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, 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 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 / 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 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

How To Deal With Air Friction Mathematically - Hockey Puck

Air friction is a different creature compared to static or kinetic friction. Static and kinetic frictions are forces between two solid surfaces, whereas air friction is between a solid surface and a fluid. Something like water friction behaves similar to air friction, where these friction forces depend on how fast you try to move through the fluid (think about how it is actually tougher to try and run in water than to walk in water). Check out how to handle this fluid friction mathematically...it is certainly more involved than dealing with static or kinetic friction, which we treat as constant forces. Air friction is non-constant, and calculus must be used to find an exponential behavior with time.

How to do Air Friction on a Sky Diver

Here is a case where air friction acts on a falling object, such as a sky diver. This is one of the trickier math problems we will do in physics, as it involves calculus (anything with air friction will, since it is a non-constant force: f = -kv). We specifically want to solve for the velocity as a function of time for the sky diver. Check this out to get a feel for how Newton's 2nd law sets up the equation, and then we do almost all algebra with a step of calculus to solve for velocity. Note that terminal velocity is the speed you reach when air friction matches the strength of gravity, and the person falls with a constant speed at that point. Also note that we do a very simplified model of air friction. Other factors we do not worry about here include the shape of the object, air density that varies with altitude, wind, air temperature that varies, the material of the object, the gaseous composition, and so on (for us, all this information is contained in the constant, k).

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.

Binary Stars and Air Friction Videos

Hey, juniors - here are two links for learning how to do binary orbits and air friction (the hockey puck example, and a sky diver example). For the air friction, this could be review of our derivations in class. For binary orbits, check out the video and see what you can do with the AP problem over the weekend. Feel free to do this with a friend or study group, and help each other through it.

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!

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.

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.

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!!  :-)

List of How to Videos on the blog

Below are links to specific “How To” videos that are relevant to 3 and 4 Chem-Phys. These show how to access programs perhaps, or how to do certain problems. It has a voice-over and screencast from Doc V’s tablet computer, so it is similar to being in class as we model how to do certain problems or run certain programs. These can be useful if you were gone the day we covered the topic, or need more examples with explanations, or want to review things from class prior to quizzams.


Student Independent Science Research
http://docvphysics.blogspot.com/2009/12/how-to-start-science-research-in-high.html


Mechanics

Air Friction – the math
http://docvphysics.blogspot.com/2009/10/how-to-deal-with-air-friction.html

Binary Orbits
http://docvphysics.blogspot.com/2009/12/how-to-find-basics-of-binary-orbits.html

Derivatives! What are they and how to do them.
http://docvphysics.blogspot.com/2009/10/how-to-define-and-find-derivatives.html

General Relativity and the Principle of Equivalence - Why does Gravity Bend Light?
http://docvphysics.blogspot.com/2010/11/basic-principle-of-general-relativity.html

Gravitational Potential Energy and Space Launches
http://docvphysics.blogspot.com/2009/12/how-to-find-gravitational-u-and-basics.html

Momentum Conservation – Why?
http://docvphysics.blogspot.com/2010/02/why-is-momentum-conserved-for-colliding.html

Momentum Conservation - How to do Inelastic Collisions
http://docvphysics.blogspot.com/2010/11/how-to-do-inelastic-collisions-where.html

Moment of Inertia Using the Integral – Disks
http://docvphysics.blogspot.com/2010/04/how-to-find-moment-of-inertia-for-solid.html

Moment of Inertia Using the Integral – Sticks
http://docvphysics.blogspot.com/2010/04/how-to-calculate-moments-of-inertia.html

Parallel Axis Theorem (finding moments of inertia)
http://docvphysics.blogspot.com/2010/03/how-to-use-parallel-axis-theorem-to.html

Pendulum: Simple Harmonic Motion for small angles
http://docvphysics.blogspot.com/2010/04/how-to-get-simple-harmonic-motion.html

Potential Wells
http://docvphysics.blogspot.com/2009/12/how-to-interpret-potential-wells.html

Quantum Numbers: Using Simple Harmonic Motion to help see where these come from
http://docvphysics.blogspot.com/2010/04/where-do-those-quantum-numbers-come.html

Rotations: Both Linear and Rotational Motion Simultaneously
http://docvphysics.blogspot.com/2010/03/how-to-handle-rotations-and-linear.html

Rotations: Collisions and Conservation of Angular Momentum
http://docvphysics.blogspot.com/2010/03/how-to-apply-conservation-of-angular.html

Rotations: NON-Constant Acceleration
http://docvphysics.blogspot.com/2010/03/how-to-do-rotational-motion-for.html

Simple Harmonic Motion: General Derivation of sine, cosine solutions
http://docvphysics.blogspot.com/2010/03/how-to-find-solutions-for-simple.html

Simple Harmonic Motion: Solving with specific initial conditions using phase angle
http://docvphysics.blogspot.com/2010/03/how-to-solve-simple-harmonic-motion.html

Special Relativity – mass and energy, where E = mc2 comes from
http://docvphysics.blogspot.com/2009/12/how-to-play-einstein-for-day-mass-and.html

Springs and Energy
http://docvphysics.blogspot.com/2010/11/spring-problems-and-use-of-energy.html

Tension problems with rotating pulleys: http://docvphysics.blogspot.com/2010/04/how-to-handle-real-pulley-in-tension.html

Tension problems with systems of objects: http://docvphysics.blogspot.com/2009/10/how-to-do-tension-problems.html



E&M

Ammeters and Voltmeters - How they work
http://docvphysics.blogspot.com/2010/12/wussup-with-ammeters-and-voltmeters.html

Ampere’s law applications
http://docvphysics.blogspot.com/2010/03/how-to-apply-amperes-law.html

Capacitance – how to find capacitance for the 3 types of capacitors
http://docvphysics.blogspot.com/2009/12/how-to-find-capacitance-for-each-type.html

Capacitor Circuits – How to find stored charge
http://docvphysics.blogspot.com/2009/12/how-to-find-charge-on-capacitors-in.html

Electric Circuit analysis
http://docvphysics.blogspot.com/2009/11/how-to-analyze-resistor-circuits.html

Electromagnetic Induction – how Induced Currents turn on (includes circulating E-field)
http://docvphysics.blogspot.com/2010/04/how-to-find-circulating-induced.html

Faraday’s law – Changing area with constant B-field
http://docvphysics.blogspot.com/2010/04/how-to-do-faradays-law-for-changing.html

Faraday’s law – Changing B-field with constant area
http://docvphysics.blogspot.com/2010/04/how-to-use-faradays-law-for-cases-where.html

Gauss’s law with conductors
http://docvphysics.blogspot.com/2009/10/how-to-do-gausss-law-with-conducting.html

Gauss’s law with NON-conductors: charge density
http://docvphysics.blogspot.com/2009/10/how-to-do-gausss-law-with-non.html

Gauss’s law with NON-uniform charge densities
http://docvphysics.blogspot.com/2010/04/how-to-do-gausss-law-with-non-uniform.html

Integration of E-fields to get Potential
http://docvphysics.blogspot.com/2009/11/how-to-integrate-and-find-electric.html

LC Circuit – similar to simple harmonic motion
http://docvphysics.blogspot.com/2010/04/how-to-do-math-of-lc-circuits.html

Magnetic Flux – Rectangular loop next to straight wire with current
http://docvphysics.blogspot.com/2010/04/how-to-find-magnetic-flux-straight-wire.html

Magnetic force between two current carrying wires
http://docvphysics.blogspot.com/2010/03/how-to-find-magnetic-forces-between.html

Mass Spectrometers and Velocity Selectors – magnetic forces, F = qv x B
http://docvphysics.blogspot.com/2010/04/how-to-think-about-mass-spectrometers.html

Point Charge Systems – finding total electric fields and potentials
http://docvphysics.blogspot.com/2010/04/how-to-find-electric-fields-and.html

Projectile Motion of Electric Charges
http://docvphysics.blogspot.com/2010/04/how-to-do-electrical-projectiles.html

RC Circuits – Charging Capacitor (series RC)
http://docvphysics.blogspot.com/2009/12/how-to-solve-charging-rc-circuit.html

RC Circuits – Discharging Capacitor (series RC)
http://docvphysics.blogspot.com/2009/12/how-to-solve-discharging-rc-circuit.html

RC Circuits – Resistor and capacitor in parallel
http://docvphysics.blogspot.com/2010/01/how-to-do-rc-circuit-with-r-and-c-in.html

RL Circuits – Current as functions of time
http://docvphysics.blogspot.com/2010/04/how-to-analyze-rl-circuits.html



Interactive Physics
Interactive Physics is software where you can design and create your own simulations; mostly for mechanics, but there are some E&M topics you can also work on. This is on school computers.
http://docvphysics.blogspot.com/2009/08/how-to-access-interactive-physics.html



iLab
See how to access the radioactivity iLab:
http://docvphysics.blogspot.com/2009/08/how-to-access-radioactivity-ilab.html

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.

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.

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!   :-)

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.    :-)

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.

The Power of Analogy in Learning

In physics, we use a lot of analogies. We compare just about all aspects of rotational motion to linear motion analogues. We compare electrical resistance to electrons bouncing in a pinball machine. Electric circuits are like roller coasters and plumbing systems. Energy and matter are like steam and ice, two forms of the same stuff. So this is not new for us, and it can really help us not only conceptually, but also in problem solving. If you are OK doing the mathematics of air friction, you can do the math of RC circuits, or if you know how to handle springs and pendulums in simple harmonic motion, you can do problems with LC circuits and even a case of Schrodinger's equation in quantum mechanics.

But on a larger scale, there is an interesting post about the power of analogy and how some are now thinking it is the key to cognition and learning in general. The more ways you can think about a system in terms of others that are more familiar and understood by you, then the more likely you are to solve the new problem. By building and modifying what you know about things through analogy, the more creative a solution you might develop when confronted by new problems that can be made familiar to things you know.

There is also a video from Doug Hofstadter at a Stanford forum on this topic. Watch it if interested, and after 13 minutes is the bulk of this topic.

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.

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!!!!!!!

How to Find Terminal Velocity of Conducting Loop Falling into B-field

Here is a different type of induction problem. This has to do with the long aluminum tube we have in the lab, and even though it is non-magnetic, a falling magnet in the tube falls with a terminal velocity. Huh?! The reason for this is as the magnet moves, it is changing flux in the loop. This induces a voltage (Faraday) and therefore a current (Ohm). In a tube these are called eddy currents.

But those currents then feel a force since they are in a magnetic field. This is F = Il x B. The force is upward, trying to stop the motion and therefore stopping the change in flux (Lenz). The mathematics turn out to be identical to that of a sky diver with air friction! We will get an exponential solution, and a terminal velocity. Check it out!

Classic footage from Moon - Hammer vs Feather

A classic experiment, done by Apollo astronauts on the moon, proved that, minus air friction, even a feather has the same acceleration due to gravity as heavier objects, such as a hammer. You can even notice that the acceleration is less than on earth by watching the fall. The acceleration of gravity on the moon is about 1/6 the earth's value of 9.8 m/s^2, which puts it at about 1.6 m/s^2.