetic and potential energy, and power
and efficiency.
Energy is the ability to do work.
Mathematically,
energy
and
work
are
interchangeable. Both are expressed in joules (j).
When work is purchased, energy is spent. The rate
at which energy is spent, or work is done, is power.
The right-hand term represents the minimum
work required to raise the object to height h.
The potential energy of an object propelled by a
spring is
PE = F•d
or
PE = mad
Kinetic energy. Kinetic energy, the energy of
motion, is proportional to the mass and the square
to the velocity.
In the first case, F is the average force the spring
exerts on the object (a spring does not exert a
uniform force); and d is the distance through which
the spring is in contact with the object. In the
second case, m is the object’s mass; and a is the
average acceleration imparted by the spring.
KE = 1/2 mv2
A car that travels three times faster has nine times
more kinetic energy than before.
Potential energy. Potential energy is the
energy of position. It is commonly expressed
Power. Power is the rate at which work is
done or energy is expended.
PE = F•d,
P = W/t
which shows that an object’s potential energy
equals the work (F • d) required to place it in its
position in a gravitational field,
Two elevators can lift equal loads up 30 feet. Both
elevators do the same amount of work; however,
one elevator does it in less time. It has more power.
PE = mgh
Efficiency. Efficiency compares the work
output to the input and is usually expressed as a
percent.
where m is mass, g is the acceleration of gravity,
and h is the height of the mass. The preceding
equation can be rewritten
efficiency = work output
work input
✍
1.24
•100%
Choose the correct answer.
Car A has twice the mass of Car B; both travel at the same speed. Compared to Car B, Car
A has
the energy.
a. one-fourth
d. twice
b. one-half
e. four times
c. the same
9
1.25
Cars A and B have the same mass, but Car A’s speed is 15 mph, whereas Car B is moving at
times that of Car A.
60 mph. The kinetic energy of Car B is
a. 1/16
d. 4
b. /4
e. 16
1
c. 2
1.26
Two bricks of the same mass are each on ledges. Brick 1 is 100 feet high and Brick 2 is 300
times more potential energy.
feet high. Brick 2 has
a. zero
d. three
b. two
e. nine
c. four
✍
Answer these questions.
1.27
Why is more damage done and more life endangered in a head-on collision of two cars each
traveling at 30 mph than in a car crashing into a brick wall at 30 mph?
1.28
Two rope tows operate on the same ski slope. When both are operating with equal loads, Tow
A can move faster than Tow B.
a. Which does the most work?
b. Which has the most power?
1.29
Two rope tows operate on the same ski slope. Tow A with a heavier load pulls as fast as Tow B.
a. Which does the most work?
b. Which has the most power?
✍
1.30
Complete these calculations.
A motor has electrical energy equivalent to 400 joules of work. It can lift a 5-kg mass 2 meters.
a. Calculate the work done by the motor.
b. Calculate the efficiency of this motor.
Review the material in this section in preparation for the Self Test. This Self Test will
check your mastery of this particular section. The items missed on this Self Test will indicate
specific areas where restudy is needed for mastery.
10
SELF TEST 1
Match these items (each answer, 2 points).
1.01
change in displacement with respect to time
a. velocity
1.02
discovered the laws governing the orbits of planets
b. energy
1.03
weight
c. acceleration due to gravity
1.04
9.8 /sec2
d. centripetal acceleration
1.05
ratio of work output to work input
e. gravitational force
1.06
spent energy
f. momentum
1.07
rate at which work is done
g. work
1.08
constant speed in a circular path
h. power
1.09
product of mass and velocity
i. efficiency
1.010
deduced the inverse square law of gravity
j. Newton
m
k. Kepler
Choose the correct answer (each answer, 2 points).
1.011
Two moving objects have the same momentum. Object 1 has three times the mass of Object
the velocity of Object 2.
2; therefore, Object 1 has
a. the same
d. three times
b. one-third
e. nine times
c. one-ninth
1.012
As an object falls,
.
a. both velocity and acceleration increase.
b. velocity increases and acceleration decreases.
c. velocity increases and acceleration is unchanged.
d. both velocity and acceleration remain unchanged.
1.013
1.014
1.015
An object on the surface of the earth weighs 90 lbs. At three earth radii above the surface, it
.
will weigh
a. 90 lbs.
c. 10 lbs.
b. 30 lbs.
d. 270 lbs.
A car turns a corner at 10 mph. If it were to turn the corner at 30 mph, the centripetal
.
acceleration would be
a. nine times larger
c. one-third as large
b. three times larger
d. one-ninth as large
A man and a fork-lift truck lift equal masses ten feet vertically. Of the following statements,
the correct one is
.
a. the man does more work than the fork lift
b. the fork lift does more work than the man
c. they do the same amount of work
d. insufficient information is given to compare the work done by the man and the fork lift
Solve these problems (each answer, 5 points).
1.016
Calculate the efficiency of an engine if the work input is 3,000 J and the work output is 1,000 J.
11
1.017
Planet A takes 1 year to go around its star at an average of 1 A.U. distance. Planet B is 4
A.U. from the star. Calculate how long Planet B takes to orbit.
1.018
A cart of mass 100 kg has a velocity of 20 m/sec. Calculate its kinetic energy.
1.019
The moon’s surface gravity is one-sixth that of the earth. Calculate the weight on the moon
of an object that has a mass of 24 kg.
1.020
Two hockey pucks on an ice rink are held together with a compressed spring between them.
The pucks are released and the spring pushes them in opposite directions. One puck of mass
0.5 kg moves at 8 m/sec. Calculate the speed of the other puck of mass 2 kg.
Score
Adult check
44
55
______________________
Initial
12
Date