yhbscience: March 2014

ASSIGNMENTS AND ASSISTANCE FOR PROJECT PROPOSALS:

SUN 9:15 AM – ALL DONE!!

SAT 11:30 PM –Jonas is done, 2 to go!

SAT 8:40 PM –I am working on the last 3 proposals and will be finished either late tonight or tomorrow morning.

FRI 6:30 PM – to save time, last 5 proposals will not have any math included now

PARENTS: Will you please review your child(ren)'s proposal(s) before submission on Thur? It will help them (and me) :|) THANK YOU!

TO MY JUNIOR SCIENTISTS: As I write these advice columns, I realize that everybody should read all of them, because there is a lot of helpful information that will improve your research project.

THIS ADVICE WILL HELP YOU COMPLETE YOUR PROJECT PROPOSAL WHICH IS DUE ON MARCH 20. FOR EACH ASSIGNED PROJECT, I WILL PROVIDE COMMENTS ON FOUR AREAS: PURPOSE, BACKGOUND, METHODS/MATERIALS, AND RESULTS. FEEL FREE TO ADD MORE IF YOU WISH. YOU HAVE TO DO THE OTHER PARTS: TITLE, AUTHOR, ASSISTED BY, CONCLUSIONS (just type in the word "conclusions" and leave the rest blank for now), and FUTURE WORK (leave rest blank here also). IN ADDITION -- PLEASE DO THE GOOGLING AND WRITE-UP FOR THE "BACKGROUND" SECTION. I HOPE YOU UNDERSTAND THIS AND YOU BRING IN YOUR TYPED PROPOSAL WITH EVERYTHING I ASKED YOU TO DO ON THURSDAY.

YOUR PROPOSAL MUST BE TYPED! UNTYPED PROPOSALS WILL NOT BE ACCEPTED until they are typed.

NOTE – You should Copy and Paste all my comments into your Proposal. Then you can start to do some of them, by Googling the Background information. EVEN IF YOU'RE NOT FINISHED, DO AS MUCH AS YOU CAN. THIS IS ONLY A PRELIMINARY VERSION OF YOUR PROPOSAL.

Science Fair Projects

1. Use the simulator to study how the length of a year (once around the sun) and the planet’s speed changes as the distance of the planet from the Sun, the Sun’s mass and the planet’s mass changes.

2. Use the simulator to study how the shape of an orbit changes as the tangential velocity changes. Also learn what is the specific tangential velocity for “never-return,” for circular orbit, and for “crash” [ASHER]

PURPOSE: Based on the tangential speed of a planet, its behavior will fall into one of four domains separated by three special conditions. The three conditions are (A) minimum clearance speed (to avoid a crash with the Sun), (B) circular orbit, and (C) minimum never-return speed (also called the ‘escape velocity”). Then the four domains are : (I) suborbit (crash) = all speeds below (A); (II) inferior ellipse (the planet will fall in towards the sun but loop around the back and then swing back out to where it started) = all speeds between (A) and (B) ; (III) superior ellipse (the planet will shoot out and around the back, passing behind at a greater distance than it started, and then swinging around and falling back to where it started) = all speeds between (B) and (C); and (IV) Hyper-escape Velocity = all speeds above (C). For condition (C), the planet will keep slowing down a little, so that by the time it reaches infinity, it will stop! For domain (IV), when the planet reaches infinity, it will still be moving!!

This project will determine “experimentally” the three condition speeds, and thereby reveal the minimum and maximum tangential speeds for each of the four domains. If the simulator allows it, we will scale the mass of the Sun and the orbital distance of the Earth, so that the circular orbital speed and all the calculated limits obtained are the true values. If not, we will just work with the numbers provided by the program to show that these four domains actually exist.

METHODS/MATERIALS: We will use the simulator’s capability to pause the motion and display the x- and y-components of a planet’s position and velocity to (1) measure the eccentricity of an ellipse or the achievement of a circular orbit, (2) check Law of Conservation of Angular Momentum (this just means that the Angular Momentum = mass x speed x distance will give the same result any time the velocity vector is perpendicular to the position vector, and since I now know how to find (R,ϴ) given (Rx, Ry)ß which the simulator displays – same for velocity – I can calculate whether ϴ(velocity) is perpendicular to ϴ(position). If so, the two angles will differ by 90^o. I should find two place where this is true, one where the planet is closest to the Sun and one where it is farthest away. If the two values of Angular Momentum are the same, this will prove that the simulator correct! If not, the simulator is wrong!! What happens when the velocity vector is NOT perpendicular to the position vector? The Conservation Law is still correct, but now we need to multiply the equation by the sine of the angle between the two vectors to get the Angular Momentum. If possible, we will also check the Law at an intermediate position where the vectors are NOT perpendicular. (The Instructor will help me with all this math.) Why to we do this sine stuff? Because this gives us the component of the velocity that is perpendicular to the position vector and that’s what we need! The velocity component parallel to the position vector is useless – it doesn’t have any angular momentum – so we ignore it.

We will require one online digital computer (to access the orbit simulator: My Solar System 2.04), and a printer to print the results of the simulator and create our poster display.

RESULTS:

· A poster display summarizing my research

· A chart on the poster (where tangential speed is plotted on the x-axis) showing the values of the transition speeds of the five domains.

· A running computer program (or a video of the running program) where I will demonstrate the Earth moving around when it is in each of these five domains.

3. Use the simulator to study how the speed of a planet changes as it traverses a non-circular (elliptical) orbit.

4. Use the simulator to study how big the moon’s orbit can get before it gets pulled into the sun. [SAVANNAH]

NOTE – use equation for force of gravity and force needed to create a circular orbit to derive a simple equation that tells me the proper tangential velocity of the Moon for a circular orbit at every distance from Earth, so I won’t have to do dozens of “trial and error” runs at every distance to find the velocity experimentally! (The Instructor will show me how to do the math!)

PURPOSE: (1) To find the true value (if possible) of how large the Moon's orbit can get before the Sun's gravity overpowers that of the Earth, and it gets pulled away from the Earth. (2) To find out what happens then. Does it go in orbit around the Sun? Does it crash into the Sun? Does it get catapulted off to infinity? If we can't model the true masses of the Sun, Earth and Moon, as well as the true speed of the Earth and Moon in orbit, we can still study these phenomena (1 and 2) for an artifical set of parameters (values).

BACKGROUND: Use Google to write a few sentences about Copernicus, Kepler, and Newton, the three giants of planetary science (who they were, when they lived, what their main accomplishments regarding planets and gravity were). Give Newton’s equation for the gravitational force between any two bodies (M_{1 &}M₂)_: F = M₁M₂/d². The Sun is much more massive than the Earth (the ratio of M_sun/M_earth = Google masses & then you calculate___), but it is also much farther away from the Moon than the Earth is d_suntomoon/d_earthtomoon = Google & calculate___), so it is not clear which force pulls harder on the Moon.

METHODS/MATERIALS: We have to try to scale the masses, distances and speeds so they match (or at least are proportional to) those of the Sun, Earth and Moon. For most of this work, I will have the Tracer on, so I can see the orbits, stop the action, and click on various points to get the x- and y-components of position and velocity.

Phase I: Two-body problem (Earth - Moon). First we will use the simulator and an equation to find the proper tangential velocity for the Moon at several distances from the Earth (beginning at “true” scaled distance and then increasing) so that all orbits are perfect circles (please review Asher’s project about orbit shapes).

Phase II: Three-Body Problem (Earth –Moon – Sun) Now we have to figure out how to make the Earth-Moon system go around the Sun in a perfect circle at the “correct” (scaled) distance.

Phase III: Three-Body Problem (Earth –Moon – Sun) Next we have to start increasing the Moon’s distance from the Earth and see what happens. As it increases the Moon’s orbit will start to get distorted, and finally the Moon will pull away from the Earth.

Phase IV: After we find the critical distance where the Moon gets pulled away, we can investigate what happens next. One thing we can do is try several larger Moon orbits and see if the same thing happens in all cases.

(The Instructor will show me how to do all the math!)

We will require one online digital computer (to access the orbit simulator: My Solar System 2.04), and a printer to print the results of the simulator and create our poster display.

RESULTS:

· A poster display summarizing my research

· A chart on the poster (where Moon-Earth distance is plotted on the x-axis) showing the results of different cases

· A running computer program (or a video of the running program) where I will show the Earth and Moon moving around for different Moon-Earth distances and different final results.

5. Investigate in more detail the string pendulum properties we have been studying.

6. Make a stiff pendulum (rod instead of string) & see what happens when you start at the top (ϴ = 180 !) [LAYEL]

NOTE – (Layel, you can skip this part for now and read it after you finish the rest of your Proposal). We are going to develop the equation that gives the tangential force on your pendulum “as a function of” (means “for every value of”) the angle of the pendulum. It’s going to have a trig function in it. As you can see the tangential force will be zero at the bottom and top (0^o and 180^o) and maximum at the side (90^o). Here’s how to do it (I suspect you’ll need some help, but give it a try anyway). Draw your pendulum out at some angle ϴ (say, around 60^o). Now draw a vector for Fgthe force of gravity. The tail will be at the center of your pendulum bob and the head will be pointing straight down (naturally). But the bob can’t drop straight down because the rod is retraining it. It can only swing in a circle. So we have to resolve the vector into two components such that one of them is pointing the way the bob can move (tangentially) and the other component is pointing in the (opposite) direction of the rod.

So you draw a coordinate system with the origin at the center of the bob, the x-axis angling down in the direction away from the rod (so the rod and the x-axis form a straight line), and the y-axis is pointing in the direction that the bob is going to start swinging in (perpendicular to the rod. Now you can draw F_gx and F_gy on the coord system. The Fg vector should make a 60^o angle with the x-axis. So we have, F_gx = F_gcos(ϴ) = F_gcos(60^o) = 0.5F_g and F_gy = F_gsin(ϴ) = F_gsin(60^o) = 0.8660F_g . F_gy is pulling the bob around, forget about F_gx. As the bob is released and starts swing down, the coordinate axes remain welded to the bob, so they rotates just as the rod rotate. Now the driving force F_gy begins to decrease as ϴ decreases, and when the bob gets to the bottom F_gy = 0. After the bob swings past the bottom, the value of ϴ starts to increase again but it is now negative! That means the force is now pushing backwards on the bob and it begins to slow down!! Finally the bob stops when the rod is at (almost) -60^o, and then the bob starts moving in the direction of the driving force again and the whole process repeats.

Notice that when the bob is at 0^o or at 180^o, the driving force is zero. This is called equilibrium and nothing happens, but 0 is stable equilibrium and 180 is unstable equilibrium. Can you guess why?

PURPOSE: (1) To study exactly what happens to the driving force of a rod pendulum as a function of the angle. (2) To understand the “small angle approximation” when the angle is about ten degrees or less (stay tuned). (3) To study the period of the rod pendulum experimentally as a function of angle all the way up to 180^o. (4) To learn how to calculate v (the maximum, i.e., bottom, speed of the rod pendulum) by using the Law of Conservation of (total) Energy. Total energy (E) = PE (potential energy) + KE (kinetic Energy) = mgh + ½ mv² (will explain later). Check this law by trying to measure the speed of the pendulum near zero (the next section may help here a lot) (5) To try to build our rod pendulum so it will operate smoothly when it is “laid back” so the circle of motion is almost horizontal. This will reduce the driving force and slow down the swing so we can measure the speed (by much better.

BACKGROUND: (Lots of Googling here. Use Wikipedia if you can understand it; otherwise, go to a kids’ site) Say a few words about Newton’s Three Laws and also the Law of Gravity. Talk about what pendulums were used for (especially clocks) and the problems that arise. (The Instructor will show me how to do all the math!)

METHODS/MATERIALS: [You’ll need an adult’s help building this.] (These are just suggestions: there are many ways to build this.] I will build a 30-32 inch rod pendulum using a thin steel rod from a hardware store or a hobby/model shop. For the bob we will epoxy together (or use metal collars to hold) a stack of 8-10 large (1 inch ?) steel washers with holes slightly larger than the rod and then epoxy the whole stack onto the rod near one end.

Another issue is how to make the pivot. . The key issues in the pivot are snugness, low-friction (oil), and low wear (you don’t want your hole getting bigger with use). Also, as we said, it is important to try to make it work just a smoothly when it is laying back 70-80^o (with a stack of books or something propping it up). NOTE – The action, especially when tilting the assembly, will be much smoother and better if the pivot rod (2” long?) is mounted (epoxied or set into snug spacers) in two ball bearings placed around 1.5” apart. HobbyTown has tiny ball bearing assemblies.

I will measure the period of the pendulum using the exact same method we used in class. (average (mean) of 10 swings, repeat 9 times (or 4 times, if I get pressed for time). Calculate mean, standard deviation and standard deviation of mean. I will measure at seven different swing angles (as small as I can, 30^o, 60, 90, 120, 150 and as close to180 as I can get). For the 180 degree data (unstable equilibrium) I will nudge the bob to start it, but not push it hard.

I will plot my data (seven points: x-axis = angle and y-axis = mean period ± 1(or 2) SDM error bars

We will require one online computer to do the calculations and the poster preparation writeup, and a printer to print the results of the experiments and calculations, and create our poster display.

RESULTS:

· A poster display summarizing my research

· A plot on the poster showing the results of my period versus angle measurements for the vertical and tilted runs

· Another plot showing measured speed and theoretical speed versus starting bob height.

· Exhibit and demonstrations of my experimental rod pendulum for the judges and attendees.

7. Compare the periods of a pendulum when it’s swinging back and forth with when it’s going in a circle. [KAI]

PURPOSE: To compare the periods of a planar and a conical pendulum relative to changes in (1) mass, (2) length and (3) angle. They look similar, but the way the gravitational forces act in the two systems is completely different , and it is difficult to guess how they will behave versus the independent parameters of mass, length and angle.

METHODS/MATERIALS: [You’ll need an adult’s help building this.] (These are just suggestions: there are many ways to build this.) I will begin by studying the best and most rigid attachment point. One way is to clamp a three-foot long 2 by 4 onto a worktable (if I use a good table, with my parent’s permission, I will lay a soft cloth on the table under the board before clamping to avoid scratching the table. (Then I can also clamp the board to the display table at B’rit for the Science Fair demo). I can drill a very narrow hole at the end of the board for the string to go through (I’ll use something that doesn’t stretch or tangle up when it’s loose -- sewing thread is terrible). Then I can hammer in two nails into the wood and get five pendulum lengths ( nail A is, say, 20 cm (8”) from the hole, and nail B is 40 cm from the hole. First, I make a tight, non-slip loop in the string. Then I can put the loop on nail A and tie the sinker so its center is, say, 100cm below the board. If I move the loop to nail B, it is 80 cm; and if I loop around B and back to A, it is 60 cm, another loop to B is 40cm, and final loop back to A is 20 cm. This is a simple and repeatable method as long as my loop knot doesn’t slip (I could put a glob of strong glue or epoxy on the know to prevent slippage.) I use or make a clip that snaps open and closed for quick changing of the sinkers to get different weights. My first try of the parameters will be:

SINKER WEIGHTS (oz*) PENDULUM LENGTHS (cm) ANGLES (deg) *convert to grams please!

1 100 10

2 80 20

4 60 40

40 80

To study Number of experiments (10 swings / experiment)

Mass effect 4 repeats x 3 masses x 1 length (80 ?) x 1 angle (40 ?) x 2 modes (planar and cone) = 24

Length effect 3 repeats x 4 lengths (drop 80?) x 1 mass ( 2 ?) x 1 angle (40 ?) x 2 modes = 24

Angle effect 3 repeats x 4 angles x 1 mass ( 2 ?) x 1 length (80 ?) x 2 modes = 24

I have 72 experiments (of 10 swings each) to do in 2 months. Each one will take less than a minute, so I can easily do 10-20 experiments a day. I should be able to do all 72 experiments in less than a week.

I will plot my data on three graphs. The x-axis will be mass, length and angle. Each graph will have two curves: one for the planar pendulum and one for the conical one. For each point (which will be the mean of 3 or 4 repeats) I will show 1 or 2 SDM error bars. I will require one online computer (for calculations, Google searching, word processing, Excel, etc.) and a printer to print the results of the experiments and calculation, and create our poster display.

RESULTS:

· A poster display summarizing my research

· 3 plots on the poster showing the results of my period measurements for the planar and conical pendulums

· Another plot showing measured speed and theoretical speed versus starting bob height.

· Exhibit and demonstrations of my experimental planar and conical pendulum for the judges and attendees.

8. Study the four oscillatory normal modes of four pendulums connected by a transverse string (coupled pendulums). [SAMUEL]

PURPOSE: To compare the periods and modes of operation of four coupled pendulums. Coupled mean that although each pendulum can swing independently of the others, with each swing it exchanges a little bit of its energy with its nearest neighbor(s). Such systems have so-called “normal modes” where the system repeats itself with every swing, and “mixed modes” which are complicated combinations of normal modes, and which take many swings to repeat (if they ever repeat at all!). I will study a coupled four-pendulum system to (1) discover what the normal modes are; (2) measure their periods; (3) select and study three or four simple mixed-modes (there are an infinite number of mixed modes) and (4) measure their periods as well.

Read about (Google) coupled pendulums and try to understand how they work. Think about whether there are any natural or man-made coupled systems in the world and how they work. Besides pendulums, what other coupled systems can I think of?

METHODS/MATERIALS: [You may need an adult’s help building this.] (These are just suggestions: there are many ways to build this.) Cut or find plywood or a plank that are at least 10” wide (in the swing direction) and 30”long (in the suspension string direction). Glue and screw two 2 by 4 pieces about 24”long vertically upright onto the baseboard (one at each end) so they are anywhere between 25” and 30” apart. Put a small nail on top of each upright and attach a long string from one upright to the other. This string should not be taut – it should sag about 2-3” when you put your finger down on the middle of the string. You can reduce (or increase) the amount of pendulum coupling by tightening (or loosening) the support string. Now I will hang four pendulums from this support string. Each pendulum will be about 18” long and the attachment points will be about 4-5” apart. The pendulum bobs may be identical fishing sinkers (best) or identical large (1-1.5”) metal nuts or something else compact and heavy with a hole. To keep the bobs swinging perpendicular to the support string so they won’t hit one another, each pendulum should have two strings that get a little farther apart as they approach the support string. Whatever separation I use must be the same for all pendulums. I will play and practice with the system until I get the best performance. If my apparatus rocks during the swinging, I will either have to weight or clamp it down, or modify the baseboard to make it more stable.

After I have obtained the best performance of my system that I can, I will start to search for the four normal modes of the system and measure their periods. To measure the periods, I will measure the time for 10 swings of the system, and find the mean time (period) of a swing. I will repeat this 9 times, and find M, SD and SDM. (It is OK to use the online calculator for these, but I should check at least once using the class method in HW 7, 8 and the class 10 sheet we did in class to make sure everything is in order.) Then I will repeat everything for the other 3 normal modes. The slowest normal mode (lowest frequency) will be called MODE N1, the next slowest one, MODE N2 up to the fastest mode = MODE N4.

The first mixed mode (MODE M1A) to check will be one with one of the outer balls pulled out and the other three balls at rest in the home position. The next one to investigate will be MODE M1B where one of the inner balls is pulled out and the rest at home. (They are called M1A and M1B because they are the first ones studied and they are very similar (but NOT identical). A mode identical with M1A would be when the opposite outer ball is pulled out the same distance. Then, based on what I get, I will try other mixed modes and record some others that I find interesting. I will carefully measure the periods of every mixed mode selected (if I can figure out what it is!)

I will plot my data on up to three sheets of paper (some might have 2-3 graphs on them) . When plotting the measured periods (which will be the mean of 9 repeated averages of 10 full periods), I will show 1 or 2 SDM error bars. I will require one online computer (for calculations, Google searching, word processing, Excel, etc.) and a printer to print the results of the simulator and create our poster display.

RESULTS:

· A poster display summarizing my research

· 3 plots on the poster showing the results of my period measurements for the normal and mixed modes

· Exhibit and demonstrations of my experimental coupled pendulums for the judges and attendees.

NOTE TO LAST THREE STUDENTS : I won’t repeat all the things I said about the first five proposals, SO IT’S ESPECIALLY IMPORTANT THAT YOU READ ALL FIVE OF THEM.

9. Study the wave motions produced by a string of many pendulums, each one a little longer than its neighbor. [JONAS]

PURPOSE – The purpose of this project is to study what happens to a family of oscillating bodies whose periods progressively become slightly longer (or shorter). In a nutshell, their motions become progressively out of phase (“phase” is explained later), creating new and beautiful patterns, that make it look like some balls are attracting others, when in reality, they are not. In particular we will examine: (1) why the patterns form and how they change with time, (2) why certain subgroups of bobs appear to form associations, (3) How can we quantitate the behavior, (4) should neighboring pendula vary by a constant difference or a constant ratio, and (5) what values for the differences (or ratios) of neighboring pendula produce the best results?

While this looks very similar to the coupled-pendulum project, it is completely different: it is a completely uncoupled –pendulum project. None of the pendula pass energy on to their neighbors.

BACKGROUND – read the other projects

METHODS/MATERIALS – It is not easy to guess ahead of time how many pendula should be used or how much variation to make from pendulum to pendulum. We will just have to “live and learn.” I have seen pendulum wave devices that have at least 12 and some have up to 29 pendula!

As the balls keep swinging the second ball gets ahead of the first one, (and the third gets ahead of the 2^nd one, etc) because the pendula are getting shorter and swinging faster!! Obviously when the first ball is at the bottom of the swing (called zero), one of the balls farther along will be at the end of its swing and even further along another ball will be on its way back, etc. That’s how the wave pendula work. But as time progresses further the gap from ball to ball obviously gets bigger and funny things happen.

Let’s think about what “phase” means in a wave. One of the trig functions we have been studying in class and on homework tells the who story. It’s called the sine wave. If we take the simple equation y = sin(x) and plot x on the x-axis (where else??) and y on the y-axis (no surprise here either). We use x-here to show it’s going on the x-axis. Actually, we should think of x as the angle ϴ, because that jives with our study of the right triangle and sin(ϴ) = a/c. Suppose we let c =1 (who can stop us J ) then we have sin(ϴ) = a. But a is the y-component of the hypotenuse c (a tells us how far c is leaning in the y direction. So now we have sin(ϴ) = y, or y = sin(ϴ). So it makes sense to plot sin(ϴ) on the y-axis, doesn’t it?

Anyway, the data for the plot here has x (think ϴ) starting at 0 and stepping along in 30 degree steps, and look what happens! Y also starts at 0, because sin(0) = 0!! And after 3 steps along (the 4^th ball), the ball is all the way out (to a y value of 1, because sin(90^o) = 1!) and we say that ball has a phase that is 90^o ahead of the first ball. If we go another 3 balls, we are back to y = 0 again (x = 180^o). x = 270^o gives y = -1 and finally x=360^o gives y = 0 AND THE CYCLE IS COMPLETE. This cycle is called a SINE WAVE. That’s where the name Wave Pendula comes from!! Now, if x kept on increasing for another 360^o (until we reached 720^o), we would have another sine wave that looked exactly like the one we just made!! Now you know how a wave pendulum works.

One of the challenges is to figure out how to make the difference from pendulum to pendulum be the right amount. But our class experiments on pendulum length ALREADY GIVES US THE CLUE. Our experiments showed that the period (full swing) depends on the square-root of the length of the pendulum !!!

x= angle (in degrees)	y= sin (x)
0	0.00
30	0.50
60	0.87
90	1.00
120	0.87
150	0.50
180	0.00
210	-0.50
240	-0.87
270	-1.00
300	-0.87
330	-0.50
360	0.00

JONAS _ I’M HAVING TROUBLE GETTING THE GRAPH TO SHOW UP. CAN YOU COPY THE NUMBERS IN EXCEL AND MAKE YOUR OWN GRAPH LIKE WE DID IN CLASS?

RESULTS- RESULTS:

· A poster display summarizing my research, including the phase calculations I need to do.

· PHOTOGRAPHS and Plots on the poster showing the results from my wave pendula.

· Exhibit and demonstrations of my experimental wave pendula for the judges and attendees.

10. Study the behavior of Newton’s Balls (five ball bearings that swing and bang into each other). [ELIE]

PURPOSE – (1) To study the behavior and properties in which momentum and energy are transferred between a series of five identical pendula that barely make contact when they are all at rest; (2) to observe the many different patterns that can arise from such a simple set-up; and (3) to show how the symmetrical patterns that arise are the combined results of the Law of Conservation of Momentum (LCM) and the Law of Conservation of Energy (LCE)!!

BACKGROUND - (Please read the earlier pendulum Background discussions)

METHODS/MATERIALS – You have to make your “Newton’s Cradle” using 5 identical chrome-steel ball bearings ( ½” to ¾” diameter would be best). You can cut five sections (about ¼” wide) from a piece of plastic or neoprene tubing to hold each of the pendulum strings (the string goes between the ball and the tubing). The diameter of the tubing should be slightly less than the diameter of the ball so it stretches and holds the ball securely. Then both ends of the string of each ball go up to two 6-8” sections of aluminum or steel angle iron. The angle iron lets you use paper spring clips (the kind with the black clamp and the two metal handles you squeeze to open the clip) to hold the strings and allow for easy adjustment of the length. The two pieces of angle iron have to be clamped, screwed or glued onto a wooden or metal support frame that holds them up in the air. (search YOUTUBE for “Newton’s Cradle” for videos that show how to mount the two string-support arms and how the patterns are obtained.).

Usually some of the balls are swung out and released while the others remain at the home position. You should also study what happens when two sets of balls are swung out and released!

We will show that the LCM and LCE, acting together, cause the patterns we observe! Rather than solving algebraic equations (difficult for 10-year-olds J ), we will try some different nathematical possibilities and show that the only ones that works are the ones we actually see.

RESULTS - See earlier proposals.

11. Study the motion of a gyroscope on a pedestal.

12. Study the effect of different jar elevations & liquids (water, soapy water, oil, etc.) as well as different tube inner diameters on flow speed in a 2-jar siphon. [TRISTEN]

PURPOSE – (1) To study how siphons work and (2) how the rate of the liquid flow depends on (a) the “pressure head” (the height between the liquid levels in the two containers, (b) the inner diameter of the transport tube, and (c) the viscosity of the liquid (water, soapy water, oil, and/or other liquids, as desired). If possible and reasonable, we will try to see if any principles (equations) of fluid dynamics can help us understand what we observe.

BACKGROUND – See earlier proposals, but shift from pendula to siphons and fluid. For example, when were siphons first used and by whom?

METHODS/MATERIALS we will need two strong transparent plastic or glass (be very careful) jars, tubing of (at least) two different inner diameters, clamps to hold the tubing in fixed positions, and various working liquids. In addition, we will need to make two adjustable and repeatable stands for our jars (something like those used on chemistry labs). Comments:

· Plastic (like peanut butter – yum – jars) is less likely to break than glass

· Tubing should only be long enough to accommodate the maximum height difference of the jars and no longer since that would add more flow resistance and be more likely to tangle up.

· Clamping or fixing the two ends of the tubes inside the jars so they can’t move will be absolutely necessary to get good measurements!

· One way to make the an adjustable stand for one of the jars (the other stays on the table!). The stand can be made of two pieces of thick (3/4” ?) marine plywood ( one base and one shelf for a jar) and a wooden dowel (3/4” diam?) to allow the shelf to be raised and lowered. Drill (¾” ?) holes in the two pieces of plywood. Drill narrow adjustment holes through the dowel every 6” (?) or so. The dowel is glued into the base, and a long (2 or 3” ) nail is put through a hole in the dowel to hold the shelf where you want it. To change elevations, just hold the shelf, move the nail where you want it. And lower the shelf back onto the nail. THIS ALLOWS QUICK AND REPEATABLE ELEVATION CHANGES! You might have to sand the dowel or the hole a bit for smooth moving of the shelf up and down. To make the dowel more steady, you might have to glue a small chunk of ¾” wood on top of the base and then drill a 1 ½ “ deep hole for the dowel to go through which will make it a lot steadier and stronger.

RESULTS – See earlier proposals.

yhbscience

Monday, March 24, 2014

Class 12

Thursday, March 13, 2014

Class 11