Here's the scoop, juniors.
All AP exams this year are 45 minutes in length, with 5 minutes needed to upload your work. For AP Physics C, both Mechanics and E&M will have 2 free response problems (NO multiple choice). Go here to find more details on any AP exam you are taking.
The first physics problem is 25 minutes and 60% of the score. It will almost certainly have multiple topics involved; it will be a bit more conceptual than just mathematical. While derivations are still fair game, it won't be completely math based. It is more difficult to BS one's way through conceptual questions than computational. Remember, they will likely want to have some calculus on the exam, and perhaps some derivation. Air friction tends to be the trickiest for most students. Go here to see some examples/reminders of where calculus comes in. Links to relevant videos are included.
The second problem is 15 minutes and 40% of the score. It will be a lab-based problem. Perhaps you need to take a bunch of data and do an analysis. Or perhaps you will be given a list of available equipment and design an experiment to measure something specific. Keep in mind that a major piece of analysis is to have a mathematical model in mind, with a constant stuck in it, and you need to find the constant's value by using data - usually it involves linearizing a graph and using the slope to get the constant's value.
These exams are open book, open note! Go here to get advice about open book exams (these occur in college more frequently than in high school).
To find old AP problems that are similar to this year's problems, I will be putting the info here. You can find them in our AP Exam page on our school website. Any exam from the past decade will have lab based problems.
To me, it sounds like the AP Physics C problems this year will be more like AP Physics 1 problems. These tend to be more writing and explaining than hard-core calculations. The College Board gave as an example problem for the first problem, #3 from the 2017 Physics 1 exam. Go here to see past AP Physics 1 exams. Just focus on those problems that are on topics we study. The scoring solutions are available.
Mechanics Topics:
- Kinematics and 1-D, 2-D motion
- Newton's laws and circular motion
- Energy and work
- Momentum and impulse
- Rotations and angular momentum
There is NO simple harmonic motion or Gravity/orbital motion/flux this year!!
Showing posts sorted by date for query air friction. Sort by relevance Show all posts
Showing posts sorted by date for query air friction. Sort by relevance Show all posts
Tuesday, April 14, 2020
Sunday, April 12, 2020
3 Chem/Phys - Welcome back from Break!!! Finishing up
With hope you all had a fun, restful and healthy spring break, welcome back!!
What's new? What's been fun for you? What time have you been waking up the past week?
As we have at the very least a few more weeks of remote learning, 3 BIG reminders:
1. be checking in with attendance each day with the school; your teachers have no choice but to go by the official list we receive, regardless of whether we see you on Zoom or get emails from you on a given day
2. remember that counselors, social workers, and psychologists are all available if you need anything personally, for college, or any other school matters.
3. there is the sharing Google Sheet, to give ideas of things to try
AP Details for Mechanics:
- will be at 11:00 AM on May 11
- 2 problems: the first you will have 25 minutes to read and write your responses (60%), similar to #3 on this AP 1 exam; and a second one you will have 15 minutes (40%).
- you can use a calculator
- just free response, NO multiple choice
- a lot of conceptual understanding will be tested, some calculations/derivations possible. The second one will be to design and analyze a lab experiment on some topic.
- No simple harmonic motion/oscillations, gravity and orbital motions
- Once you submit the first problem you will not be able to go back to it.
- Go Here to get details of any AP exam for this year
Completing the Course:
To hopefully have something a little different and physical, try to do a few of the options in this at-home mini-lab for rotations. Depending what you have available at home, try at least 3 of the options in the lab by the end of Friday, April 17. These are just some fairly simple things to do. For instance, if you happen to have any hard boiled eggs, there is one quick option for those and raw eggs.
Even though it will not be on the AP exam, today just a brief introduction into simple harmonic motion (SHM). The standout example of SHM is something oscillating on a spring. The gist of this will be using F = ma = -kx to give us our one case of a second order differential equation (a is the 2nd derivative of position). Of course, this is different from things we've already done, such as with basic motion or air friction, which have all been first order differential equations that we can do an integral (antiderivative) to solve.
For our 2nd order DE, the solutions for functions of time will be sines and cosines. Hopefully this makes sense, if you want to describe a periodic motion mathematically, we should probably use periodic functions, and those happen to be the solutions to what Newton's 2nd law gives us for a spring.
Relevant Videos:
Because we won't do all of SHM like we normally would, relevant videos are linked here for those who are interested. For those who have an interest in learning all of SHM, I can do some other examples on Tuesday's 3 pm Zoom session.
- simple harmonic motion, the basics
- SHM more details: initial conditions and phase angle
- simple pendulum and small-angle approximation
- more advanced: SHM for a stick oscillating due to a spring (rotating, oscillating stick)
- a 1-D example of the Schrodinger equation to see where quantum numbers (integers) come from!
Lab: PhET Simulated Experiment for SHM: if you want to vary parameters and see the effects on the oscillations.
There is a simple harmonic motion packet in our SHM folder of the 3 Chem/Phys school web site. There are some recommended practice problems for those who want to try any. These will not be 'assigned' since we won't need them for the AP exam. We will do a couple together as examples, so you can see what all this is about.
AP Review Materials:
Review sets are all available on the 3 Chem/Phys site. There are three sets to get the basic ideas back for the material that is fair game for this year's AP exam:
AP Review Set I
AP Review Set II
AP Review Set III
Each has solutions files available, and we had some of these for the review for the 1st semester final.
All of my videos are here.
And then the AP Exam page. You need to be logged in to your eths202 account to access.
The College Board has online review sessions for all AP courses.
What's new? What's been fun for you? What time have you been waking up the past week?
As we have at the very least a few more weeks of remote learning, 3 BIG reminders:
1. be checking in with attendance each day with the school; your teachers have no choice but to go by the official list we receive, regardless of whether we see you on Zoom or get emails from you on a given day
2. remember that counselors, social workers, and psychologists are all available if you need anything personally, for college, or any other school matters.
3. there is the sharing Google Sheet, to give ideas of things to try
AP Details for Mechanics:
- will be at 11:00 AM on May 11
- 2 problems: the first you will have 25 minutes to read and write your responses (60%), similar to #3 on this AP 1 exam; and a second one you will have 15 minutes (40%).
- you can use a calculator
- just free response, NO multiple choice
- a lot of conceptual understanding will be tested, some calculations/derivations possible. The second one will be to design and analyze a lab experiment on some topic.
- No simple harmonic motion/oscillations, gravity and orbital motions
- Once you submit the first problem you will not be able to go back to it.
- Go Here to get details of any AP exam for this year
Completing the Course:
To hopefully have something a little different and physical, try to do a few of the options in this at-home mini-lab for rotations. Depending what you have available at home, try at least 3 of the options in the lab by the end of Friday, April 17. These are just some fairly simple things to do. For instance, if you happen to have any hard boiled eggs, there is one quick option for those and raw eggs.
Even though it will not be on the AP exam, today just a brief introduction into simple harmonic motion (SHM). The standout example of SHM is something oscillating on a spring. The gist of this will be using F = ma = -kx to give us our one case of a second order differential equation (a is the 2nd derivative of position). Of course, this is different from things we've already done, such as with basic motion or air friction, which have all been first order differential equations that we can do an integral (antiderivative) to solve.
For our 2nd order DE, the solutions for functions of time will be sines and cosines. Hopefully this makes sense, if you want to describe a periodic motion mathematically, we should probably use periodic functions, and those happen to be the solutions to what Newton's 2nd law gives us for a spring.
Relevant Videos:
Because we won't do all of SHM like we normally would, relevant videos are linked here for those who are interested. For those who have an interest in learning all of SHM, I can do some other examples on Tuesday's 3 pm Zoom session.
- simple harmonic motion, the basics
- SHM more details: initial conditions and phase angle
- simple pendulum and small-angle approximation
- more advanced: SHM for a stick oscillating due to a spring (rotating, oscillating stick)
- a 1-D example of the Schrodinger equation to see where quantum numbers (integers) come from!
Lab: PhET Simulated Experiment for SHM: if you want to vary parameters and see the effects on the oscillations.
There is a simple harmonic motion packet in our SHM folder of the 3 Chem/Phys school web site. There are some recommended practice problems for those who want to try any. These will not be 'assigned' since we won't need them for the AP exam. We will do a couple together as examples, so you can see what all this is about.
AP Review Materials:
Review sets are all available on the 3 Chem/Phys site. There are three sets to get the basic ideas back for the material that is fair game for this year's AP exam:
AP Review Set I
AP Review Set II
AP Review Set III
Each has solutions files available, and we had some of these for the review for the 1st semester final.
All of my videos are here.
And then the AP Exam page. You need to be logged in to your eths202 account to access.
The College Board has online review sessions for all AP courses.
Tuesday, March 17, 2020
4 Chem/Phys Remote Class - Practice sets for EM Induction
Happy _____day, everyone, depending on the day you see this!
If you missed Tuesday's 10 am class session, click here for the video recording.
Electromagnetic induction: This is one of the greatest discoveries in physics history, if not science history, since it helped create our modern electrical civilization. The primary players in this were Michael Faraday on the experimental side, and James Clerk Maxwell on the theoretical side. You've already 'discovered' the gist of em induction in our magnet lab a couple sessions ago - I asked you to play with magnets and a solenoid to see if you could create voltage using nothing but the magnet.
How did you do it?
You had to move the magnet around inside the solenoid. So some combination of coils of wire, a magnet, and motion allow us to create electricity. I will demonstrate this in Wednesday's Zoom session, if you are able to join us. I brought some equipment home so we can still at least do demos.
We are starting with Packet 1 (you either have a hard copy or it is in the EM Induction folder of our school site). This introduces magnetic flux and Faraday's law of em induction.
Note that I will still be giving recommended practice sets, and we have relevant videos for each concept and type of problem. I hope you will still try them, and discuss with any study group or individuals as you normally do - but remotely!! Call or Face-time or use other social media platforms, or use Zoom or Skype to meet with each other remotely; we strongly discourage you from meeting in person. The whole point is social separation for the next couple weeks, not only to protect you, but to prevent the spread to those who have contact with older individuals who are much more susceptible to this virus than you probably are. Send pictures/video of your work to me or each other when stuck so we can discuss, or ask questions when we have our Zoom sessions. I'll be checking email a lot, as usual.
*With 'Act of God' days, teachers are not taking attendance. Even if we were to grade work and enter into the gradebook, it will not be counted by the school. So while this is the case, I hope you will keep up with your classes. Be curious! Enjoy learning! When you go to college, you will still be expected to know some of this stuff! Complete what you started, and give it your best shot! And at this time, we don't know the status of any AP exams.*
Magnetic Flux
Faraday's law revolves around magnetic flux. From Gauss's law, electric flux = (E-field)*(area it flows through); so same idea, magnetic flux = (B-field)*(area it flows through) = BA.
But what Faraday discovered is that if one changes the magnetic flux flowing through the area of a wire hoop, voltage is turned on, or induced. That's it!! Make a system where the magnetic flux through wires is changing, and you can power things with electricity. This is an electric generator, and the basis for how power plants work all around the world! Related to it are electric motors (think about how many electric motors are in your house and in your life).
Faraday's law: Amount of induced voltage = emf = -d(BA)/dt
Here, emf is what he called electromotive force...it is just voltage that gets turned on when the magnetic flux changes. We will study the 2 main ways to change the flux:
i. induced voltage = B dA/dt, which is Packet 2
ii. induced voltage = A dB/dt, which is Packet 3
For Wednesday:
- Watch a short video on finding flux through a loop of wire.
- Try Ch. 27 #11, 13 and Ch. 29 #1, 7. These are on pages 5 and 6 of Packet 1. Answers are in the back of your textbook, and check examples in chapters 27, 29 that are similar if you get stuck. We'll go over these and introduce Faraday's law in Wednesday's Zoom session.
Thinking ahead:
For Thursday and Friday, we will focus on Packet 2. This will be the case where we leave the B-field alone, and move things around so that the flux area changes (this is how generators in power plants work). We will focus on videos for a moving piece of metal in a magnetic field, moving a metal hoop through a B-field, and dropping metal hoop through a B-field. Believe it or not, these cases will be the same mathematically as an old favorite, air friction!! 😉😨
Note there are worked examples/notes in packet 2 that go along with the video examples. And we will be trying the AP problems in Packet 2. Don't forget we have AP solutions on the school website, in the AP Exams page, in the AP Exam Solutions folder. You need to be logged in your eths202.org account in order to access these solutions.
If you missed Tuesday's 10 am class session, click here for the video recording.
Electromagnetic induction: This is one of the greatest discoveries in physics history, if not science history, since it helped create our modern electrical civilization. The primary players in this were Michael Faraday on the experimental side, and James Clerk Maxwell on the theoretical side. You've already 'discovered' the gist of em induction in our magnet lab a couple sessions ago - I asked you to play with magnets and a solenoid to see if you could create voltage using nothing but the magnet.
How did you do it?
You had to move the magnet around inside the solenoid. So some combination of coils of wire, a magnet, and motion allow us to create electricity. I will demonstrate this in Wednesday's Zoom session, if you are able to join us. I brought some equipment home so we can still at least do demos.
We are starting with Packet 1 (you either have a hard copy or it is in the EM Induction folder of our school site). This introduces magnetic flux and Faraday's law of em induction.
Note that I will still be giving recommended practice sets, and we have relevant videos for each concept and type of problem. I hope you will still try them, and discuss with any study group or individuals as you normally do - but remotely!! Call or Face-time or use other social media platforms, or use Zoom or Skype to meet with each other remotely; we strongly discourage you from meeting in person. The whole point is social separation for the next couple weeks, not only to protect you, but to prevent the spread to those who have contact with older individuals who are much more susceptible to this virus than you probably are. Send pictures/video of your work to me or each other when stuck so we can discuss, or ask questions when we have our Zoom sessions. I'll be checking email a lot, as usual.
*With 'Act of God' days, teachers are not taking attendance. Even if we were to grade work and enter into the gradebook, it will not be counted by the school. So while this is the case, I hope you will keep up with your classes. Be curious! Enjoy learning! When you go to college, you will still be expected to know some of this stuff! Complete what you started, and give it your best shot! And at this time, we don't know the status of any AP exams.*
Magnetic Flux
Faraday's law revolves around magnetic flux. From Gauss's law, electric flux = (E-field)*(area it flows through); so same idea, magnetic flux = (B-field)*(area it flows through) = BA.
But what Faraday discovered is that if one changes the magnetic flux flowing through the area of a wire hoop, voltage is turned on, or induced. That's it!! Make a system where the magnetic flux through wires is changing, and you can power things with electricity. This is an electric generator, and the basis for how power plants work all around the world! Related to it are electric motors (think about how many electric motors are in your house and in your life).
Faraday's law: Amount of induced voltage = emf = -d(BA)/dt
Here, emf is what he called electromotive force...it is just voltage that gets turned on when the magnetic flux changes. We will study the 2 main ways to change the flux:
i. induced voltage = B dA/dt, which is Packet 2
ii. induced voltage = A dB/dt, which is Packet 3
For Wednesday:
- Watch a short video on finding flux through a loop of wire.
- Try Ch. 27 #11, 13 and Ch. 29 #1, 7. These are on pages 5 and 6 of Packet 1. Answers are in the back of your textbook, and check examples in chapters 27, 29 that are similar if you get stuck. We'll go over these and introduce Faraday's law in Wednesday's Zoom session.
Thinking ahead:
For Thursday and Friday, we will focus on Packet 2. This will be the case where we leave the B-field alone, and move things around so that the flux area changes (this is how generators in power plants work). We will focus on videos for a moving piece of metal in a magnetic field, moving a metal hoop through a B-field, and dropping metal hoop through a B-field. Believe it or not, these cases will be the same mathematically as an old favorite, air friction!! 😉😨
Note there are worked examples/notes in packet 2 that go along with the video examples. And we will be trying the AP problems in Packet 2. Don't forget we have AP solutions on the school website, in the AP Exams page, in the AP Exam Solutions folder. You need to be logged in your eths202.org account in order to access these solutions.
Thursday, October 24, 2019
For Thursday classes
My sincere apologies for being out with illness today.
Please take a look at a video on air friction. While the math details may not make total sense on a viewing, it will introduce you to the conversation for tomorrow. Also, especially if you are in pre-calculus or need a review if in calculus, watch and take notes for a video on the chain rule, which is something that is used for finding derivatives of slightly more complex functions than what we have experienced so far in class.
After the videos, you have a chance to get a lot of work done. Lab groups can get together and complete anything that is left with data collection, and then the analysis report. We are looking to have the report shared with Doc V by the end of Friday evening. If your group completes the lab, please work on the various practice problems for Newton's laws, which are listed on the usual white board.
Many thanks, and cannot wait to see you Friday! :-)
Please take a look at a video on air friction. While the math details may not make total sense on a viewing, it will introduce you to the conversation for tomorrow. Also, especially if you are in pre-calculus or need a review if in calculus, watch and take notes for a video on the chain rule, which is something that is used for finding derivatives of slightly more complex functions than what we have experienced so far in class.
After the videos, you have a chance to get a lot of work done. Lab groups can get together and complete anything that is left with data collection, and then the analysis report. We are looking to have the report shared with Doc V by the end of Friday evening. If your group completes the lab, please work on the various practice problems for Newton's laws, which are listed on the usual white board.
Many thanks, and cannot wait to see you Friday! :-)
Monday, March 18, 2019
The rest of the week
Below are some things to work on Wednesday - Friday, and then get a well-deserved break before we start the last quarter!
Wednesday (3/20)
Periods 3-4, 8-9:
We're going to try to pick up as much as possible about Faraday's law of electromagnetic induction. This is one of the biggies in all of science, not just physics. It is responsible for understanding electric motors, electric generators, transformers (which make our power grid work properly), different types of stoves and amusement park rides, all the way down to how light works as an electromagnetic wave! There's a lot of applications with a relatively basic observation:
If one changes magnetic flux, flux = BA, through a conductor, voltage is induced. This induced voltage is sometimes called emf (electromotive force). It was discovered by Michael Faraday in the 1820s and 1830s.
emf = d(BA)/dt
This is a video for moving a loop of wire through a magnetic field. This is the case emf = B dA/dt. To get the essence of this phenomenon, also check out a video on what happens just by moving a piece of metal through a magnetic field...it polarizes, and can act like a battery!
In the B dA/dt packet, try the 1981 AP Problem on page 7 and the glider problem on page 8.
Period 5:
Get your data for the resistance lab. This means NOT connecting the circuit to a power supply. Try to set up all the various circuits on your breadboard, and measure the total resistance (set your multimeter to ohms, ) for series, parallel, and combinations of the two. The big goal is to look for patterns - how does the total resistance change as you put in other resistors? Does the total increase or decrease? By how much does the total resistance change as you add in more resistors? Use the data page as a guide of what each circuit should look like.
Thursday (3/21)
Periods 3-4, 8-9:
This is video for a loop falling through a magnetic field - the magnetic forces act like air friction, and with gravity we get terminal velocity! This is another case of emf = B dA/dt.
Use the example of the video to try the 1990 problem on page 9 and 'the hardest ever' on the last page.
Period 5:
Today, connect the power supply to the circuit using the short wire jumpers connected in the breadboard. Try the two experiments on the Ohm's law lab sheet. Have a fixed resistance on the breadboard and vary the voltage to measure the currents (in milliamps). Then, change the resistance on the breadboard and set the voltage to the same value each time, to see what effect resistance has on the electric current.
Friday (3/22)
Periods 3-4, 8-9:
This is a video for the second case of changing magnetic flux, where the metal loop stays still and the magnetic field changes. Physically this happens because a changing B-field induces a circulating electric field! This is the reverse of a changing E-field, due to moving charges, inducing a circulating magnetic field. Also watch this video going through an example of circulating E-fields created when there is a changing B-field.
The problems are in the new AdB/dt packet. Try the 2010 and 1978 AP problems on pages 4 and 5.
Take the past three days as far as you can in class, and we will have time to answer questions, break things down, see physical examples, synthesize and expand after spring break! We'll all figure it out! :-)
Period 5:
Be sure to complete the data collection for the two labs. When you have all the data, try the analysis questions for each lab, and take things as far as your group can. You will need to make some graphs using the chromebooks for the Ohm's law lab. We will look at the data and go through the big results after spring break!
HAVE WONDERFUL, RELAXING SPRING BREAKS!!!!!!!
Wednesday (3/20)
Periods 3-4, 8-9:
We're going to try to pick up as much as possible about Faraday's law of electromagnetic induction. This is one of the biggies in all of science, not just physics. It is responsible for understanding electric motors, electric generators, transformers (which make our power grid work properly), different types of stoves and amusement park rides, all the way down to how light works as an electromagnetic wave! There's a lot of applications with a relatively basic observation:
If one changes magnetic flux, flux = BA, through a conductor, voltage is induced. This induced voltage is sometimes called emf (electromotive force). It was discovered by Michael Faraday in the 1820s and 1830s.
emf = d(BA)/dt
This is a video for moving a loop of wire through a magnetic field. This is the case emf = B dA/dt. To get the essence of this phenomenon, also check out a video on what happens just by moving a piece of metal through a magnetic field...it polarizes, and can act like a battery!
In the B dA/dt packet, try the 1981 AP Problem on page 7 and the glider problem on page 8.
Period 5:
Get your data for the resistance lab. This means NOT connecting the circuit to a power supply. Try to set up all the various circuits on your breadboard, and measure the total resistance (set your multimeter to ohms, ) for series, parallel, and combinations of the two. The big goal is to look for patterns - how does the total resistance change as you put in other resistors? Does the total increase or decrease? By how much does the total resistance change as you add in more resistors? Use the data page as a guide of what each circuit should look like.
Thursday (3/21)
Periods 3-4, 8-9:
This is video for a loop falling through a magnetic field - the magnetic forces act like air friction, and with gravity we get terminal velocity! This is another case of emf = B dA/dt.
Use the example of the video to try the 1990 problem on page 9 and 'the hardest ever' on the last page.
Period 5:
Today, connect the power supply to the circuit using the short wire jumpers connected in the breadboard. Try the two experiments on the Ohm's law lab sheet. Have a fixed resistance on the breadboard and vary the voltage to measure the currents (in milliamps). Then, change the resistance on the breadboard and set the voltage to the same value each time, to see what effect resistance has on the electric current.
Friday (3/22)
Periods 3-4, 8-9:
This is a video for the second case of changing magnetic flux, where the metal loop stays still and the magnetic field changes. Physically this happens because a changing B-field induces a circulating electric field! This is the reverse of a changing E-field, due to moving charges, inducing a circulating magnetic field. Also watch this video going through an example of circulating E-fields created when there is a changing B-field.
The problems are in the new AdB/dt packet. Try the 2010 and 1978 AP problems on pages 4 and 5.
Take the past three days as far as you can in class, and we will have time to answer questions, break things down, see physical examples, synthesize and expand after spring break! We'll all figure it out! :-)
Period 5:
Be sure to complete the data collection for the two labs. When you have all the data, try the analysis questions for each lab, and take things as far as your group can. You will need to make some graphs using the chromebooks for the Ohm's law lab. We will look at the data and go through the big results after spring break!
HAVE WONDERFUL, RELAXING SPRING BREAKS!!!!!!!
Wednesday, April 4, 2018
Wednesday
Periods 3-4, 8-9:
VERY sorry to miss you again...please hang in there!
Check out an example of this Faraday's law where a second force is present, such as gravity. This is going to be mathematically the same as n old friend, air friction, from last year; this will be a terminal velocity thing. Be sure to get some notes on it.
As a bonus problem, you can try the last problem in the B dA dt Induction packet, page 9 (nicknamed 'the hardest ever').
Then, check out the second version of Faraday's law, and how we can change magnetic flux. This is where the area stays constant (just have a metal hoop sitting there) and we change the magnetic field. This is physically a different process where a moving magnet creates (i.e. induces) an electric field. This is true E&M - so a moving charge turns on a B-field, and a moving magnet (or any type of changing B-field) turns on an E-field. This video is on induced voltage = emf = AdB/dt.
For some initial practice, try the 1978 and 1999 AP problems (p. 5, 7) in the AdB/dt packet in the EM Induction folder. (called A dB dt Induction.pdf)
VERY sorry to miss you again...please hang in there!
Check out an example of this Faraday's law where a second force is present, such as gravity. This is going to be mathematically the same as n old friend, air friction, from last year; this will be a terminal velocity thing. Be sure to get some notes on it.
As a bonus problem, you can try the last problem in the B dA dt Induction packet, page 9 (nicknamed 'the hardest ever').
Then, check out the second version of Faraday's law, and how we can change magnetic flux. This is where the area stays constant (just have a metal hoop sitting there) and we change the magnetic field. This is physically a different process where a moving magnet creates (i.e. induces) an electric field. This is true E&M - so a moving charge turns on a B-field, and a moving magnet (or any type of changing B-field) turns on an E-field. This video is on induced voltage = emf = AdB/dt.
For some initial practice, try the 1978 and 1999 AP problems (p. 5, 7) in the AdB/dt packet in the EM Induction folder. (called A dB dt Induction.pdf)
Wednesday, January 24, 2018
For Wednesday
I am terribly sorry for missing again, but let's make the most of it. I'll make it up somehow.
Periods 3-4, 8-9:
Now that all the groups have observations and some data for RC circuits, we want to get a sense of the theory and math behind them. There are two cases for RC circuits in series: connecting a battery and charging the capacitor, and having a charged capacitor and then removing the battery so the capacitor discharges. Check out the following videos on your Chromebooks and take notes...you probably have guessed that, yes, we will all need to be able to do these derivations. Keep in mind that, for whatever reason, this is the same math that we used last year with air friction!
Watch this for CHARGING capacitors. Watch this for DISCHARGING capacitors.
After watching these, you can complete the lab (theory into reality, last part). After receiving the RC packets, give a try on the two AP problems on the second and third pages (2002, 2003). If you have spare time, see what you think of the derivative calculator in the previous post....looks pretty cool.
Period 6:
We will start the process for our bridges. First, decide on who you will work with. To maximize your hands-on experience and have a chance to still talk through designs, we will work in pairs. However, you do have the option of working on your own if you wish to try.
Next, you have the period to go through the information passed out yesterday. Use the information for the various forces bridges experience, such as tension, stress, strain, compression, and so on - you will need to be able to define these. Then work on reaching a decision of design. Remember the specifications: the bridge will need to be between 30 cm and 40 cm in length, and span a 30 cm gap. Feel free to look online at designs, there should be lots of information since there are numerous bridge building contests around the country.
Keep in mind you will need to explain to Doc V and the class why you chose the design you ultimately make (think in terms of how forces are distributed in order to make the bridge stronger).
Periods 3-4, 8-9:
Now that all the groups have observations and some data for RC circuits, we want to get a sense of the theory and math behind them. There are two cases for RC circuits in series: connecting a battery and charging the capacitor, and having a charged capacitor and then removing the battery so the capacitor discharges. Check out the following videos on your Chromebooks and take notes...you probably have guessed that, yes, we will all need to be able to do these derivations. Keep in mind that, for whatever reason, this is the same math that we used last year with air friction!
Watch this for CHARGING capacitors. Watch this for DISCHARGING capacitors.
After watching these, you can complete the lab (theory into reality, last part). After receiving the RC packets, give a try on the two AP problems on the second and third pages (2002, 2003). If you have spare time, see what you think of the derivative calculator in the previous post....looks pretty cool.
Period 6:
We will start the process for our bridges. First, decide on who you will work with. To maximize your hands-on experience and have a chance to still talk through designs, we will work in pairs. However, you do have the option of working on your own if you wish to try.
Next, you have the period to go through the information passed out yesterday. Use the information for the various forces bridges experience, such as tension, stress, strain, compression, and so on - you will need to be able to define these. Then work on reaching a decision of design. Remember the specifications: the bridge will need to be between 30 cm and 40 cm in length, and span a 30 cm gap. Feel free to look online at designs, there should be lots of information since there are numerous bridge building contests around the country.
Keep in mind you will need to explain to Doc V and the class why you chose the design you ultimately make (think in terms of how forces are distributed in order to make the bridge stronger).
Wednesday, September 6, 2017
Projectile Review
As we get back into motion, projectiles are a classic case of 2-D motion from sophomore year. Let's bring it back! Check out one video that focuses on the basic properties and concepts of projectiles, a video with a couple examples of how to set up these problems (and they are all pretty much the same!), and if interested, one that goes into the reason why projectiles move on a parabolic path, as well as the effect of air friction on that parabola.
Check these out as needed as you bring back the problem solving skills with the homework set of problems.
Check these out as needed as you bring back the problem solving skills with the homework set of problems.
Friday, August 18, 2017
Understanding some Properties of Projectiles
Forget the math for a few minutes - focus on some of the important concepts and interesting properties of projectiles, at least under ideal conditions (i.e. no air friction!). This gets into the importance of independent horizontal and vertical motions that are really the key to understanding projectile motion, and multi-dimensional motion in general. To understand why parabolic paths form, check out this video. To check out some basic math for projectile problems, check out this video.
Check it out, and hopefully this will make some sense to help you understand what the math is telling us when we do problems.
Check it out, and hopefully this will make some sense to help you understand what the math is telling us when we do problems.
Thursday, August 17, 2017
Projectile trajectories - With and Without Air Friction
All of us are familiar with the arch-shaped path, or trajectory, a ball follows when we throw it. When symmetric, this is a parabola, and is the common shape we use in physics classes for projectiles. But WHY is it an arch of any kind, let alone a parabola? And why are we lying to you about projectiles???
We ignore air friction when we do projectile problems, but in life this makes it more complicated, and also no longer a perfect parabola. Check out this video to get a sense of why parabolas form when there is no air friction, and what the trajectory looks like in a more realistic environment, with air friction.
We ignore air friction when we do projectile problems, but in life this makes it more complicated, and also no longer a perfect parabola. Check out this video to get a sense of why parabolas form when there is no air friction, and what the trajectory looks like in a more realistic environment, with air friction.
How to do Projectile Motion problems
Projectiles are objects that fly through the air or space, under the influence of gravity (and ignoring air friction for now), but not using any of its own energy to do so. It has been 'projected' by something else to start moving, like kicking or throwing a ball, shooting an arrow, a satellite, or even when you run and jump - you're a projectile once in the air!
Projectiles follow an arch, which is technically a parabola when there is no air resistance.
The key to understanding this motion is to realize there are two motions simultaneously: constant horizontal velocity, and constant vertical acceleration due to gravity. And when two things are perpendicular to each other, they are also independent of each other. Sideways motion could care less about what happens vertically, and vice versa!
Check out this video, which goes through two related projectile problems, and how to set them up.
Projectiles follow an arch, which is technically a parabola when there is no air resistance.
The key to understanding this motion is to realize there are two motions simultaneously: constant horizontal velocity, and constant vertical acceleration due to gravity. And when two things are perpendicular to each other, they are also independent of each other. Sideways motion could care less about what happens vertically, and vice versa!
Check out this video, which goes through two related projectile problems, and how to set them up.
Tuesday, April 4, 2017
EM Induction Links
For Tuesday:
Check out the case emf = B dA/dt, where the circuit moves and the area changes. This is an example of a magnetic brake, where the loop will start to slow down due to the weird induction phenomena.
Then, a special example of this type of induction, where the circuit falls through a magnetic field (in other words, when there is a constant force trying to accelerate the circuit/loop. This is going to end up looking a lot like air friction on a skydiver, with a terminal velocity!
By the way, check this one out if you want to see a strange case of finding the magnetic flux through a circuit due to the magnetism from a long, straight wire next to the circuit.
On Wednesday, which you have off, check out a preview of the other case, where emf = A dB/dt. This is going to involve a circulating electric field! Weird, but welcome to the world of electromagnetism. Here is a video specifically on the circulating E-field that is created when there is dB/dt. :-)
Check out the case emf = B dA/dt, where the circuit moves and the area changes. This is an example of a magnetic brake, where the loop will start to slow down due to the weird induction phenomena.
Then, a special example of this type of induction, where the circuit falls through a magnetic field (in other words, when there is a constant force trying to accelerate the circuit/loop. This is going to end up looking a lot like air friction on a skydiver, with a terminal velocity!
By the way, check this one out if you want to see a strange case of finding the magnetic flux through a circuit due to the magnetism from a long, straight wire next to the circuit.
On Wednesday, which you have off, check out a preview of the other case, where emf = A dB/dt. This is going to involve a circulating electric field! Weird, but welcome to the world of electromagnetism. Here is a video specifically on the circulating E-field that is created when there is dB/dt. :-)
Thursday, December 22, 2016
Mechanics Semester Review
Here is a list of topics for our final, the second week back from winter break:
Basics:
Vector algebra - vector addition, multiplication (dot and cross products)
Derivatives - finding them; what does it mean graphically; instantaneous values
Define v = dx/dt; a = dv/dt
Antiderivatives - finding them; what does it mean graphically
Motion graphs
Kinematics:
Constant acceleration equations, how to use them in a variety of problems
Free fall
Relative motion (e.g. boat going across a river)
Projectiles
Newton's laws:
Know them by number; conceptually what do they mean? Examples.
Finding resultant forces (vector addition)
Equilibrium, balancing forces in multiple dimensions
Applications of Fnet = ma, all types
Tension, friction, on inclines (gravity triangle), springs
Systems problems, such as multiple blocks tied together
Circular motion, how to set up mv^2/R in problems; horizontal vs vertical problems
NON-constant forces and accelerations
Air friction, f = -kv; derivation of v(t); chain rule
Gravity - Newton's law of universal gravitation; Einstein's thoughts on warped space-time
Orbital motion - orbital speed, Kepler's laws; Binary orbits
Energy:
Conservation law
Different types, conversions of energy
Work redefined as an integral; work is the amount of energy transferred between objects
Using work and conservation to solve a variety of problems, especially with speeds and non-constant forces
Potential energies (gravity, springs)
How to do gravity the right way with energy, U = -GMm/r; what does - sign mean?
Potential wells - U-x graph vs F-x graph; positive force vs negative force
Gradient, F = - dU/dx; what this means
Escape velocity; Schwarzschild radius
Power
Special relativity implications, Einstein's energy equation
Resources:
Videos on most of the topics above. For practice multiple choice, the SAT II site has notes, sample questions, and explanations on all these topics. There is a Learn AP Physics C site, with practice questions. We have our AP Exams folder (but you must be logged in only on your eths202.org account). Note there is a multiple choice folder, with hundreds of practice questions. There are review sets in each of our unit folders. Read up on any topic and check out dozens of worked examples in Chapter 1-7, which is what we have covered so far. You have your old quizzams and solutions, homework sets, and labs.
Basics:
Vector algebra - vector addition, multiplication (dot and cross products)
Derivatives - finding them; what does it mean graphically; instantaneous values
Define v = dx/dt; a = dv/dt
Antiderivatives - finding them; what does it mean graphically
Motion graphs
Kinematics:
Constant acceleration equations, how to use them in a variety of problems
Free fall
Relative motion (e.g. boat going across a river)
Projectiles
Newton's laws:
Know them by number; conceptually what do they mean? Examples.
Finding resultant forces (vector addition)
Equilibrium, balancing forces in multiple dimensions
Applications of Fnet = ma, all types
Tension, friction, on inclines (gravity triangle), springs
Systems problems, such as multiple blocks tied together
Circular motion, how to set up mv^2/R in problems; horizontal vs vertical problems
NON-constant forces and accelerations
Air friction, f = -kv; derivation of v(t); chain rule
Gravity - Newton's law of universal gravitation; Einstein's thoughts on warped space-time
Orbital motion - orbital speed, Kepler's laws; Binary orbits
Energy:
Conservation law
Different types, conversions of energy
Work redefined as an integral; work is the amount of energy transferred between objects
Using work and conservation to solve a variety of problems, especially with speeds and non-constant forces
Potential energies (gravity, springs)
How to do gravity the right way with energy, U = -GMm/r; what does - sign mean?
Potential wells - U-x graph vs F-x graph; positive force vs negative force
Gradient, F = - dU/dx; what this means
Escape velocity; Schwarzschild radius
Power
Special relativity implications, Einstein's energy equation
Resources:
Videos on most of the topics above. For practice multiple choice, the SAT II site has notes, sample questions, and explanations on all these topics. There is a Learn AP Physics C site, with practice questions. We have our AP Exams folder (but you must be logged in only on your eths202.org account). Note there is a multiple choice folder, with hundreds of practice questions. There are review sets in each of our unit folders. Read up on any topic and check out dozens of worked examples in Chapter 1-7, which is what we have covered so far. You have your old quizzams and solutions, homework sets, and labs.
Monday, October 31, 2016
Classes on Halloween
Periods 1-2, 8-9
The students should break into groups of 3-4 and try the 8 circular motion questions, and get it turned in. Once this is completed, watch and take detailed notes on videos for the two types of air friction cases we do. The first is when air friction is the only force acting on an object, like a hockey puck. The second is when there is a second force acting on an object with air friction, such as on a skydiver. Note that something that comes into play for teh skydiver type problem is the chain rule. Check out a video for chain rule if this is a new concept for you.
Students should then be sure to have the pendulum mini-lab completed and shared with Doc V at vondracekm@eths202.org. We will go through the priorities Tuesday.
Period 3
Students will get there tests back with solutions. They should review and make corrections together, in small groups of 3 or 4. They should talk through and make sure everyone in the group is OK with each answer/solution.
Then, students should watch and take notes on two videos. One is an introduction to circular motion, and the idea that a force is needed to allow a car to make a turn. And then a second that introduces the concept of centripetal force - a force pointing inwards, towards the center of the circle the object is moving around. We will start to make sense of this tomorrow, using pendulums.
The students should break into groups of 3-4 and try the 8 circular motion questions, and get it turned in. Once this is completed, watch and take detailed notes on videos for the two types of air friction cases we do. The first is when air friction is the only force acting on an object, like a hockey puck. The second is when there is a second force acting on an object with air friction, such as on a skydiver. Note that something that comes into play for teh skydiver type problem is the chain rule. Check out a video for chain rule if this is a new concept for you.
Students should then be sure to have the pendulum mini-lab completed and shared with Doc V at vondracekm@eths202.org. We will go through the priorities Tuesday.
Period 3
Students will get there tests back with solutions. They should review and make corrections together, in small groups of 3 or 4. They should talk through and make sure everyone in the group is OK with each answer/solution.
Then, students should watch and take notes on two videos. One is an introduction to circular motion, and the idea that a force is needed to allow a car to make a turn. And then a second that introduces the concept of centripetal force - a force pointing inwards, towards the center of the circle the object is moving around. We will start to make sense of this tomorrow, using pendulums.
Friday, March 18, 2016
For Classes on March 18
Happy Friday everyone!
Periods 1-2, 8-9:
Yesterday you saw something on Faraday's law for a moving hoop/changing area example. This is the case where induced voltage = B dA/dt. Today extend on this by looking at cases where a second force is trying to push a circuit through magnetism, such as dropping a metal hoop into a B-field. What you will see is that, because this process depends on speed, it ends up looking a lot like air friction and terminal velocity from last year! Weird, but true. Remember the case of you trying to swing the metal hoop through the big magnet, and you felt the forces on it trying to slow it down (this is a magnetic brake). Take good notes so you can try to make sense together of the home work problems - see if you can complete things before leaving.
Homework set:
The glider problem on page 6 is based on yesterday - use the notes on page 2 and 3, could be helpful
The 1990 problem on page 7 - notes on page 4 could be helpful
The challenge problem is on page 9! Have fun!
Periods 3-4:
Take a look at the problems for yesterday, and see if there is any consensus. Ampere's law depends on the current inside the region you are looking at, analogous to Gauss's law depending on teh charge inside the region.
One application of Ampere's law for straight wires, where B = (mu)I/(2*pi*r), is to get the force between two currents. Check out a video on the forces between two long wires with currents - they are both producing magnetism, so the wires should either attract or repel each other! Take good notes, this will be needed for some of the homework. Note that the force on currents is F = IL x B, where L is the length of a segment of the wire.
Then, take a look at a video on the initial exposure to Biot-Savart law. This is the rule that allows us to determine the magnetic field for things more exactly (Ampere is only for long wires, solenoids, and toroids, so it is limited). We will look at what a single moving particle does in terms of producing a magnetic field. Take good notes, because we will build on this.
Try the following from the packet:
Ch. 28 #8 (B-S law), 31 on page 7
AP Prob from 1983, page 11
Periods 1-2, 8-9:
Yesterday you saw something on Faraday's law for a moving hoop/changing area example. This is the case where induced voltage = B dA/dt. Today extend on this by looking at cases where a second force is trying to push a circuit through magnetism, such as dropping a metal hoop into a B-field. What you will see is that, because this process depends on speed, it ends up looking a lot like air friction and terminal velocity from last year! Weird, but true. Remember the case of you trying to swing the metal hoop through the big magnet, and you felt the forces on it trying to slow it down (this is a magnetic brake). Take good notes so you can try to make sense together of the home work problems - see if you can complete things before leaving.
Homework set:
The glider problem on page 6 is based on yesterday - use the notes on page 2 and 3, could be helpful
The 1990 problem on page 7 - notes on page 4 could be helpful
The challenge problem is on page 9! Have fun!
Periods 3-4:
Take a look at the problems for yesterday, and see if there is any consensus. Ampere's law depends on the current inside the region you are looking at, analogous to Gauss's law depending on teh charge inside the region.
One application of Ampere's law for straight wires, where B = (mu)I/(2*pi*r), is to get the force between two currents. Check out a video on the forces between two long wires with currents - they are both producing magnetism, so the wires should either attract or repel each other! Take good notes, this will be needed for some of the homework. Note that the force on currents is F = IL x B, where L is the length of a segment of the wire.
Then, take a look at a video on the initial exposure to Biot-Savart law. This is the rule that allows us to determine the magnetic field for things more exactly (Ampere is only for long wires, solenoids, and toroids, so it is limited). We will look at what a single moving particle does in terms of producing a magnetic field. Take good notes, because we will build on this.
Try the following from the packet:
Ch. 28 #8 (B-S law), 31 on page 7
AP Prob from 1983, page 11
Thursday, February 4, 2016
3 Chem-Phys Classes
Watch the two videos we have for details of air friction.
The first video is the 'easier' case of horizontal motion, where air friction is the only horizontal force acting on the object.
The second video is for things that fall, such as sky divers or coffee filters in our lab. The end result is terminal velocity.
Take careful notes of the derivations in these videos. I suggest anyone in trigonometry sit by someone in calculus, especially where the chain rule comes into play on an integral. Also, explain to anyone not in calculus where natural log (ln) comes out. You will be expected to know how to do these derivations in the near future - if you need to replay any part(s) of a video, go for it, or you can watch these any time. We will summarize the math on Monday.
After the videos and notes, you can work on the homework set and/or lab write up.
Have a wonderful weekend!! :-)
The first video is the 'easier' case of horizontal motion, where air friction is the only horizontal force acting on the object.
The second video is for things that fall, such as sky divers or coffee filters in our lab. The end result is terminal velocity.
Take careful notes of the derivations in these videos. I suggest anyone in trigonometry sit by someone in calculus, especially where the chain rule comes into play on an integral. Also, explain to anyone not in calculus where natural log (ln) comes out. You will be expected to know how to do these derivations in the near future - if you need to replay any part(s) of a video, go for it, or you can watch these any time. We will summarize the math on Monday.
After the videos and notes, you can work on the homework set and/or lab write up.
Have a wonderful weekend!! :-)
Thursday, January 29, 2015
Details on Air Friction
Thanks to Nathan H. for finding this site.
There is a useful NASA site that gets into air friction a little deeper than we do in class. This link takes you to a description of the drag coefficient (like the constant we use) - see some of the details and other factors that go into the drag term, which leads directly to an understanding of how strong air friction will be on an object. Have fun with it!
There is a useful NASA site that gets into air friction a little deeper than we do in class. This link takes you to a description of the drag coefficient (like the constant we use) - see some of the details and other factors that go into the drag term, which leads directly to an understanding of how strong air friction will be on an object. Have fun with it!
Sunday, November 16, 2014
Advanced Topics for Olympiad
Here are some quick links to videos about topics that are more likely to make appearances on the Olympiad exams than on the AP.
- air friction, horizontal
- air friction, with a second applied force (think sky diver)
- Gauss's law for gravity
- Gauss's law for gravity (inside earth)
- Non-gauss cases for gravity
- Momentum, ballistic pendulum type cases
- Moment of inertia, sticks
- Moment of inertia, disks
- Moment of inertia, where axis of rotation is not center of mass (parallel axis theorem)
- Pendulum, finding tension as it swings
- Pendulum, small-angle approximation for SHM
- SHM for springs, general
- SHM for springs, initial conditions (i.e. phase angle)
- SHM, spring and stick system oscillating through small angle
- Springs in series and parallel
Go to video page of this blog for numerous videos on all aspects of rotations.
- air friction, horizontal
- air friction, with a second applied force (think sky diver)
- Gauss's law for gravity
- Gauss's law for gravity (inside earth)
- Non-gauss cases for gravity
- Momentum, ballistic pendulum type cases
- Moment of inertia, sticks
- Moment of inertia, disks
- Moment of inertia, where axis of rotation is not center of mass (parallel axis theorem)
- Pendulum, finding tension as it swings
- Pendulum, small-angle approximation for SHM
- SHM for springs, general
- SHM for springs, initial conditions (i.e. phase angle)
- SHM, spring and stick system oscillating through small angle
- Springs in series and parallel
Go to video page of this blog for numerous videos on all aspects of rotations.
Monday, October 20, 2014
Classes for Oct. 20
For periods 1-2 and 8-9, check out this video on finding potentials at various locations of the charged sticks. Focus on how to set up the integrals, and what the proper limits of integration are. You can try the 1980 (back page) and 2002 problems (second to last page) of the packet from Friday.
For periods 3-4, check out this video for air friction and terminal velocity. You can try the 1984 problem, and then try to complete the lab (don't worry about the last analysis question for the time being).
For COMAP teams, have at least one person from each team come to one of the organizational meetings on Tuesday, either before school at 8 am, period 5, or period 6. Note that there are some online resources that can be found here.
For periods 3-4, check out this video for air friction and terminal velocity. You can try the 1984 problem, and then try to complete the lab (don't worry about the last analysis question for the time being).
For COMAP teams, have at least one person from each team come to one of the organizational meetings on Tuesday, either before school at 8 am, period 5, or period 6. Note that there are some online resources that can be found here.
Tuesday, August 19, 2014
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 multi-dimensional 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
write-up. 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, fair = -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 2-3 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
/ tavg)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 solid-dashed-dotted 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
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