Here's to a wonderful 201415 school year!!
For my mechanics classes, if you need some vector addition review, check this out.
If you want a review of vector multiplication, check this one out.
A motto for us:
Learn a ton while having some fun!
Monday, August 25, 2014
Wednesday, August 20, 2014
Lab Activity: Series RC Circuit Behavior
Purpose: Observe general behavior of RC circuits
before getting into the details in class. We'll look at both charging and discharging cases.
General Setup: You’ll have a power supply, some
resistors, a large capacitor, and some multimeters. Set up a circuit with the power supply, resistor and capacitor all in series with each other.
Case A – Small resistance
 Connect a 10ohm resistor in the circuit with the power supply set to zero. Make sure there is no initial potential difference across the capacitor.
 With one person measuring the potential difference of the capacitor and another measuring the potential difference of the resistor, quickly turn up the voltage of the power supply (to ~10 V or so). Write down observations below:
What happens to the voltage across the capacitor?
What happens to the voltage across the resistor?
Try to explain what you think is physically happening in the
circuit based on your observations:
Sketch graphs of V_{Cap} vs. time, V_{R} vs.
time, and I vs. time, as the capacitor charges. *Challenge: What function might produce each graph? Try to guess before we find the details!
 When the voltage across the capacitor is a maximum, how much charge is it storing? Use your max. voltage measurement.
 When the voltage across the capacitor is a maximum, how much energy is it storing? U = ½ QV = ½ CV^{2}.
 Calculate the product RC. This actually has units of time and is called the time constant of the circuit. Show that (ohms)(farads) = seconds.
Quickly turn off the power supply. What happens to the voltage across the
capacitor?
What happens to the voltage across the resistor? Explain
what you think is happening now, and sketch
graphs of V_{Cap} vs. time, V_{R} vs. time, and I vs. time,
as it discharges.
Case B – Large resistance
 Measure the resistance of the other resistor: __________ W. Connect it in the circuit with the power supply set to zero. Make sure there is no initial potential difference across the capacitor.
 With one person measuring the potential difference of the capacitor and another measuring the potential difference of the resistor, quickly turn up the voltage of the power supply (to ~10 V or so). Write down observations below:
What happens to the voltage across the capacitor?
What happens to the voltage across the resistor?
Is there anything different compared to your first
circuit? If so, what? Think rates.
Try to explain what you think is physically happening in the
circuit based on your observations:
 Calculate the time constant, RC. Based on the two circuits you have observed, interpret what the value of the time constant of the circuit refers to.
Wait a couple minutes to let the voltage build up on the
capacitor. Quickly turn off the power
supply. What happens to the voltage
across the capacitor?
What happens to the voltage across the resistor? Explain what you think is happening now.
Theory into Reality: (wait until we do this type of
calculation in class)
What is the equation we
derived for charge as a function of time for a charging capacitor?
For the first circuit (10ohm resistor), how much charge is
on the capacitor after 0.05 seconds?
After 0.5 seconds?
What is the equation we
derived for charge as a function of time for a discharging
capacitor?
When the capacitor discharges, how long does it take
to lose 25% of its original charge?
Tuesday, August 19, 2014
The Need for Cybersecurity
For those who have an interest in computer science, politics, economics, international relations, business, the military, espionage, and many other subjects and topics, cybersecurity is something you have hopefully heard of, but does not get an enormous amount of coverage in the popular press. In my opinion, this is perhaps the most important topic for personal and national security that exists in the modern era. Here is a discussion with Richard Clarke, who has served multiple presidents on national security issues over many years, giving examples of what will almost certainly happen at some point somewhere in the world, via attacks on computer networks.
Lab Activity: Determine Speed and Error Analysis of Data
Purpose: Given the essential
equipment, you and your partners will have to determine methods of measuring
speed as precisely and with as little uncertainty as possible. The focus is on data analysis, particularly
on methods to determine uncertainties and propagate them to results.
Materials: Marble Ramp Meter Stick Stopwatch Graph
paper
Procedure:
You are given the task of trying to
measure the speed (distance / time) of a marble that rolls off a ramp. You want to try and maximize accuracy and
precision while limiting uncertainties.
As far as procedure, write detailed steps you decide on for a method
that involves extracting a speed from
a graph.
Do not expect much help from me as
far as measurements. I suggest that you
take a few minutes before starting to write down possible uncertainties (experimental,
which you may be able to minimize) and then give this a try.
Data Table: Develop a neat, organized,
and appropriate data table for all measurements for your procedure. Your group will need to take some number of
trials for time measurements for each distance that you use. In your data table(s), include the standard deviation for each set of time measurements.
s_{time} = æ [S(t_{avg} – t_{i
})^{2}] ö ^{½}
è N – 1 ø
Questions/Analysis:
1. What potential experimental
errors did you and your partner(s) decide were the most significant? Explain why these caused the most worry. Do not just say something like “human error”
or “calculation error;” but be detailed and thorough.
2. Is it possible to “minimize”
errors in this experiment? Why or why
not? (Think about your equipment) What did you try in order to minimize
uncertainty on time measurements?
3. Why is it important to be
able to accurately determine
speeds? Think in terms of everyday
events or situations; try to come up with two examples.
4. Why is it important to be
able to precisely determine speeds
(i.e. measure down to more decimal places)?
Think in terms of everyday events or situations; try to come up with two
examples.
5. Make a graph of distance (y)
versus time (x) using Excel. Find the bestfit line and R^{2} value
for your data. Then, put on error bars
in the time dimension (this will likely have to be done by hand after printing
out your graph. Don’t forget to label
axes, include units on the axes, and so on, when making a graph). The error bars for time will make use of the
standard deviation for that particular set of time trials. It is OK for different points on a graph to
have different sized error bars; in fact, you should expect to have different
sized error bars for each data point.
6. If you started your marble
at the same height on the ramp each time you can assume it is going the same
speed when it rolls off on a flat surface.
When you made your graph of distance versus time, this is why you would
expect a straight line. Are all your
points on the line? Don’t feel bad if
they are not; rarely will data lie on the same line. Determine
and report the “best” speed of your marble as well as estimates of uncertainties on your speed result from your graph,
using max and min slope lines as determined by your error bars. In class, you will see an example of this.
7. Calculate the uncertainty for your speeds by
using the quadrature method for
independent measurements (it is safe to
assume that distance and time measurements
are independent of each other and random
since you’re using different measuring
devices for each). Do
this for each individual point of
distance and time. How do
these uncertainties compare to those from
your graph, using the max and min lines?
dv = v
[(dx/x)^{2}
+ (dt/t)^{2
}] ^{½} , where dt is
the standard deviation for that set
of times, and dx = 1 cm = 0.01 m.
Note that dx/x
and dt/t
are called the fractional uncertainties of the distance and time
measurements.
We are adding the
fractional uncertainties in quadrature (looks a lot like Pythagorean theorem!).
Grading:
Title (always have this) 1
point
Purpose (always have this) 1
point
Materials and Methods (Procedure) 3 points

procedures should be written such that someone who has not done this before can
recreate your lab
Data and Graph 5
points
Analysis Questions 10
points
Above and Beyond: If interested in learning the theory behind leastsquares fits to linear data, look here.
Lab Activity: Air Friction
Purpose: You will
investigate how air friction causes terminal velocity using coffee filters. Part of this will include Interactive Physics computer simulations
for multidimensional motion and air friction; this program is only on school
computers.
Materials: Meter stick Stop watch and/or video Coffee Filters
For your report:
You will need purpose; materials; data; and analysis sections for your
writeup. It is always a good idea to organize data in tables so they are clear
and neat, and include units on all measurements and results.
Keep in mind the BIG IDEA is that air friction (and friction in fluids in general) depends on how fast
you move, f_{air} = kv, where k is a positive constant.
Read through each analysis part below carefully, because it
will guide you through what we are looking for.
Write things up using complete sentences. I recommend Google Docs for your report (just
need a single report for the group).
Procedures:
Make some predictions prior to actually measuring the
terminal speeds of the falling coffee filters.
Question: Does
mass affect the terminal speed?
You can
control the mass by using different numbers of filters.
Predict: What
should happen to terminal speed as the mass increases?
Do it…make an appropriate data table with terminal velocity
as a function of mass. Do several time
trials and include standard deviations. Bonus: Determine the
uncertainties on the terminal velocity results. You will need to do this using propagation of
uncertainties as we have done in the past; see Above and Beyond below.
Do your best to estimate how long it takes for the filters
to reach terminal velocity upon release.
You’ll probably want to drop the filters from 23 meters high, so you
get terminal velocities.
Questions/Analysis:
1. Determine
the terminal speeds for at least five different masses of coffee filters. Estimate all measurement uncertainties and
record those with your data.
Above and Beyond: This includes using the quadrature method for
determining dv
values for each terminal speed. Remember
units are important on data and results.
dv = v
[(dt_{
}/ t_{avg})^{2} + (dd / d)^{2 }] ^{½}
You and your partners need to come up with a reasonable
estimate of uncertainty on the distance that the filters will fall; think of
how well you can read the metersticks.
2. Use
your measurements of terminal speed to determine values for k. Include these in a data table. What are the units of k?
3. Write
concise conclusions of what your data suggest about the effect of mass on
terminal speed. Make a graph in Excel of terminal speed as a function of mass (#
filters) from your data. Use as large a
range of mass as possible, up to a point where it does not have a measureable
terminal speed (where it continues to accelerate before hitting the floor).
4. Sketch graphs (i.e. do not need numbers
on the graph) of velocity as a function of time and acceleration as a function
of time. Put graphs for different masses
on the same set of axes so you can show a comparison of the effect of mass on
terminal velocity and acceleration. Use different colors, or soliddasheddotted lines, to distinguish the different graphs.
5. Do
a few trials for the other sized coffee filters, and draw any conclusions about
how the size of coffee filters affect the terminal velocity. Explain/support your conclusions in terms of
data and observations. Try to do this by
holding mass constant between the filters as best you can.
6. For
two of your small coffee filter examples, determine the percentage of kinetic
energy that is lost due to air friction. Hint:
think about how fast a filter should land if there is no air friction, and
compare to your terminal speed at which it lands.
7. Log
into your school account. Unfortunately, Interactive Physics is not online, only on school computers. Go to Programs, and go into the Science group of programs. You should find Interactive Physics. Go into IPFiles,
and then Physics Experiments. In that folder find the Air Resistance folder. There
should be 4 computer simulations, and run all four.
In each one, you can select
different values of k. In some you can change mass, and in some you can change
surface area. Run a series of controlled
computer experiments for each simulation, and write summaries of
observations/measurements and your conclusions about the effect of the
various parameters on the trajectories of projectiles when varying air
friction, terminal velocity, and so on.
Are these computer experiments consistent
with what you see with the coffee filters?
Explain.
The point of all this is to gain a good conceptual understanding of what air friction is all about,
and gain a better understanding of the complexity of reality, as opposed to the
‘physics land’ we tend to visit in most problems. Still, keep in mind that we
are using a highly simplified model for air friction, and reality is still quite
a bit more complex than we are treating air friction for things like cars,
planes and rockets moving through the atmosphere (aerodynamics). Aerospace engineers need to deal with the
complexities in a major way. J
Lab Activity  Simulate Halflife with M&Ms
Radioactivity  Mmmm & Mmmm, Good
Purpose:
Radioactivity was a phenomena that helped change the nature of science as the
twentieth century began (helped lead to fundamental changes in chemistry,
nuclear physics, biology, archeology and geology). And one of the most important ideas to come
from the studies of radioactivity is the concept that it is a statistical and probabilistic process. This means that one can apply statistical and
probabilistic methods to the study of radioactivity, and one of those
statistical measures is the halflife.
You will begin to gain understanding of halflives by using some pretty
sophisticated equipment.
Equipment: M & M’s (pretty sophisticated, huh?!)
Procedure:
Work
your way through the following questions with your M & M’s; choose one side
of your M & M’s to represent a ‘living’ radioactive atom, and the other
side to represent a decayed atom that will be removed from your sample. Dump your ‘living’ pieces on your table and
remove those that have just decayed. Continue this until all have decayed.
Questions and Analysis:
1.
Make a
data table to keep track of how many M & M’s decay each time you dump them
on the table. Make sure to count the
original number of pieces before you begin.
After all the pieces have decayed, make a graph of the number of pieces
left after each ‘halflife’ versus the number of the turn you dumped them. Is the shape of your graph linear? If not, how would you describe it?
2.
The
halflife for carbon14 (this is an isotope of normal carbon12; it just has
two extra neutrons that make it radioactive) is about 5700 years. What does this mean if you have a sample of
1000 carbon14 atoms? What does this
mean if you have a single carbon14 atom?
3.
Make a graph of the number of carbon14 atoms (suppose you have an
initial
sample of 1000 atoms) as a function
of time, knowing the halflife is 5700 years.
For an initial sample of 1000
carbon14 atoms, approximately how long would it
take to have only 100 carbon14
atoms remaining from the original sample?
Make your approximation from
your graph. Then, calculate it
from the decay law:
N = N_{o}e^{
t / }^{t}
where t = t _{½} / ln2; this is sort of like
an average time that is used for radioactivity
and is different for each radioactive
material. Work together to figure this
out, just
like a biologist or archeologist
would have to do. Some call τ the decay constant or
time
constant for the material being considered.
We will see time constants again for
certain types of circuits in E&M.
4. Explain how scientists can
use carbon14 as a way of measuring the age of bones.
Would you trust carbon14
dating for objects that may be millions of years old?
Why or why not?
5.
Name
three other phenomena, events, activities, etc., that require probability to
describe them. Also, in your own words, define “probability.”
Above and Beyond: If curious, check out details about radiometric dating techniques and the math behind those techniques.
Lab  Video Game Physics Analysis
Lab: Video Game Physics Analysis
Purpose:
The research question is: does your video game follow
physics phact or phiction? You and a partner will need to play about 1020
seconds of an online video game that involves some type of collision, and then
analyze the motion to determine speeds, accelerations, and whether energy and
momentum are conserved.
Materials:
Students will need a computer with Internet access. Students also need an analysis program such
as Logger Pro or Tracker, which will be used to better analyze features of the
game being played. A screencast video of
the student playing the game will be made using the online program called Screencastomatic.
Background:
Using video technologies of all kinds have opened up new
ways of making connections between the physics we study and any phenomenon that
can be captured on video, including video games. Any game that has moving objects,
interactions between objects, projectiles, orbits, collisions, and any other
physical event, can be analyzed to see if our real laws of physics are being
used to create the video game environment, or if the game is simply, for lack
of a better word, being ruled by nonsense as far as the physics is concerned.
By measuring distances, times and paths, and estimating
masses, and scaling them by some appropriate scaling factors to better match
them to real object and events, you will be able to see if those measurements
and results are realistic, or if your game is being played in some other world
or parallel universe, with different laws of physics. You will be able to calculate speeds, accelerations,
forces, momentum, and so on.
PreLab: What do you
need?
You will need to make sure you have Internet access on your
computer. This will allow you to use
Screencastomatic (found at http://screencastomatic.com/),
as well as access an online video game.
It is possible to analyze a video game without additional
software, just by using the screencast video directly and playing it
framebyframe. You would need a small
ruler and possibly a protractor for 2D interactions to make measurements
directly on the computer monitor.
However, a more accurate analysis can be done with other
software, such as Vernier’s Logger Pro or Tracker, which is a free, open source
piece of software off the Internet. You
can download Tracker at http://www.cabrillo.edu/~dbrown/tracker/,
if you choose to use it for your lab.
Procedures:
I.
Set up Screencastomatic:
Go to the Screencastomatic site, http://screencastomatic.com/, and
simply click on Start Recording. There
is nothing to download. When you get a
small setup window, the default is to record the whole screen, which will be
fine.
To start recording, all you will need to do is type ALTP (press these two buttons at the
same time), and you will get a countdown to recording. That’s it!
II.
Before typing ALTP, use a different tab/window in your Internet browser (this
should work well in either Chrome or Firefox) to go to a site of a favorite video game. Be sure the video game has motion and
interactions between multiple objects, because that makes for a more
interesting and useful analysis and discussion of how realistic the game is. For example, one of my favorites is a game I
grew up with, Asteroids. There is a free
online version at http://www.play.vg/games/4Asteroids.html,
if you are interested.
III.
Start Recording! All you need to do at this point is type ALTP, wait for the countdown, and then
when Screencastomatic tells you it is recording start playing the game. All you want to record is about 30 seconds –
that will be more than enough for an analysis sample. When you have what you want, type ALTP again to pause Screencastomatic.
IV.
To complete the screencast video, after
pausing Screencastomatic, you should get a window with an option to be Done with the screencast. Click on Done.
This will take you to a screen to
publish the video. It is best to choose Publish to Video File. This will then give you some options. First is the type of file you want. It is recommended to use the default option,
a QuickTime MP4 file. This will work
with other analysis software if you have it.
Keep the size Full Size (the default setting). Then click on Save Video.
You
will be asked where to save the file and to name the file. It might be easiest to save on your Desktop,
or start a folder for video files – that is all your choice. Choose an appropriate name for the file, and
then save it! Congratulations, you just
made a screencast video, and hopefully this entire process took no more than
about 5 minutes!
I.
Play and Analyze the video. Doubleclick the video file to make sure it
works and that you captured the action you wanted. You can always go back through this procedure
as many times as you want, with any and all video games you enjoy playing.
KEY GOAL: Determine with your partner if energy and momentum
are conserved? Is your game following
physics phact or phiction??
If you want to do a ‘quick
and dirty’ analysis and have no access to other analysis software, then
by pausing the video you can scroll it framebyframe. Each frame will be onetenth of a second of
time, so this is the time step we will use for your analysis. Use a small ruler and set a reasonable
distance scale for your video game.
For example, on my Asteroids video, I assumed the spaceship
was a oneperson ship that was 10 meters in length (about 30 feet seemed a
reasonable, realistic size – this is 1/5^{th} the length of a full
space shuttle, and I assumed a single, small fighter spacecraft for the
game. See Wikipedia.). Below is how one would analyze the Asteroids
video:
Measure the length of the ship
with your ruler. Let’s say the ship is 1
cm on your monitor. So the scale is 1 cm
of the video = 10 meters in reality; this is no different than a scale on a
map, where 1 inch = 10 miles, for example.
The large asteroids flying around might be 2.5 cm on the monitor, so
this would make them large rocks of about 25 meters in diameter. You’ll
need to set a scale for any video game, to find lengths, distances, masses,
speeds, etc.
I need the masses for each
object. Here we may need to do some
research. I looked up the mass of the
space shuttle on Wikipedia, and it is listed as about 2000 tonnes = 2 x 10^{6}
kg. Onefifth of this would be 4 x 10^{5}
kg, which is the mass of the spaceship I would use.
For a large asteroid in the game,
I wanted a good, realistic estimate for the mass of a 25 meter asteroid. I
looked up 'Asteroid' on Wikipedia and found that this is a reasonable size, as
the vast majority of asteroids are under a 100 meter diameter. The data for density of some asteroids
averaged around 3 g/cm^{3} = 3000 kg/m^{3}, so assuming a 25
meter diameter (volume of a sphere is (4/3)πR^{3}) spherical asteroid,
this gives a mass of around 2.5 x 10^{7} kg.
We would need to do a similar
estimate of mass for smaller asteroids, when they are blasted apart in the
game. The diameters would need to be
measured, and then scaled in a similar way to get the masses.
Now, think about the physical
quantities that can be measured/calculated.
Speed = d/t, so suppose you run move the paused screencast video 10 time
steps. This would be one second of real
time. You measure one of the asteroids
moving 1 cm on the monitor in that time.
This means the asteroid moved 10 meters in one second, and its speed is
10 m/s. You can measure the speed of the
bullets the spaceship shoots in a similar manner, or the speed of the ship if
you have it drifting around. Or suppose
the ship is at rest on the screen, and you accelerate in a straight line. You can measure how many cm it moves in a
certain number of time steps, and then calculate the acceleration (assume a
constant acceleration) with d = ½ at^{2}. You could also calculate its final speed once
the acceleration ends.
When you blast an asteroid, if you
know its initial speed and direction (you can measure angles with a protractor
on the monitor or with the analysis software), you can measure the final speeds
and directions of the smaller chunks of rock – determine if momentum was indeed
conserved.
With the masses and speeds,
calculate the momenta of each object, and the kinetic energy of each
object. Is momentum conserved when you
shoot an asteroid? Is energy
conserved? If not, is the change in
kinetic energy negative or positive?
Calculate the gravitational forces
between different objects. Are those forces relevant? That is, are they strong enough to affect
each other’s motions?
How much would you weigh if you
stood on one of the asteroids?
Would you be able to jump off the
asteroid by exceeding the escape velocity with your jump?
What would the acceleration of
gravity be on one of the asteroids?
How does the mass and speed of one
of the alien spaceships compare to your spaceship?
Do all of these calculations and
see what the results are!
Summarize
your results: how realistic are they?
Does the video game seem to follow more
closely to phact or phiction?
For teachers, you may want to specify a game, or at least a type of game, and have students focus on figuring out if one or two physical quantities are realistic or not, such as is energy conserved, or are speeds and accelerations reasonable, rather than having students look at numerous quantities.
Have phun!! J
Wednesday, August 6, 2014
Lab Activity: Distance vs. Displacement Vector
Goal: To find
the total distance and displacement vector to your house from ETHS!
Problem:
Here is the
question for you – how can you determine the total distance you walk from ETHS
to your house, as well as the displacement vector from ETHS to your house? Think about what information you need to find
these, and how can you use Google Maps to help. ETHS is 1600 Dodge Avenue.
How:
On graph paper, make a map (to scale) from ETHS to your house and use data from Google
Maps to get the total distance and displacement vector. These will all be different for each person
in class. Be sure to define your scale,
such as 1 cm on the map is equal to 100 feet, or whatever you want it to be for
your map. Also orient your map with N,
S, E, W, so you can calculate the angle of the displacement vector from ETHS to
your home! Give your angle in terms of
how many degrees from 0degrees, which is the positive xaxis. Let ETHS be the origin of your graph.
Analysis/Questions:
1. In
your own words, what is the distinction between ‘distance’ and ‘displacement?’
2. Write
down your results for distance and displacement vector measurements from your
map. You’ll need the total x component
(along EastWest axis) total ycomponent (along the NorthSouth axis) of your
displacement vector, as well as the direction (i.e. angle) of the displacement
vector from ETHS to your house. Express
the results in feet, meters and miles.
1 mile = 5280 feet = 1609.3 meters
3. Can
the magnitude of displacement ever have a larger magnitude than distance? Explain.
4. Explain
how displacement vectors would be used in the navigation of ships or planes.
5. What
about global travel – motion over a 3D surface – does anything change? If so,
what new variables do you need to consider? Explain any thoughts on this (talk
it through with others if you wish). Think of the Sphereland movie.
Bonus: How do space scientists and engineers navigate space probes
that are sent to other objects in the solar system? For instance, what
navigation issues and considerations come up with sending people to Mars?
Lab Activity: Use of Pendulum to Find g and Mass of Earth
Purpose: In this activity, you will determine the
acceleration of gravity and the mass of the Earth using a simple pendulum.
Background: A pendulum is a simple device that exhibits
periodic motion when the bob is lifted and given potential energy. Gravity does work on the bob and transforms
the potential energy into kinetic energy.
As potential energy and kinetic energy take turns transforming into each
other, the resulting motion is of a periodic nature. The period of a pendulum, which refers to the
time it takes to swing back and forth once (a full swing), is related to the
length of the pendulum and the acceleration of gravity (this assumes a ‘small
angle’):
Period = T = 2p(L / g)^{1/ 2}
Materials:
Stop
watch or video (phone, camera)
endulum
Meter
stick Your brain
Procedure:
You and
your lab partners need to determine an accurate way of determining the
acceleration of gravity, from which you will also calculate a value of the mass
of the Earth! You will need to do this
using a pendulum, which you know something about because of your last
experiment in determining a pendulum’s properties. Decide
what the best measurements and methods are, as well as how to minimize any
potential errors. Then, write down your
stepbystep procedure, and clearly and neatly present your data.
Analysis (answer in complete sentences):
1.
Based on your
measurements, determine the acceleration of gravity, g. Show your calculation.
2.
Using your result
in (1), calculate the percent error relative to the accepted g = 9.81
m/s^{2}. Recall that %error =
{[your value – accepted value] / [accepted value]} x 100.
3.
Explain, in your
own words, why the period of a pendulum is independent of the mass of the bob.
4.
What should the
period of your pendulum be if you performed this experiment on the moon
(gravity is about 1/6 that of the Earth)?
What about on Jupiter (gravity is about 20 times that on Earth)? Is this a direct or inverse relationship
between T and g?
5.
What are the main
sources of error in this particular activity?
How did your group try to minimize those errors?
6. Explain what a Foucault pendulum is
used for. You may need to look this one
up.
7. How long would you need to make a pendulum
in order for it to have a period of 1.0
second?
Show your calculation.
8. From your value of g, determine the mass of
the earth! Show your calculation. Other
useful information may include the radius
of the earth and G.
G = 6.67 x 10^{11} Nm^{2}/kg^{2}
and R_{E} = 6.4 x 10^{6} m.
*Note that by knowing the size (radius) of other
moons and planets, you could take a pendulum, measure the period, and determine
their masses, too. Sensitive
measurements of a pendulum’s period anywhere on earth also allows us to
determine small difference in g, which tells us something about how the radius
changes as well as densities of the earth at those locations.
Tuesday, August 5, 2014
Lab Activity: Develop Empirical Formula for Ohm's Law
Purpose: Using measurements taken in class, you will
develop an empirical formula for Ohm’s
law.
Background: You don’t get any this time since it might
“spoil the surprise.”
Materials:
Power supply Resistors
Multimeter/Ammeter Wires
Breadboard
Procedures:
(A) The
data you want consist of measurements of resistance, voltage and current, the
“Big 3” of electricity. Set up a data
table where you will have a single and constant resistance
value. Select a voltage value and then
measure the current. Do this for 5
different voltage values, and don’t go over 4 volts and do not max out the
ammeter. You will be making a graph of voltage vs current. Remember that resistors get hot
after a while!
(B) Change the
resistance value. Select a voltage and
record the current.
After turning down the voltage,
select another resistance value. Set the
power supply back to the same voltage (bustobus) you just had, and
record the new current. Do this for at
least 4 more resistance values, and reset to the same bustobus voltage value
each time. Try predicting what current
you will measure as you change resistance values.
Measure the
diameter and length of the resistor material (the cylindrical portion of the
resistor, and not the metal legs); use the digital micrometer for this. You will need these measurements for the last
analysis question.
Analysis:
1. Make
a graph of your data in part (A) above.
The graph should be one of Voltage (y) versus Current (x). Also make a graph of your data in part (B)
above. This graph should be one of
Current (y) versus Resistance (x). Make
your graphs using Excel, and find the bestfit functions for each graph.
2. What
shape are your graphs? What type of
relationship exists between voltage and current for a constant resistance? Between current and resistance for a constant
voltage? Find the bestfit functions to
your graphs.
3. Based
on your data and your graphs, combine the two bestfit functions from your
graphs and write down an empirical equation that shows how current depends on
resistance and voltage.
4. For
the following arrangements of resistors below, calculate the total resistance. (you’ll
get these in class)
a. b.
5. Why
do electronic devices get hot? Where
does the energy come from that you eventually feel as heat?
6. Based
on your observations, what role might resistors have in electronic
circuits? After all, resistors waste
energy and increase your power bill…why use them?
7. From
a chemistry perspective, why are conductors and insulators so vastly
different? What is it about these
various materials that make their electrical properties different? Also, from chemistry, what are
semiconductors, and why are they important to electronics? Discuss in terms of band theory.
8. In
your own words, why is the relationship E = dV/dr the key to understanding how
an electric circuit works? Be thorough,
and write in terms of potential and electric fields, and what they do to
delocalized electrons inside the wires/conductors of the circuit. Start with the
battery/power supply of the circuit.
9. Using
the diameter and length measurements of the resistor, along with the actual
resistance value, calculate the resistivity
of the material used to make the resistor.
Include appropriate units.
On your own:
PostLab
Run the following PhET computer simulations, in order to get
some good visuals related to what you directly observed and measured in this
experiment. The simulations are:
Ohm’s law  http://phet.colorado.edu/en/simulation/ohmslaw
Basic
Circuit  http://phet.colorado.edu/en/simulation/batteryresistorcircuit
Look at the Netlogo simulation for an electron moving
through material. Follow a single electron, and note the path. What defines ‘more
resistance’ versus ‘less resistance’ for an electron?
Lab Activity: Equipotential Lines and the Electric Potential Gradient
Minilab: Equipotential Lines and Gradients
Purpose: We will measure equipotential lines on
a sheet and determine the electric field patterns through the use of the
gradient concept.
Procedure: Hook up two cables from a power supply to one
of the conductive sheets. Turn up the voltage in
order to set up a potential difference between the two ends of the sheet.
Using a multimeter, measure
the voltage going down the center of the sheet from one end to the other at 2
or 3 cm intervals.
Now
try to measure equipotential lines going side to side. You may want to find the lines every 0.25
volts apart, for instance. Draw these
lines on a clean sheet of white recording paper in pencil, and once you have a pattern draw in
the electric field lines in ink, indicating the direction of the Efield.
Observations and Questions:
1. In words, what does E =
dV/dr mean physically. Some find it
easier to think of this more generically as E = DV / Dr, instead. Indicate the significance of the minus sign.
2. On your sheet, include arrows showing which way
the electric field vectors are directed.
To do this you will have to determine which end of your sheet is at a
higher potential, and which is at a lower potential. Use measurements from the multimeter to
determine this.
3. Why can an
electric field vector not run parallel to an equipotential line?
4. How can
you tell on your ‘map’ where the electric field is strongest? Weakest?
Explain your reasoning.
5. Pick two
equipotential lines on your map. Using
the voltage values you measured and distance measurements, determine the
approximate strength of the electric field between those two lines.
6. How much
work would be done if you moved an electron from one of the equipotential lines
used in #5 to the second equipotential line?
The charge of an electron is 1.6 x 10^{19} C. Also, what is the maximum speed an electron and
proton could attain if energized by that voltage? The mass of an electron is
9.1 x 10^{31}
kg, and that of a proton is 1.6 x 10^{27} kg.
7. In problems like #6, what determines if positive work is done by the electric field? Give your answer both in words and with a mathematical argument.
8. I’d like you to work your way through the ActivPhysics simulation 11.11, Electric
Potential: Qualitative Introduction lesson (11.11). Try the simulations with the questions being
asked; I’ll be looking for feedback from you about whether you think this is
helpful or not.
When done with your lab, do the 1986 AP problem with
equipotential lines.
Lab Activity: Develop a Math Model for the Period of a Pendulum
Purpose: In this activity you will investigate how
hanging mass, length, the strength of gravity and starting angle affect the
period of a pendulum. Then, form a math model for the period of a pendulum.
Materials:
Pendulum apparatus Stop watch or other timing device/technique
Pendulum apparatus Stop watch or other timing device/technique
Meter
stick Various masses for pendulum bob
Balance Protractor or other means
of measuring angle
Logger Pro or Tracker Electronic force sensor Video camera or phone
Logger Pro or Tracker Electronic force sensor Video camera or phone
Background:
A
pendulum is a classic example of periodic motion, which is a motion that
is repetitive, redundant, keeps repeating itself, keeps going back and
forth…oh, I’ll stop now. A pendulum only
works when there is gravity, and of course can be used as a clock. It is also an example of circular motion,
which means there is a net centripetal force, mv^{2}/R. Because we began studying circular motion and
will be getting deeper into gravity, we will try to figure out the basic
properties of a pendulum and see how we can combine gravity and circular motion
together in a few different ways, whether it is a pendulum, an amusement park
ride, or satellite motion. Keep the
force diagram for a pendulum in mind (what does it look like?).
Research
Questions:
What effect(s), if any, do mass of the bob, length of the
pendulum, and angular amplitude of a pendulum, have on the period of the
pendulum? Our goal is to use mathematical fits to data to determine an empirical formula for the period of a pendulum.
Your group is looking to combine
your graphical fits into the form T = f(L)g(angle)h(m)s(g).
Develop Hypothesis:
Before doing any measurements, state what you think the
effect of mass, angular amplitude, length, and the acceleration of gravity have
on the period of the pendulum. Remember,
reality always tends to be a bit complex!
Procedure:
You
will be trying to determine the best fits to data using Excel. Your measurements will use four different
techniques for collection.
i.
Use a stop watch to measure the period as
a function of length of the pendulum;
ii.
Use video to determine the period as a
function of mass hanging from the pendulum. NOTE: when changing masses, you
will need to adjust the length of the string accordingly to maintain the same
total length to the center of mass;
iii.
Use an electronic force sensor to measure
the period as a function of angular amplitude;
iv.
Use the PhET simulation for pendulums to
determine the effect of gravity on the period – check out the blog post which provides the links and information
for this portion.
You will need to
get data to make four graphs:
i.
Period as function of length. Note the constant
mass and angle;
ii.
Period as function of mass. Note the constant
length and angle;
iii.
Period as function of starting angle. Note the
constant mass and length;
iv.
Period as function of g (using PhET simulation,
keep constant mass and length and angle).
Keep in mind, you should always
be thinking of estimating errors on all measurements (in any experiment you
ever do!) as well as how to minimize those errors. Think about what might be the best way of
measuring a given quantity. Also, do not
forget to include units on all measurements, along with a reasonable estimate
of the uncertainty of all measurements!
For anything measured in trials, think standard deviation.
For
your writeup: Purpose, Materials, Procedure, Data Tables, Questions
and Analysis (with appropriate graphs; these should be titled and labeled with
quantities being graphed and units!
Graphs need to be done on the computer.). Do a group report, and consider Google Docs if that works best for the
group.
Definitions:
Period
= time it takes the pendulum, when released from rest, to swing over and back
to where it started; or the time for one roundtrip.
Length
= length from the point where the string is free to swing to the center of mass
of the bob at the end of the string.
Mass: we assume massless string, so just
the mass of the hanging bob.
Angular amplitude: the starting, maximum
angle for the period, as measured from the vertical.
Questions/Analysis:
1. For
the graph of period as a function of length, figure out errors on
measurements and include them as error bars on your graph. The error bar for period measurements (some
number of trials with the stop watch) should be the standard deviation, as
always. Find the bestfit function for the graph in Excel. Include the
equation and R^{2} value.
Include the point (0.01,0.01) on your graph and in your fit, since (0,0)
won’t allow certain fit options.
2.
For the graph of period vs. mass, use five
different masses and use a video to get period measurements in Logger Pro or
Tracker. Make sure to adjust the
length of string so the overall lengths of the pendulum are always the
same. For instance, when you hang a
larger mass on the string, you will need to shorten the string a bit since the
object will be longer (think about where the center of mass is). Try to estimate errors in length and in
period from your video measurements in LoggerPro or Tracker. Find
a bestfit function for the data. Include
the equation and R^{2} value.
3. For
the graph of period vs. angle, use the electronic force sensor and measure the
period in the Logger Pro display. Plot
your data using Excel and obtain
a bestfit function to the data to get an idea of the relationship. Go from small angles around 10^{o},
and go up to around 90^{o}.
4.
Last but not least, graph period vs. g from
the PhET simulation. Find a bestfit function for the data. Include the equation and R^{2}
value.
Keep in mind you will only have 3 points, so do what you can with
this.
5. There
are only three significant forces acting on the mass at any time, those being
tension, gravity and air friction. Which
of these are constant, which are nonconstant?
If any are nonconstant, when are they the strongest, and when are they
the weakest? Explain, and include a
force diagram/freebody diagram for a pendulum.
6. Using
your graph in #1, how long should a pendulum be in order to have a period of
1.0 sec (on earth)? How long should a
pendulum be to have a period of 2 seconds? Use your fit to do so. Keep in mind the first mechanical clocks were
made with the pendulum! (way to go Galileo)
7. What
exactly does F_{centripetal} = mv^{2}/R mean? What does the value of mv^{2}/R tell
us, and what does
it
depend on specifically for a pendulum? Think
about what force or forces keep the pendulum
moving in that portion of a circle.
Consult our notes and the book for assistance.
Write a brief,
tothepoint (i.e. one paragraph) summary of your findings/conclusions about what the period of the pendulum depends
on and how it depends on specific
quantities.
*Use and
combine the results of your individual bestfit functions for your four graphs
to obtain an empirical mathematical model for the period of your pendulum as functions of
length, mass, g, and angular amplitude.*
Put it in the form: T = f(L)g(angle)h(m)s(g)
Assess the techniques. Based on your experience:

Rank the ease of the four measuring techniques.

Rank the accuracy of the four measuring
techniques.
Provide any other feedback you think is relevant to this
set of experiments!
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