TREBUCHETS!!!

Hey all,

First off, I would just like to say thank you to everyone who visited this blog over the past year- its been a great ride! A total of over 700 views in less than 5 months (from around the world!)... thank you for taking the time to visit this blog- I hope it helped you survive IB physics! And if you're taking IB/AP Chem at Interlake next year, I'll do the same thing (it helps me too!). This will be my last post on this page. I hope everyone has a great summer!

Okay, now we're done with the IB/AP tests! WOOOOOOOOOOOHOOOOOOOOO!!!!

 At Interlake, that means that its time for our amazing end of the year project- TREBUCHETS!

So what exactly IS a trebuchet, you ask? Essentially, a trebuchet is a massive lever that uses a weight and a sling to shoot a projectile (like a large rock) over a great distance. Medieval siege engineers in charge of leading attacks on castles experimented with trebuchets as a possible alternative to catapults (which were too inaccurate), ballistae (think big crossbow), and siege towers/battering rams (which have to come all the way up to the walls of a castle to do any damage). Trebuchets performed beyond their designer's wildest dreams, and were only replaced when cannons (and other gunpowder-based weapons) became more popular siege weapons.

How does a trebuchet work?

A trebuchet is a lever. When the counterweight is allowed to fall, it creates rotational force, or torque. Because the arm is a single piece, the same rotational force is applied to the throwing arm, forcing it UP. In a fixed sling trebuchet, as the throwing arm gains angular velocity, the sling holding the projectile is forced up as well, and it swings, applying an outward force on the projectile in the sling. When the projectile reaches critical velocity, the centripetal force generated by the circular motion is no longer enough to keep the projectile moving in a circular path with the sling, and the projectile is released in a straight path.



























Some trebuchets release their projectiles a little differently. In these trebuchets, one end of the sling is firmly attached to the throwing arm. The other end is loosely attached to the throwing arm by a pin. When the throwing arm reaches critical velocity, the end of the sling slips off the pin, launching the projectile.

Tips about trebuchet design:

1. You'll get the most range from your trebuchet if your release angle is as close to 45 degrees as possible.
2. Wide bases are more stable than narrow ones.
3. You have two main options for the counterweight design: a swinging counterweight or one that is attached to the counterweight arm and is not allowed to move. Keep in mind, however, that a non-moving counterweight will have massive recoil, because the entire arm will swing with the counterweight. The best way to compensate for this is to put wheels on the trebuchet, to neutralize some of the recoil. Swinging trebuchets do not need wheels, because the counterweight's free rotation makes it neutralize most recoil from the release of the projectile.
4. An aiming jig is a good idea. A jig allows you to easily realign the trebuchet after every shot.
5. Short lengths of PVC pipe are more sturdy than long lengths of PVC pipe.
6. Make sure your trigger mechanism is simple and reliable. A very simple trigger is a stick or piece of PVC that holds the counterweight up and can simply be yanked out to fire the trebuchet.
7. The optimum ratio between the length of the counterweight arm and the length of the throwing arm is approximately 1:3.
8. Bending the release pin forward on the sling will result in a later release.
9. Longer sling = later release, shorter sling = earlier release.
10. Use tips 8 & 9 to get the release angle you want.
11. Try to find a way to increase the mass of the trebuchet's base. This will make it more stable.

Once again, thank you! Its been a great ride- have a good summer!

The Top 6 mistakes people make on the IB SL Physics Test

Okay, so with the IB SL Physics and AP Physics B tests coming up fast (yikes!), there are 6 things that most IB SL Physics kids screw up on when they are taking the test. These are six things that you WON'T screw up on, because you'll know to watch out for them!


1. Unit Conversions: This may seem obvious, but the test is timed- its easy to forget to convert wavelengths of light (for example) to meters before plugging them into the v = fλ equation. Remember to read the question and make sure that the units are right BEFORE you start calculating! 


Use your brain! If you're converting a big unit to a small unit (ex. meters to centimeters), simply raise the number to a POSITIVE power (because there are more centimeters in a meter than meters in a centimeter). If you're converting a small unit to a big one (ex nanometers to meters), raise the number to a NEGATIVE power (same reason as above, I'm just too lazy to type it out ;))


2. Radians/Degrees: ESPECIALLY for AP Calculus students! Remember to set your calculator mode to DEGREES before you start. Also, remember that the formula Θ = λ/b gives you an answer in radians, not degrees!


3. Explanations: Remember, even if your answer makes sense, you can only get points if you explicitly cite a physics law, principle, or equation!

4. Mass of an electron/proton & elementary charge: A lot of people stare at problems like this: 

"A proton moves in a circular path perpendicular to a 1.14 T magnetic field. The radius of its path is 8.00 mm. Calculate the energy of the proton." 

and say "wait, what? I don't have enough information! I can't solve this!" 

You get a MASSIVE list of constants in the IB data packet (the yellow one). USE IT! The gravitational constant, elementary charge, coulomb constant, and masses of protons, neutrons, and electrons are all in there. You also get conversion constants for kg->amu->MeVc^-2

(really helpful!)

5. Definitions: Look at the number of points on a question. If the maximum number of points is 2, try to write 3 things- cover all your bases, so if you get something wrong, you can still get some points. Remember, definitions are graded on the number of points you hit.

6. Trying to memorize formulas (and doing it wrong :P): How do I know that this can screw you up (ToK moment?)? Personal experience... I memorized the fv = λ formula backward ( fv = λ) and it messed me up for weeks... Its like trying to memorize a piece of music- if you memorize it wrong, nothing can help you, and you'll mess up even with the music right in front of you. Either DON'T try to memorize the formulas (my advice) or if you choose to do so, make sure you do it right!

Good luck! And may we beseech the blessing of almighty test graders upon this great and noble undertaking.

--

Satya

Electric Circuits (Yay, I'm psychic!)

Okay, today, I'm going to prove my psychic abilities. I guarantee that what I'm going to talk about now is EXACTLY what Mr. Thompson will talk about on Monday. If you want to sound like an absolute freakin' GENIUS in class on Monday, read on!

Okay, the activity we did yesterday was to help us understand some basic circuit terminology, and more importantly, introduce us to the concepts of voltage, current, and resistance.

So what ARE voltage, current, and resistance?

Electric current is basically made up of flowing electrons (going back to basic chem). It helps to imagine that a wire is a hose, and that the electrons flowing through the wire is the water flowing through the hose.

Voltage (or electromotive force) is defined as the work required to move a charge between two points. Hose comparison: the pressure of the water, or the "pushing force." In English: The phrase "electromotive force" says it all. Electro- (electron) + motive (move) + force = work to move a charge. EMF is measured in Volts. Symbol: v, EMF

Current is the magnitude of the flow of charge. In English: The number of electrons flowing past a point per second. Hose comparison: the amount of water flowing through the hose per second. Current is measured in Amperes (one coulomb/second). Symbol: I (very strange, but true)

Resistance is defined as the opposition of a medium to the flow of electrons. In English:... that's pretty much it. Hose comparison: The tap on a hose, which changes the strength of a hose's pressure without changing the amount of water going through it. Symbol: Ω (Greek letter omega)

These three quantities are interrelated through a relationship called Ohm's law. Resistance is directly proportional to EMF and is inversely proportional to current.

This relationship is:

I * Ω = v

Where I is current, Ω is resistance, and v is voltage/EMF

Drawing a circuit: Tips
1. Wires are straight lines: it makes life less confusing for you. On my robotics team, we often have to make schematic diagrams of electronic and pneumatic systems, and they need to be simple - but accurate. That's exactly what you're shooting for when you draw a circuit diagram- even a moron should be able to read the diagram and know what you're talking about.

2. Make sure that positive and negative terminals are the right way around! A lot of electrical circuits work one way, but not the other- making sure that everything is the right way around is essential.

3. Parallel Circuits Vs. Series circuits: All circuits are NOT created equal. Two bulbs connected in series (left) are NOT the same as two bulbs connected in parallel (right). They have different voltages and current values.

4. Voltmeter position: Don't worry about this yet, but whenever we have to put voltmeters (they measure EMF) in a circuit diagram, they MUST be connected in PARALLEL!!! They tend to "eat" the voltage passing through them... why? Voltmeters have a huge resistance, meaning that there is a large voltage "drop" across a circuit with a voltmeter in it.

5. Use the right symbols: You have a list of electrical symbols in the IB data book thing. Use it!

How light bends

Hey Everyone!

Since Mr. T wasn't here today, I felt that it would be a good idea to talk about all the random light stuff we covered today.

Reflection.
When light tries to enter a new medium at an angle, a portion of the wave's energy is reflected back into the original medium.

The angle that the original ray makes with the normal line is known as the angle of incidence, and the angle that the reflected ray makes with the normal line is the angle of reflection. The most important thing to remember about reflection is that the angle of incidence ALWAYS equals the angle of reflection.

Refraction
Right, so we know that when a wave reaches a new medium, part of the wave's energy just bounces back. What happens to the other part of the light's energy? The remainder of the energy continues on into the new medium, but guess what?

Waves BEND! When light moves from one medium to another, its speed changes, which changes the direction of the wave's travel. This is called refraction.

Note: When objects go from a less "optically dense" medium (i.e. air) to a more "optically dense" medium (water), they bend toward the normal line, but when objects go from a more "optically dense" medium to a less "optically dense" (ex water to air) medium, they bend away from it.

Equations to know and use:

Total internal reflection occurs when none of the light is refracted into the new medium, and all of it is reflected back into the original medium (hence the name). The smallest angle of incidence between 0 and 90 degrees at which this can occur occurs when the angle of refraction = 90 degrees.

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Wave Interference Part 2- 2-dimensional Wave interference and PLD

Hey Everyone!

Now that we've talked about one-dimensional wave interference (standing waves) we can talk about something a little more complex: 2-dimensional wave interference.

In most situations, waves aren't interacting on a string, right? They tend to work across the surface of a two-dimensional space (think water waves). The two sources produce pulses at the same time, and for our purposes, with the same frequency and wavelength.

Remember how standing waves have nodes and antinodes? Well, this is true with 2D wave interference as well. The really cool thing about nodes or antinodes in two dimensions is that they line up! This forms a nodal line (or an antinodal one)! (see diagram below) Those weird grayish line on the diagram are nodal lines- they NEVER move!

A critical term to know when talking about 2D wave interference is path length difference. Essentially, the two waves produced by the two sources have to travel a certain distance to reach a given point. The absolute value of the difference between the distances traveled by both waves from the center to that point is the path length difference.

The highest possible value for the path difference is equal to the distance between the two sources (the source separation).  The lowest possible value is at any point that is equidistant from both sources (and is therefore equal to 0 wavelengths)

The formulas for Path length difference are:

Path length difference = |pathlength1 - pathlength2|

Path length = n * wavelength

Whoa, hold it. What the heck is n? Where did THAT random variable come from? Essentially, n is the path length difference in terms of wavelength.

When n is a whole number, an antinodal line exists. When n ends in ____.5, a nodal line passes through that point.

See diagram or "di a" ... never mind. You see what I did there? Red lines are antinodal, blue are nodal, and green (should be red) is the line of source separation.

The last thing I'm going to talk about before I let you amazingly patient people go to bed are the EQUATIONS we can use.

path length difference = n* wavelength


v = f * wavelength

Thanks for your time and patience, everyone! Remember to share this page and help me get more followers- so we can help more people!
Thanks, and as always,  contact me on Facebook or at Satya.root.beer@gmail.com if you want physics help!

Wave interference Part 1- Standing Waves

Hey Everyone! 

I know its been a while, so thanks for your patience!

Right... we know what waves are, how they behave, etcetcetc. Now, we can start to understand what the heck happens when two waves interact. This post is going to cover very simple, one-dimensional wave interference, and the next post (in about an hour at most) will cover more complex two-dimensional wave interference

One-dimensional wave interference between two continuous waves of an equal amplitude, wavelength, and frequency produces a standing wave. A standing wave has NO net transfer of energy from one point to another. This means that a standing wave... well, stands. 

When the crest of one wave meets the crest of the other (or a trough meets a trough), it results in constructive interference- the amplitude of the resultant wave is 2x greater than the amplitude of either of the two waves. When a crest meets a trough, however, it results in destructive interference- the amplitude of the resultant wave is less than either of the two waves. In the case of a standing wave, this simply means that the two 

waves cancel out.

There are two very important points on a standing wave: Nodes and antinodes. An antinode is a point where there is ALWAYS constructive interference, while a node is a point where there is ALWAYS destructive interference. At a node, both waves always cancel each other out- the nodes never move!

The equation we need for standing waves are: 

Where n is the number of nodes along the length of the medium, lambda is wavelength, and l is the length of the string/medium. Then, of course, there is the standard equation for waves:

wave speed = wavelength * frequency

Wavy stuff

Hey Everyone!

Nah... This isn't the kind of wave I'm talking about (unfortunately).

Today, I'm going to be talking about the Physicsy kind of waves- what a wave IS, the two types of waves, the 5 main properties of waves, and electromagnetic waves.

First off, what the heck IS a wave?

Essentially, a wave is ENERGY. Nothing more, nothing less. A wave is energy that is transmitted from one point to another through a medium- i.e. THROUGH something. That medium can be practically anything, from air (say "heloooooooooooooooooooo") to water (glugglugglug) to an electromagnetic field (more on that later on).

Every wave forces particles to move- a wave transfers energy to particles in its way. Waves can be classified to two ways based on HOW they force particles to move. A wave is either transverse or longitudinal based on how they force particles to move.


In a longitudinal wave, the energy forces particles to move in the direction of the wave's travel. Longitudinal waves cause compressions and rarefactions- basically, the medium has a higher density in a compression and a lower density in a rarefaction. The diagram below represents the density of the medium at any given point.

In a transverse wave, the energy forces particles to move up and down- this is perpendicular to the direction the wave is traveling. Transverse waves are made up of a series of crests and troughs (See below)

Electromagnetic waves are a very special kind of transverse wave. Most waves only force matter to move in two dimensions (i.e. up and down). An electromagnetic wave, however, forces matter to move in three dimensions. How does it do that? An electromagnetic wave actually consists of two waves (an electrostatic wave and a magnetic wave) that are "in phase" and perpendicular to each other (see diagram).

Whoa, hang on! How can BOTH the waves be perpendicular to the wave's direction of travel?

The answer: The waves travel in 3-dimensional space. Imagine a three-dimensional coordinate plane (with an x, y, and z-axis). x is length, y is height, and z is depth. Our electromagnetic wave is traveling along the x-axis.

The relation between any two of the three axes is that they are perpendicular to each other. For example, the x-axis is always perpendicular to the y-axis.

So, if a wave is traveling along the x-axis, its direction of travel is PERPENDICULAR to the y-axis AND the z-axis. This is how electromagnetic waves exist- both parts of the wave are perpendicular to the direction of the wave's travel, but along different axes.

Waves have 5 essential properties- every wave does all five of these things. I'm going to go over the simple ones really quickly so I can get to the more complex stuff.

1. Reflection: Basically, when a wave hits an obstacle, part of the wave's energy is reflected back. Best examples: Mirrors and echoes. If you're standing at the edge of the Grand Canyon and yell down, you hear an echo. When the sound wave hits the rock at the bottom of the canyon, part of the soundwave is reflected back to you.

2. Transmission: When a wave hits an obstacle, only PART of the wave's energy is reflected back. The rest of the wave's energy is transferred to the new medium (aka the obstacle). Example: If you're under water, you can still hear someone talking above the surface of the water.

3. Refraction: When a wave transmits part of its energy to a new medium, the wave changes directions. Example: Have you ever stuck a pencil/straw in a glass of water? The pencil looks like it bends at the water's surface.

4. Diffraction: When waves meet an obstacle, they move around it. Plain and simple. Does this seem to conflict with points 1&2 (reflection and transmission)? Why would a wave reflect off an object or pass through it if the wave could just go around? The answer: Diffraction DOES occur for large objects, but not to a very large extent. Diffraction is only noticeable with relatively SMALL obstacles. Example: You can hear a violinist play even if said violinist closes the door.

5. Superposition: When two waves traveling through the same medium collide, they affect (interfere with) each other- but only while the two waves are in contact with each other. Once the two waves separate, they have no further effect on each other. There are two main types of superposition: Constructive and  Destructive interference (saved for next post :) )

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Thanks!