Grade 12 Unit 10
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. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates’, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
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.
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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
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. makes no claim of ownership to any trademarks and/or service marks other than their own and their affiliates’, and makes no claim of affiliation to any companies whose trademarks may be listed in this material, other than their own.
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
