Homework Assignments for Physics 104

Assignment 1. Due Thursday, February 4, 1999
 

  1.  Join the HyperNews group (link available from our web page).
  2. Post a message under First Homework Assignment. This message should be titled with your name and should include where you are from, what your major is and anything else you wish to share with the class
  3. Come to Professor's Goodman's office (room 4324) and check your name off the list.
Do the following exercises from the book on page 20:

5, 11, 16, 22

Do the following problems from the book on page 21:

1, 3, 10, 11, 12

Solutions to assignment 1
5.  Because the mass of the anvil is larger, the anvil resists
acceleration more than the steel plate, and will not move as much when the
blacksmith strikes a piece of hot metal against it.  The hot metal
consequently gets squeezed between the moving hammer and the stationary
anvil.

11. South.  Stopping (slowing down) requires an acceleration in the
direction opposite to the direction of motion.

16.  The acorn's velocity is not constant; it takes time for it to
accelerate from 0 to -9.8 m/s.  The acorn would only reach the ground in 1
second if it were falling at a constant velocity of 9.8 m/s.  Since it
takes time to speed up to 9.8 m/s, it must take longer than 1 second to
reach the ground.

22. The person must jump up, because gravity will accelerate him
downwards while he is jumping between buildings.

1. F = ma  = 800kg*4m/ss = 3200N

3. v = v_0 + a t = 0 m/s + 3.71 m / s^2 * 3 s = 11.13 m/s

10.   Weight is a force, so
         w = f = ma
         On Earth, a = g = 9.8 m/(s^2)
         w = 60kg*9.8m/ss=588N

11.  When the person stops rising (at the top of the jump) his velocity
is zero.

       v=v_o+at
       => 0 m/s = 2 m/s - gt = 2m/s - 9.8 m/s^2 * t
       => 2 m/s = 9.8 m/s^2 t
       => t = .204s

12. To calculate how high you are when you stop rising, use the formula
for displacement:   x = x_0 + v_0 t + (1/2) a t^2

where

 x_0 = 0
 v_0 = 2 m/s
 t = 0.204 s
 a = -g = -9.8 m/s^2

Solving the equation for x yields a height of  .20 m.
 
 

Assignment 2. Due Thursday, February 11, 1999

Finish Reading Chapter 1

Do the following exercises from the book on page 33&34:

1, 8, 12, 19, 22, 28, 29 ,31

Do the following problems from the book on page 34:

1, 4, 7, 11

Do the following exercises from the book on page 50:
1,  2, 12, 13
 

Solutions to assignment 2.

Page 33,34

1. Both the floor and the barbell experience their weights.  The floor exerts a large upward force on the barbell and the barbell exerts an equal but opposite downward force on the floor.

8. Both times: Pulling it in and reeling it out both require exerting a force over a distance.

12. 0, Newton’s law: If speed is constant, net force equals zero.

19. 850N in the opposite direction

22. Both pulling and pushing the saw requires work.

28. Gravity.  The hill causes some of the skater’s weight to oppose their motion by acting in the direction opposite to the direction of motion.

29. Transferred into gravitational potential energy you get from attaining a height above the Earth’s surface.

31. Stamping causes your foot and the snow on it to accelerate, when you rapidly change the direction your foot is accelerating, the snow keeps accelerating the original direction and flies off your foot.

Page 34.

1. Since the ramp moves you up 1m for every 20m traveled, it cuts the force required by a factor of (1/20).  The weight of the brick is 20,000kg*9.8=196,000N.  196,000N*(1/20) = 9,800N

4. Potential Energy = (1000kg)(200m)(9.8m/ss) = 196,000J

7. Work = Force * Distance
    25N*.5m = 12.5J

11. Gravitational PE = Mass * Height *Acceleration of Gravity
     (380m)(60kg)(1.6m/ss)=36,480J

Page 50.

1. Torque = Force at a distance from the axis of rotation.  Here there is no distance from the axis so there is no torque.

2. Torque is generated by a force applied perpendicular to the to the radius of rotation.  When you apply the force directly along the axis there is no force perpendicular to the radius of rotation and consequently no torque produced.

12. Same as the example in class with the scissors and the chalk: At the back
of the jaw the teeth are closer to the axis and consequently there is more force being applied through a shorter distance resulting in more crushing power.

13.  Weight on the unbraced shelf will generate a torque causing the board to collapse downward against the wall.  Bracing the board provides a torque to oppose the torque generated by the weight of objects on the shelf.
 

Assignment 3. Due Thursday, February 18, 1999

Look over cases on Pages 72-76 at the end of Chapter 1

Do the following problems from the book on page 50:

1, 2, 5, 9

Do the following exercises from the book on page 70 & 71:

1, 4, 7, 9, 14, 24

Do the following problems from the book on page 71:
1,  5, 6, 9, 10

Solutions for Homework 3
Problems, p. 51

1.  Torque = Force * lever arm = 700 N * 0.175 m = 122.5 N/m

2.  Here, the torque is zero, because the force has no component that is
at right angles to the lever arm.

5.  Torque = Rotational Inertia * Angular Acceleration = I*alpha.  To
increase the angular acceleration by a factor of three, we must also
increase the torque by a factor of three.

9.  The torque is the same at both points, but the forces are different
because they are exerted at different distances from the pivot.

Let r be the distance from the pivot to the nut.  I am using "T" for
torque.

Let F1 be the force of your hand on the end of the nutcracker (F1 = 20 N).
Let F2 be the force of the nutcracker on the nut.

Then,

  T = 5r*F1 = r*F2.

Cancel the r's.  Then,

  F2 = 5*F1 = 5*20 N = 100 N.

The interesting thing about this problem is that we don't need to know the
distance r to find F2.

____________________________________________________________

Exercises, p. 70

1.  Angular momentum.  Since there is no net torque acting on the wheel,
and very little friction, the wheel will keep spinning for a long time.

4.  For the same reason an air bag helps during a car crash.  The leaves
increase the amount of time over which your velocity goes to zero.  You
can think of it like this:

Change in momentum = force * time = mass * change in velocity = constant

So if the time over which the force is applied is increased, the force
required to stop you will be less at any given time.

7.  The skier uses his kinetic energy to do work against sliding friction,
which creates heat.

9.  The rolling pin experiences *static* friction, like a wheel.

14.  The sprinter has to do work against sliding friction, and the
transferred energy becomes heat.

24.  L = I*angular velocity must be conserved.  I is greater when mass is
further from the center of the Earth.  So, when snow melts and the water
runs down the mountains, I decreases.  Therefore, to keep L constant, the
angular velocity must increase.

________________________________________________________
 

Problems, p. 71

(I will use w instead of omega to represent the angular velocity, and T
instead of tau for torque).

1.  K = (1/2) I*w^2
 Let I' = 5*I.
 Let w' = w'/5.

 Then, K' = (1/2)*(I')*(w')^2 = (1/2)*(5I)*(w/5)^2 = (1/2)I*w^2/5
     = K/5.
 Therefore, K' = K/5.

 *Note* A lot of people weren't quite sure what notation to use and
 gave answers like "K = 1/5."  I hope this solution helps a little.
 

5.  p = m*v = (800 kg)*(3 m/s) = 2400 kg m/s forward.

6.  Impulse = change in momentum

 Ft = p
 => t = p/F
      = (2400 kg m/s)/200 N  = 12 s
 (we calculated p in problem 5).

 *Note* Lots of people used F = ma.  That works, too.  This is
 easier.

9.  Momentum is conserved, so 450 kg m/s right.

10.  p = mv = (6 kg)*(5 m/s) = 30 kg m/s.
 

Assignment 4. Due Thursday, February 25, 1999

Answer the following questions from the book on page 261:

1, 2, 5, 7, 9

Do the following exercises from the book on page 262:

4, 7, 9, 10, 19, 21, 22

Solutions for Homework 4.

Solutions for Homework IV

Page261

1. Chemical energy stored in the stick gets transferred into thermal energy (heat).
2. These atoms are held together in the sense that it takes energy to separate them, to move them away from each other.

5. The paper represents a stable configuration of atoms bonded together.  To release the potential in these bonds requires a chemical reaction (burning).  Starting this reaction, however, requires a certain amount of energy called activation energy.  If you light a piece of paper with a match, the lit match is supplying the activation energy.

7. Heat itself does not rise only the heated fluid rises.  Fluids change density when heated and it is this change in density that causes heated air to rise.

9. Conduction, convection and radiation are all mechanism which transfer heat without transferring atoms of molecules.

Page 262

4. The foil reflects the radiated thermal energy from the heating element which is on one side and absorbs heat through conduction evenly across the foil’s surface.  This in turn distributes the thermal energy to the food more evenly.

7. The fire sets up a convection current in the air in the fireplace.  If the wood is raised above the ground air can be more easily supplied to the fire from underneath.  If the fire is well supplied with air it will burn better.

9. A blackened one will absorb more thermal radiation than a shiny one. The shiny one will reflect thermal radiation.

10. Radiation.  Thermal energy can radiate through space.  Heat from the sun is transferred to Earth through radiation. The shuttle has radiators in the cargo bay.

19. The jets in the whirlpool move the water around much faster than before causing the heated water to be circulated, replacing water that had cooled down next to your skin with hotter water.

21. This an example of convection.  Air heated by the Earth rises and gets carried out over the water where it cools and consequently sinks. This cool air is then drawn back toward the warmer land resulting in a strong land breeze.

22.  Because warm air rises, any warmer air in the refrigerator compartment will rise.  If the freezer is place at the top, all the rising warmer air will be cooled when it rises to the top.  If the freezer were at the bottom, warmer air could settle at the top causing a temperature gradient within the refrigerator.  This sets up a convection current.
 

Assignment 5. Due Thursday, March 4, 1999

Do the following exercises from the book on page 274:
1, 2, 4, 6, 8

Do the following problems from the book on page 274:
1,  3

Do the following exercises from the book on page 282:
1, 2, 10, 16

Do the following exercises from the book on page 290:
1, 5, 9

Also Read and Study the cases on pages 291 - 292.

PHYS104 HW5 Solutions
3/11/99

_________________________________________________________________

p. 274 (Exercises)

1)  The more volume the down takes up, the more air is trapped.  Air is a
good insulator.

2)  When there is a difference in temeperature between the top and bottom
of the soup, convection currents are set up.  The hot soup moves to the
surface and cools off.  In thicker soup, it is harder for this to happen.
So, the thicker soup stays hotter longer.

Many of you answered that the thermal conductivities of thick and thin
soup are different.  Although this is probably true to some extent, I am
not sure how significant it is.  No matter how thick your soup is, it is,
after all, mostly water and I doubt that there is *that* much difference
in the thermal conductivities.

4)  The air provides an insulating layer between you and the metal.
The metal has a very high thermal conductivity and so will burn you
instantly.  The air, however, is a poor conductor and so it will take much
longer for heat to pass through it and into you.

6)  The conductivity of the tile floor is greater than that of the mat,
which has lots of insulating air trapped in its fibers.  See p. 273, #4.

8)  This is basically the opposite of wind chill (see the section on
Convection).  After your arm sits in the warm water for a while, the water
right around your arm comes to equilibrium with your arm, i.e., heat flows
out of it and into you.  So the water cools off.  When you move your arm
through new water, that water has not had time to reach equilibrium with
you yet.  So it feels warmer, because it is.

______________________________________________________________________
 

Problems, p. 273

1)  P = e*Stefan-Boltzmann Constant*T^4*A
    e = 1 for a black object
    T = (800 + 273.15)K (about half of you forgot to convert to Kelvin)
    so P = 1*5.67e-8 J s^-1 m^-2 K^4 * (1073.15 K)^4 * .25 m^2
         = 1.88e4 W = 18.8 kW (1 J/s = 1 W).

It is a good idea to put in units when you solve the equation for P, not
just in your final answer.  It helps you remember to convert the
temperature to Kelvin, and also you can check to see if your answer has
the right units.  Just my $0.02; of course you don't have to do this.

3)  P = e*Stefan-Boltzmann Constant*T^4*A
      = 1*5.67e-8 J s^-1 m^-2 K^-4 * (6000K)^4
      = 7.35e7 W = 73.5 MW

_________________________________________________________________________
 

p. 282
 

1)  It sublimes.

2)  At lower temperatures (dimmer light), the bulb is *less* efficient
because its spectrum is shifted towards the infrared range (i.e., it emits
less *visible* light, and more heat).  This is a waste of energy.  See
Fig. 6.3.4 on p. 277.

10)  They determine the wavelength at which the star emits the most light.
From this, they can estimate the temperature.

16)  The filament can be heated to extremely high temperatures, *much*
higher than body temperature.  So, by the Stefan-Boltzmann Law (P ~ A
T^4), lots of power will be genrerated.  Althugh the area of the filament
is much much less than that of the human body, the power depends on the
fourth power of T and only the first power of A.

p. 290

1)  Cars are made of different types of metal, which have different
coefficients of thermal expansion.  So, as the car cools, some parts will
contract faster than others, causing bending.  That is why you hear
creaking noises.

5)  The cookie sheet bends for two reasons.  First, it heats unevenly, so
some parts expand more than others.  Secondly, it may be made of different
types of metals, with different coefficients of thermal expansion.

9)  The metal lid has a higher coefficient of volume expansion than the
glass jar.  So, the lid expands faster and the jar opens more easily.

Many of you said that the lid expands.  But that's not enough, because the
jar expands, too.  The important part is that the lid expands *more*.
 
 

Assignment 6. Due Tuesday, March 16, 1999

Read Chapter 7

Answer the following Questions on pages 303-304:
3, 6, 8, 11
Do the following exercises from the book on page 304:
2, 3, 6, 9, 11, 12, 14

Solutions for Homework VI

Pages 303-304

3. The first Law of Thermodynamics is a restatement of the conservation of energy because the law states that an object’s energy is equal to the energy flowing into it minus the energy it expends doing work.  Since this law accounts for all of the energy flowing into and out of the system it is basically saying that energy cannot be created or destroyed-a restatement of the law of conservation of energy.

6. If an object loses entropy its temperature is going to drop by the third law of thermodynamics.  Since entropy never decreases, the entropy of the object’s surrounding must increase.  When the entropy of the surrounding environment goes up, so does its temperature.

8.  The cold water.  Think of the example where you have a party of old people and a party of hyperactive four-year olds.  Transferring an old person to the four-year olds’ party will have little effect.  Transferring a four-year old to the old people’s party will have a significant effect.

11.Since an air-conditioner moves thermal energy from a cooler object to a hotter one (decreasing entropy), to obey the second law of thermodynamics, it must create enough entropy so that the total entropy of the system is increasing.  The creation of this added entropy requires ordered energy.

Page 304

2. The refrigerator removes heat from its interior and transfers it to the surrounding room.  When you open the door you are raising the temperature inside the refrigerator.  The refrigerator will consequently removes this added heat back into room expending energy in the process.  The heat from the interior of the refrigerator combined with the heat the refrigerator produced doing the work to lower its temperature get dissipated into the surrounding room and as a result make the room warmer.

3. The temperature of the gas rose.  The work gravity performed on the gas by compressing it manifests itself as thermal energy.  The added thermal energy in the gas makes it hotter.

6. Compressing a gas raises its temperature.  Work is being performed on the gas which comes out as thermal energy.  This thermal energy then gets transferred to the pump making it hotter.

9. The gas in the container does work to push out the gas leaving the container.  By performing work this gas loses some of its thermal energy and thus its temperature drops.

11. It transfers heat from the house to the outdoors.

12. It transfers heat from the outdoors to the interior of the house.

14. It will increase.

Assignment 7. Due Tuesday, March 30, 1999
Answer the following Questions on pages 316:
1, 3, 4, 7, 9, 10
Do the following exercises from the book on page 316:
5, 11, 12, 15, 16
Also Read and Study the cases on pages 316-317.

Solns to HW7 (Chapter 7)
4/4/99

p. 316, Review Questions
1) It increases.  See the discussion on p. 299, particularly, the example of the 4 year-old at the tea party.
3) The heat engine needs sources of both thermal energy and order to operate; the cold object is the source of that order.  The heat engine transfers heat to the cold object, so that the overall entropy increases and the 2nd Law is satisfied.
4) Greater temperature difference -> greater efficiency.

7)  The piston compressing the fuel/air mixture does work on the mixture.  This causes the internal energy of the mixture to increase.  This increase in internal energy shows up as an increase in temperature and the mixture heats up.
9) A diesel engine avoids preignition (knocking) by introducing the fuel/air mixture just as the power stroke begins.

The efficiency of either a gas or diesel engine is limited by the following factors:
? All the thermal energy of the burned gas cannot be converted into work (2nd Law).
? Leakage of heat from the burned gas into the cylinder walls.
? Sliding friction.

See pp. 310-311 for a complete discussion.  As long as you gave one of these reasons I gave full credit.
10) The transmission can decouple the engine from the wheels.

Exercises, p. 316
5) Heat flows from the hot object (the sun) to the cold object (the house).
11) Work must be done during the compression stroke.  Since there are no other cylinders, the work must be done by the blade.  Without the blade, the compression step could not happen.
12) On a hot day, the fuel-air mixture will be hotter and thus easier to ignite prematurely.
13) When the gas is compressed, work is done on it.  Its internal energy will increase, causing it to heat up.

16)  The first fan does work on the air.  The air does work on the second fan.
 
 

Assignment 8. Due Tuesday, April 6, 1999
Answer the following Questions on page 385:
1, 4, 7, 9
Do the following exercises from the book on page 385:
2, 3, 5, 11, 12
Do the following problems on Page 385:
1, 4
Answer the following Questions on page 394:
2, 4, 8
Do the following exercises from the book on page 395:
2, 4,  6, 7, 9, 18
 
 

Solutions For Homework VIII
 

 Page 385 Questions
1. Dust does not fall at that rate due to buoyant force and the viscous drag force.

4.  Charge is conserved it cannot be created or destroyed.

7.   Since like charges repel, bringing positive charges to the positively
      charged ball requires a force.  Since the particles need to be moved
      through a distance with this force , you are doing work.

1. The paper becomes polarized.  Inside the neutral paper charges are moving due to the presence of the spoon.  Charges attracted to the spoon will move in the material to get as close to the spoon as possible and charges repelled by the spoon will move in the opposite direction to the get far away from the spoon.  The paper is still neutral but the charges within it have been rearranged.

Page 385

2. Since charge of the same sign repels itself and in a metal is free to move, it moves to the outside of the conductor to get as far away from itself as possible.
3. Since the paint or coating is charged it will attract opposite charges in the
     material to which it is being applied.  It will polarize the material.  This
attractive force between the coating and the material helps fix the coating to the surface.

5. Neither. The forces, which slow the descent of dust on earth, are due to the Earth’s atmosphere.  Since the moon has no atmosphere these forces are not present and both objects will behave in the same manner.

11.  A Corona discharge occurs at the tip of the needle removing charge
       from you and putting it into the air.
12. The glow is caused by corona discharges from the wire into the air. This happens when there is a strong electric field. It is stronger at the joints because the joints have sharp points. At sharp points the field is strongest and therefore so is the glow.

Page 385

1.  Using Coulomb’s Law:
             Force = (Coulomb Constant*charge1*charge2)/Distance^2
     Since charge1=charge2
    Force = (Coulomb Constant* charge^2)/Distance^2

          Force = .001N
 Distance = .01m
          Coulomb Constant = 8.988*10^9 N*m^2/C^2

         Solving for charge yields an answer of  3.3*10^-9 C

4. Using Coulomb’s Law:
           F = (8.988*10^9 N*m^2/C^2) *(1C)*(1C)/(384,500,000m^2)
           F = 6.08 *10^-8 N
 
 

Page 394
2. Two electrons can occupy the same quantum level, when they have different spins.

4. The material in which the electrons fill all the way up to the middle of the band is a metal. When charge is applied nearby, the balance of electrons in the material will be offset causing a net flow of charge through the material.  The material in which the electrons fill up the levels up to the top of the band is an insulator and consequently there will be no net flow of electric charge when charges are applied nearby.

8. If you place a small positive charge in an electric field it will experience a force which will cause it to accelerate.  The direction of field is the direction in which the charge will accelerate, since it is positive it will move away from a positive charge.  The magnitude of the field determines how much force the charge will experience.

Page 395

2. If the electron had four possible internal states, four electron could occupy the same level without violating the Pauli exclusion principle.

4. It increases the semi-conductors ability to conduct electricity.

6.  As an insulator, when it is dark photoconductors behave as insulators.

7.  The red light does not have enough energy to shift electrons from the valence level to the conduction level in the photoconductor.

9. Since the light passing into the semi-conductor is absorbed in the process of transferring electrons between levels, it does continue on and pass through the material.  Since light does not pass through, you cannot ‘see’ through- it is opaque.  In an insulator, light does not usually raise electrons from the valence levels to the conduction levels thus it passes right through the material. Since light goes through it, you can ‘see’ through it and it is opaque.

18.   All of the charge in the metal object behaves as if it were concentrated in the point.  Thus the field is very strong near the point and the field lines of the electric field are close together near the point.
 

Assignment 9. Due Tuesday, April 13, 1999
Answer the following Questions on pages 405-406:
4, 5,
Do the following exercises from the book on page 406:
1, 5, 8, 11, 14
Read and study the cases at the end of the chapter (Page 407).

Solutions to HW9 (Ch. 11)
4/20/99

________________________________________________________________________

Review Questions, p. 405

4)  Anything that involves moving charge also involves a current.  This
means that the negatively charged falling ball, the spinning battery, and
the loop of wire with charge flowing through it all involve a current.
However, no current is associated with neutral objects or charged objects
that are not moving.

5)  For our purposes, we can consider the electron to be a spinning
charged object, which behaves like a small current loop, and therefore
acts like a dipole magnet.  See p. 398.

________________________________________________________________________
 

Exercises, p. 406

1)  The fast-moving car has less time to acquire the upwards velocity
needed to pass over the bump.  So, the car's upwards acceleration is much
greater, and the upward force on the car (remember, F = ma) will also be
much greater.  So, your car is damaged less if you drive slowly over speed
bumps.

5)  Both the pencil and the magnets are examples of systems in unstable
equilibrium.  Although they are temporarily at equilibrium, the
slightest disturbance will cause the system to fall totally out of
that equilibrium.

8)  Current flows through the filament loop, inducing a magnetic field.
In fact, a loop of current is essentially a magnetic dippole (see Fig.
11.3.1, p. 398).  The field of this dipole interacts with the field of the
permanent magnet.

11)  North, because of Lenz' Law (p. 401).

12)  The magnet induces currents in the coins, which in turn induce
magnetic fields.  The coin's induced magnetic poles then repel those of
the permanent magnet.  A coin that is a good conductor allows more current
to flow, thus, a larger magnetic field is induced and the repulsion is
stronger. This repulsion causes magnetic drag, just like for a Maglev
train; the drag slows the coin down (see p. 402).  Because there is more
repulsion for the better-conducting coins, they slow down more.
 
 
 

Assignment 10. Due Thursday, April 22, 1999
Answer the following Questions on page 419:
1, 4, 10, 11
Do the following Exercises from the book on page 420:
4, 8, 10, 14
Do the following Problems from the book on page 420:
1, 3, 7, 8
Answer the following Questions on page 429:
2, 3, 8, 11
Do the following Exercises from the book on page 430:
4, 7, 12, 14
Do the following Problems from the book on page 430:
1, 2, 3, 7
 

Solutions to Homework X

Questions on page 419: 1, 4, 10, 11.

1. Counterclockwise.  Current is defined as the flow of positive charge.  Since electrons are negatively charged, electrons moving in one direction is the same as positive charge flowing I the opposite direction.
4. The circuit needs to be closed so that electrons can flow and not accumulate somewhere along the path.  If electron accumulated along the path they would repel the flow of additional electrons.
10. The voltage increases.
11. The voltage decreases.

Exercises from the book on page 420: 4, 8, 10, 14.

4.  The higher voltage is the on the strip through which the current enters.  Voltage is lower when it leaves because the current has done work (heating the window) which required energy.  Since voltage is like the potential of the current, the potential of the current leaving is lower because it ‘used up’ some of its potential doing work.

8.  If he touched the wire and the pylon simultaneously he would have been closing the circuit between the wire (High Voltage) and the pylon (Low Voltage) with his body.  This would have resulted in a large current flowing through him, which can be painful and or deadly.

10. Since current is flowing into your hand from the battery, electrons are flowing out of your hand, but as many are going in as coming out so you accumulate NO net electric charge.
14. By creating a circuit with the two batteries connected in series you can tell which is terminal is positive and which is negative.  If the batteries are connected at opposite terminals you can add voltages giving you have a voltage of 3 which makes the bulb glow the bulb glows.  If you have them connected so that the batteries are joined at a similar terminal you have to subtract voltages, giving you a net voltage of 0 and the bulb will not glow.

Problems from the book on page 420: 1, 3, 7, 8.

1. P = I*V
12W = 12V*I
I = 1 amp

3.   P =  (1.5V + 1.5V)*. 05amp = 3V*.05amp = .015W

5. In the first flashlight:  P = 2 amp *1.5V= 3W
In the second flashlight: P = 2amp* 4.5V = 9W
Since the question asks for the power per battery, must divide 9W/number of batteries, thus 9W/3 = 3W

8. P = 2amp *6V= 12W

Questions on page 429: 2, 3, 8, 11.

2. Since a thicker wire has a smaller resistance than a thinner one and since resistance and voltage drop are proportional, a thicker wire has a smaller voltage drop than thinner one for a given current.
3. Since current and voltage drop are proportional, doubling the current also doubles the voltage drop.  Inserting these values into P = IV we get P = 2I*2V = 4*IV.  Thus since the total power is multiplied by 4, the amount of power wasted is multiplied by 4.
8. Transformers operate on the electromagnetic principle that a changing electric field (in the primary coil) creates a magnetic field.  Since a changing magnetic field creates currents (in the secondary coil), you need a changing current to generate this changing magnetic field.  If the current was constant you could not generate a changing magnetic field and thus not generate a current in the secondary coil.
11. The current in the low -voltage system will be higher than the current in the high-voltage system.

Exercises from the book on page 430: 4, 7, 12, 14.

4. The fuse will allow too much current to flow and the current could heat up an element of the circuit enough to ignite and cause a fire.
7.  The circuit is wired in series with the outlets coming before the room lights.  Thus
Plugging in something which consumes a lot of power (like a hairdryer) lowers the
       voltage of the current when it gets to the lights  making the lights appear dimmer.
12. In the same way as a transformer.  The current in the transformer magnetizes the iron core in the toothbrush, which in turn creates a current in the coil around the core, which then transfers power to the toothbrush.
14. Since the secondary coil makes 1/3 the number of turns the primary coil does, the resulting voltage in the secondary coil is only 1/3 the voltage of the primary one.

  Problems from the book on page 430: 1, 2, 3, 7.

1. V = I*R
4V = 80A*R
R = (1/20) ohms

2. V = (1/40)ohms*80A
V =  2V

3. V = 20A*.1ohms
V=  2V

7.  P = IV
P = 600A*400,000V = 240,000,000A
 
 

Assignment 11. Due Tuesday, May 4, 1999

Answer the following Questions on page 439:
2, 5, 7, 8
Do the following Exercises from the book on page 439:
2,  8, 9, 14
Answer the following Questions on page 448:
1, 3, 4, 6
Do the following Exercises from the book on page 448:
1, 2, 5, 11
Answer the following Questions on page 458:
2, 5, 8, 11
Do the following Exercises from the book on page 458:
1, 4, 6, 14, 16, 19
 

Solutions to HW11; Motors, Semiconductors, and Tape Recorders
5/13/99

______________________________________________________________________

R.Q. p. 439

2)  See p. 432.  When a magnet and coil move past each other, the flux
through the coil changes and current flows.

5)  Unlike n-type and p-type semiconductors, a pure semiconductor has
neither empty valence levels nor filled conduction levels.  Therefore,
current will not flow.

7)  The p-type side of the depletion region is negatively charged, and
repels electrons.  So, the electron flow and thus the current can only go
in one direction.  Don't forget that, for some strange reason, the
direction of current is defined as opposite the direction of electron
flow.

8)  See p. 436.  When you add positive charge to the n-type material,
conduction level electrons are pulled away from the depletion region and
the depletion region becomes even thicker.
 

p. 439, Exercises

2)  The energy will take several forms; potential energy is stored in the
electric and magnetic fields that are created, and because the Al has some
resistance, there will also be some I^2*R heating (thermal energy).

8)  Sorry, I don't have time to make GIF's for all these pictures.  But
just basically draw Fig. 11.2.4 twice.  Then, for n-type semiconductors,
add are a few extra electrons in the valence band.  For p-type
semiconductors, erase a few electrons from the conduction band.

9)  Adding just the right number of e-'s will fill the valence levels.

14)  As in R.Q. #7, electrons cannot approach the depletion region from
the p-type side and current will not flow backwards through the diode.

p. 446 R.Q.'s

1)  If there were only permanent magnets, the rotor would just align
itself so that its poles were as close as possible to the opposite poles
of the stationary magnets.  Anyway, nothing would move, so you'd have a
pretty useless motor.

3)  The poles should reverse when the poles of the rotor are closest to
the opposite poles of the permanent magnets.

4)  To reverse the current.  Batteries by themselves provide DC, not AC.

6)  Reversing the current reverses the induced magnetic fields in the
electromagnet and thus reverses the torque on it.

p. 448, Exercises

1)  Again, I can't really draw the picture here.  But draw the forces on
the magnet, use the right-hand rule and you will find that both torques
point in the same direction.

2)  A force is exerted over a distance, and a component of that distance
is parallel to the force.  Therefore, work is done.

5)  This is exactly the same question as R.Q. #6.  Reversing the battery
reverses the current.  This reverses the magnetic field of the
electromagnet, and the torque on the electromagnet is reversed.

11)  Rotational inertia.

p. 458, R.Q.'s

2)  In most materials, the electrons pair up and their magnetic fields
cancel.

5)  The domains return to their original size.

8)  It aligns the poles in a particular direction.  The direction and
depth of the polarization depend on the volume of the sound.

11)  The tape is recorded at a constant speed, so the amount of
information stored per unit length of the tape is constant.  You want
information to be played back at the same rate, so you have to play the
tape back at the same constant speed.

Exercises

1)  OK, I realize this isn't the best picture, but it's the best I can do
with ASCII. But the point is that it is *not* all in one direction because
the current is alternating.

-----------------------------------
... S-N   S-N   N-S   S-N   S-N ...
... S-N   N-S   N-S   N-S   S-N ...
... S-N   S-N   N-S   S-N   S-N ...
... S-N   N-S   N-S   N-S   S-N ...
-----------------------------------

4)  The refrigerator becomes magnetized by the magnet.

6)  Same thing.  Steel is a (hard) magnetic material and if exposed to a
magnet, will itself become magnetized.  The magnet magnetizes the first
paper clip, the first paper clip magnetizes the second, etc. and
eventually you get a whole chain stuck together, as opposite poles
attract.

14)  A tape made from soft magnetic material will lose its magnetization
and be erased as soon as it leaves the recorder's magnetic fields.

16)  As in R.Q. 14, tapes use hard magnetic materials and so it is
difficult to change their magnetization.  If the particles already have a
magnetization, and the sound is very soft, the weak magnetic field
produced will be insufficient to knock the particles out of their old
polarization.  You will get both sounds superimposed, which you probably
don't want.

19)  It's attracted to the poles of the magnetic recording particles.
 
 
 

Assignment 12 (The Last One!). Due Thursday, May 13, 1999

Answer the following Questions on page 473:
2, 4, 7, 11
Do the following Exercises from the book on page 473-474:
3, 4, 9, 10, 18
Answer the following Questions on page 498:
1, 3, 8
Do the following Exercises from the book on page 499:
3, 6, 10, 13, 14, 22
Answer the following Questions on page 509:
1, 6
Do the following Exercises from the book on page 509:
8, 11, 12, 13, 14
 

Solutions to Homework XII

Questions on page 473: 2, 4, 7, 11

2. An amplifier boosts a signal without changing the information in that signal thus what comes out of the amplifier must be proportional to what goes in.  For this reason the voltage drop going I should be proportional to the voltage rise going out.
4.  By Ohm’s law: V=I*R
7. The capacitor stores energy as the voltage difference across a
       separation of charge.
11. Placing a charge on the gate of a MOSFET attracts conduction level electrons into the channel will conduct.
 

Exercises from the book on page 473-474: 3, 4, 9, 10, 18

3. The signal from the phonograph needs to be amplified more than the signal from the CD player, so when the phonograph is plugged into the CD player it does not have enough amplification.
4. It is significantly boosting the signal from the phonograph so that when it gets to the amplifier in the CD player it will be as strong as the CD signal is.
9.  The resistor takes power from the current passing through it converting
       some of the current’s energy into thermal energy.
10.   The power in the circuit is 6Watts, if the resistor could not handle that
        the resistor could overheat and cause a fire.
18. Wire the transistor in series in to the circuit between the battery and the bulb.

Questions on page 498: 1, 3, 8

1. The inductor uses Faraday’s law to create a current in the circuit, which will push charge toward the bottom conductor.
3. An electromagnetic wave is made up of changing electric and magnetic fields.  The fields of a charge moving with constant velocity do not change.  The fields of a charge that is accelerating are changing.  Thus only accelerating charges, whose fields are changing, emit electromagnetic waves.
8. AM represents the changing air pressure of a sound wave with the changing amplitude of the electric signal.  The amount of charge on the antenna is proportional to the amplitude of the signal it transmits, so AM stations need to change the amount of charge moving up and down the antenna.
 

Exercises from the book on page 499: 3, 6, 10, 13, 14, 22

3.The accelerating charge produces an electromagnetic wave, which is
    received by the antenna and introduces noise into the radio.
6. The build up of charge at the end creates an electric field which stops the electrons.
10. Inserting an iron core into the inductor creates a stronger magnetic field that just the inductor alone and allows the inductor to store more energy.  The iron core, behaves like a ferromagnet and gets magnetized by the magnetic field of the inductor and thus creates its own magnetic field.

13. The inductor stores energy in its magnetic field, and both reach their largest values when the conductor’s energy is 0.

14. These resistances cause some of the energy in the current passing through them to be dissipated in the form of thermal energy.  As time passes the current in the circuit will lose energy.
22.Since in AM the amplitude of the signal corresponds to the amplitude of the sound, louder sounds get louder amplitudes.  Since a signal of stronger amplitude will travel further, the louder parts of the AM signal will travel further.  FM uses the frequency of the signal to carry the information of the sound.  The amplitude of the FM signal stays relatively the same. Thus you either receive the whole signal or you receive none of it.

Questions on page 509: 1, 6

1. The tinier the spot on which the beam can focus, the greater the number of spots on the TV screen which can be different.  The greater the number of spots on screen, which can be different, the greater the resolution of the resulting picture.
6. Modulating the carrier wave introduces sidebands.  These sidebands can be viewed as being added to the carrier wave and thus adding new frequencies to the signal.
 
Exercises from the book on page 509: 8, 11, 12, 13, 14

8. In the tube some light shot at the screen is emitted back into the tube.  This thin layer of aluminum prevents this light from bouncing around and decreasing the image resolution.
11. The deflecting coils used to steer the picture tube horizontally would do this.
12. The screen is positively charged to attract the particles when they come out of the tube.
13.   The magnetic field changes the trajectories of the electrons and thus alters the image.
14.  If the television does not know where each horizontal line starts it cannot assemble the picture correctly and the television displays the horizontal signal as just one long stream.