The Basic Physics Behind Helicopters

The in class demonstration on the conservation of angular momentum inspired me to look at the physics behind how helicopters fly.

The rotation of the propellers creates a force that pushed down on the air. Given Newton's third law, the air pushes back with an equal and opposite force. When that force is greater than the force of gravity, the helicopter can move up.

But, given the conservation of angular momentum, why doesn't the helicopter spin in the opposite direction of its propellers? It has to do with the spinning tail motor that opposes the rotational force of the blades.

Here is an example of what happens to a helicopter that loses its tail motor.

—http://www.youtube.com/watch?v=hnK9bGCvYtU

Physics Behind Auroras

Auroras are natural light shows, usually seen in locations very far north or south. Although they don't have much to do with mechanical physics, they exemplify principles of magnetism, as well as the transfer of energy between different forms.

For an aurora to occur, a large amount of energy is required. This comes from solar winds, which send charged particles (mostly electrons) towards Earth. Since these particles are charged, they can't just travel in a straight line--they must follow the magnetic field of the Earth. For this reason, they usually enter near the poles. That's why auroras usually are seen near the Arctic and Antarctic Circles.

When the electrons reach the atmosphere, they collide with gaseous molecules, raising their energy. These higher-energy forms are more unstable, so the fall to the ground state is inevitable. When the energy falls, it is emitted in the form of light energy. This is the same principle that traditional neon lights utilize. The color that we see is dependent on the chemical makeup of the gas: lower altitude, molecular oxygen emits green light; high altitude, elemental oxygen emits red light; nitrogen emits blue light.

A time-lapse video of the Aurora Borealis (Northern Lights) can be seen at

http://youtu.be/sBWPCvdv8Bk

Physics of the domino amplifier

In 1983, Lorne Whitehead of British Columbia set up a domino amplifier, with each domino 1.5 times larger in size than the previous domino. Usually dominos are equal in size, but here, a chain reaction can still be achieved with dominoes less than 1.5 times larger than each preceding domino.

In 2009, a world record of the largest toppling dominoes was set in Netherlands using a similar arrangement.

It seems impossible that a light push on a small domino in the domino chain is able to result in such a heavy fall by the last domino that is the size of a building. This is how it works. In a normal domino set up with equal sized dominos, some energy is lost to sound and heat, but the kinetic energy transferred from one domino to the next is approximately equal. In this domino set up, in which each domino is increasingly larger than the preceding domino, kinetic energy increases along the domino chain. Each increasingly large domino holds a larger potential energy because its center of mass is higher and has a larger mass, and thus, the potential energy that is transferred to kinetic energy as the domino topples over is also larger.

In the original experiment with 13 dominoes, in which each domino is 1.5 times larger than the preceding one, the 13^th domino is calculated to have 280,000,000 times the energy of the 1^st domino.

http://www.youtube.com/watch?v=APoL-Gw9jMQ

Physics of a Roundhouse Kick

The martial arts have fascinated many people for generations, most notably through films such as those of Bruce Lee and even Chuck Norris. Often, the martial arts are associated with gravity-defying jumps and kicks. One of these kicks that has always interested me is the spin-kick, or the roundhouse kick.

For this Physics News, I looked specifically at the spin-kicks of the Thai form of martial art known as Muay Thai, although these kicks are generally quite consistent in their form and function across different schools of martial art. It has been shown that Muay Thai roundhouse kicks are about as deadly as being clubbed by a baseball bat (generating around 480 pounds of force per strike).

As elucidated in the diagram to the left, the physics of a spin-kick follows the general rules of uniform circular motion. The foot, which is the object at the edge of the circle, is trying to move in a tangential manner to the circle, but a force is exerted inwards towards the body (center of rotation) that is keeping the foot in circular motion.
Keeping in mind Newton's third law, every action has a reaction, so for the force moving inwards towards the body that is keeping the foot in circular motion, there is a force exerted by the body against the leg, thereby canceling out the two forces. This then makes it so that the mass of the foot, with the force of gravity acting upon it, has to be overcome for the kick to be kept in a spin. This is when we try to do spin-kicks, we tend to fall forwards before completing a full spin.

This additional force that has to be applied to over come the mass of the foot is the torque, which is the tendency of a force to rotate an object about an axis or a fulcrum. Torque is defined as:

τ = r × F

where,

τ = torque
r = length or radius of the arm lever
F = magnitude of the force applied

Now that we know how a spin-kick is maintained in a spin, we can move on to the additional factor that makes spin-kicks so deadly. This is where the power equation comes in:

P = Fd / t

= τ x ω

where P = power,
τ = torque,

ω = angular velocity

We can then deduce from this equation that the faster the spin of the kick, the more power it is likely going to generate upon hitting the opponent. Moreover, because the torque is determined by the radius of the lever (or Muay Thai fighter's leg, in our case), it is to the fighter's great advantage the he or she extend his or her leg as far as possible, so as to generate as much power as possible.

The picture on the left shows a fighter (in black) extending his foot so as to achieve maximum radial proportion. He is also twisting his body so that his leg is swinging at an angle, which contributes to the angular velocity with which the leg rotates.

For additional information and live-action demonstrations of Muay Thai spin-kicks, see the following video:
http://www.youtube.com/watch?v=gyb2iUVY0oQ&noredirect=1

Physics of Scuba Diving

While people may think that the physics behind scuba diving is pretty simple, with just a steady supply of oxygen all that is necessary to breath underwater, this is not at all the case. When diving deep underwater, several factors must be accounted for in order for the diver to make a safe journey down and back. The most important of these are the gas laws. Water has different characteristics than air, so gases will tend act differently as well. Water, unlike air, is uncompressible, and also happens to be denser than air. In order to account for these differences, divers make use of several gas laws to insure their safety.

The first of these is Boyle’s Law, which relates the volume and pressure of a gas at held at a constant temperature. The equation for Boyle’s Law looks like this:

PV = k

Where P=pressure of gas, V=volume of gas, and k is a constant. Basically, Boyle’s Law states that when you increase the pressure on a gas, the volume decreases, and visa versa. As a diver descends, the pressure of the water on himself and the oxygen he is breathing increasing, decreasing the total volume. The opposite holds for while he is coming up. This is why it is important to breathe out as you are rising, so your lungs to not over-inflate. Here’s a video demonstrating Boyle’s Law as it relates to scuba diving.

http://www.youtube.com/watch?v=XoytjcUmR90

Another important gas law when looking at scuba diving is Henry’s Law, which states that the mass of a gas that dissolves in a volume of liquid is proportional to the pressure of the gas. The equation goes as follows:

P = KC

Where P=partial pressure of gas, C=concentration of gas, and K= Henry’s Law constant. This law is important to divers because it means that at a higher pressure, a diver’s body will absorb more gasses. This law relates to decompression sickness, when a diver swims deep and then rises too quickly, causes gas bubbles to form in the tissue. A video showing Henry’s Law as it relates to scuba diving can be found here:

http://www.youtube.com/watch?v=taTh0uBJ4RE

Physics of the Giant Backwards Circle (A Complex Gymnastics Skill)

The Giant Backwards Circle (or "Giant" for short), is a circling skill that completes a 360 degree rotation around a single bar

How is it done?

1. Start in a handstand on top of the bar

2. Swing downward through the bottom of the bar

3. Then swing upward and end in the same handstand position

While this may look simple and sound easy, there is actually much skill involved in getting the technique right and overcoming the opposing physical forces

In order to complete this skill, the gymnast must overcome the opposing forces of gravity and friction. The force of gravity is overcome by a "tap", which is when the body bends at the shoulders at the bottom of the circle, thus shortening the radius. In doing so, the acceleration of the whole body increases, and if done correctly, it can be enough to overcome gravity. The force of friction between the gymnast's hands and the bar can never be eliminated. One's grip should be tight for 270 degrees of the skill and loose enough for the remainder of the circular motion to allow the entire body to rise to the handstand position at the top of the bar. Some quick tips for performing the giant correctly are to stretch the body on the downward swing to achieve enough momentum, to keep the head tucked "in", and to lift your toes as opposed to arching your back. While these methods may appear to increase one's rotation, their improper form could lead to serious injury.

Note in this picture that the body is in a hollow position for 330 degrees of the giant. In the 30 degrees at the bottom of the circle, the body is in an arch position due to the tap. It is important that the gymnast's shoulder be pushed straight for a majority of the giant, and they should only bend for a short period in order to increase their acceleration to get back to the handstand position on top of the bar.

For more information, see this website: http://www.gymnasticsrevolution.com/Parents%2021.html

Physics of a trebuchet

A trebuchet is a machine that used for a siege since 4th century B.C. It throws a heavy object with a high velocity by using the force of gravity. The basic structure of the trebuchet is shown in the figure below.

It uses two physical mechanisms to shoot the projectile: a lever and a sling. As the force of gravity acts on the counter weight, the counter weight end of the lever would go down and the other end of the lever would be lifted. Also, depending on the location of the pivot of the lever, the velocity would be amplified. When the projectile end of the beam reaches certain height, it starts to lift the projectile by the force of tension acting on the sling. Then the projectile would follow a circular path by the sling at the same time as it follows the circular motion by the lever.

The sling releases when it reaches certain angle and the projectile would be fired (the angle can be controlled).

The velocity and the expected distance of the projectile can be estimated by the calculation using the potential energy and the kinetic energy of the counter weight. However, the precise calculation is very complicate.

For further information on calculation you can access:

http://www.real-world-physics-problems.com/trebuchet-physics.html

Interesting question to ask:

Is the scene in the movie realistic? (at 18s of the video: http://www.youtube.com/watch?v=7bFTw95pJp8)

Physicists in Tune with Neurons

Have you ever wondered why some sounds are so pleasant and others annoying (think nails on a chalkboard)? Recent research examined that question by modeling the neural signaling of the auditory pathway (http://physicsworld.com/cws/article/news/47171). The findings were very interesting and have physics principles at their core.

The spacing of action potential signals was the dependent factor on the harmony of a certain sound frequency. The authors explained that pitch was the ability to differentiate between sounds of two different frequencies and that the intervals of firing determine if a chord is harmonious or disharmonious. Sensory neurons in the periphery form synapses on what is called an interneuron. The way that these signals add up in space and time determine if a sound has a regular pattern of firing or an irregular pattern of firing. Constructive and destructive interference determine how the sound waves sum up together. Constructive interference produces a larger amplitude than either wave component alone and destructive interference produces a lower amplitude. Sound waves are longitudinal waves and, therefore, the way they sum up is by adding together the pressure differentials they form in the air. At the end of the article, the authors mention entropy, a measure of disorder. Low entropy patterns of signal firing were associated with harmonious sounds while the opposite was true for disharmonious sounds. This makes sense because there are many more ways that the waves can be added together to form disharmony than harmony. Overall, this article presents an interesting finding as to what types of sounds (literally) sync in the human mind.

Physics of rowing

For my Physics News, I decided to look at my sport, rowing.

In rowing there are many physics principles used. To name a few, rowing uses propulsion, resistance, kinetic energy, speed variation, center of mass, buoyancy and many others. For my presentation, though, I chose to focus on speed and power variation. In class we have focused mainly on averages of speed and power, but in rowing there is large variation in both speed and power over each complete stroke cycle. 

            As you can see in the graphs above, the speed varies depending on where the oar blade is in relation to the water. When the stroke is in the recovery phase (or out of the water), the speed decreases because there is nothing propelling the boat forward, but as the rower takes a stroke and catches the water with their blade, the speed of the boat increases. This alternating increase and decrease can also be seen in the power variation graph, with the power decreasing when the blade is recovering over the water and the power increasing as it is pulling through the water.

            This alternating increase and decrease of speed can be observed in this Myth Busters clip where they tied a water-skier to the back of an mens 8+ to see if it could produce enough speed to allow a person to ski behind it. The increase and decrease of speed proved to be a significant problem, but it was found that with the right technique that there was a fast enough average speed to water-ski behind a boat. - written by Kate Thomson

(Start the clip at 5:30)

• http://www.youtube.com/watch?v=Gs9oVbbK04o&feature=results_video&playnext=1&list=PL5194FD54AB3D1CDC

For more information on the physics of rowing:

• http://www.atm.ox.ac.uk/rowing/physics/basics.html#eq22

Pressure

I found a very cool video on youtube

http://www.youtube.com/watch?v=BECx4E4Ug9Y

The video was a demonstration of the principle of pressure.

In mathematical terms, pressure is equal to force divided by area.

In this case, the gravitational force was large but the area is also
large.  Hundreds of nails support the weight of the person's body
instead of just one. The resulting force is distributed over all of
the nails, so the person wasn't injured. - written by Eric Hu

The Physics of Fire

Fire seems almost like magic. What is it exactly? Chemistry tells us that fire is the energy released from the chemical reaction between oxygen and organic material. This is known as combustion. This energy is released in the form of heat and light. But chemistry only goes so far in our understanding. Why does fire acts the way it does? Here's where physics comes into play.

Examples of combustion equations

Physics not only explains the shape fire takes but also why certain flames glow in different colors. Gravity makes warm air rise and this principle is what shapes the flames into their distinct shape. In fact scientists at NASA have done experiments with flames in zero gravity and the flame actually spread out in a spherical shape as seen below:

As for the light we see, physics explains this too: specifically quantum physics does. The heat from the reaction excites the molecules to emit light of a certain color, in most cases blue. Red flames are actually heated up ash and soot around the flames glowing and can sometimes cover up the blue light from the actual reaction.

The Physics of the Heart

The blood flow through the heart, or as physicists call it, hemodynamics, can be described by the equation: Flow= pressure difference on either side of the valve/the resistance to flow.  For example, when the blood is in the left ventricle, its next step is to move into the aortic arch, which then pumps the blood to the rest of the body.  However, this movement is blocked by a valve known as the aortic valve.  In order for this valve to open, the pressure in the left ventricle needs to be greater than that in the aortic arch.  Therefore, when measuring blood flow from the left ventricle to the aorta, the pressure difference would be the intraventricular pressure minus the aortic pressure.  When the left ventricle has a sufficient amount of blood in it, its pressure will surpass that of the aorta, and the valve will open.  Flow is also dependent on resistance, which refers to the relationship between the blood and its surroundings.  In the heart, resistance has to do with the size of the valve opening.  When the valve opening is small, the resistance is high, and the blood flow is slow. However, when the valve is large, the resistance is low, and the blood flow is fast.- written by Olivia McKennon

More information on this topic can be found at:

http://www.cvphysiology.com/Hemodynamics/H001.htm

 

Physics of the Eye

The eye acts as a camera, refracting light to focus an image on sensory cells to produce neural responses from which an image is constructed in our brain, thus enabling us to see. Your eyeball possesses a transparent opening on the front called the cornea. The cornea is shaped like a converging lens (meaning that it is thicker in the middle). Therefore, it converges rays of light traveling parallel to a single point, optimally on the back of the eye, or retina. The cornea also refracts light thanks to its index of refraction of 1.38, significantly greater than that of air. Light next passes through the pupil, which is basically just an opening. The pupil appears black because all of the light behind it is absorbed by the sensory cells of the retina, such that no light is reflected out of the eye. The colored part of the eye, or iris, is a muscular ring that adjusts the size of the pupil depending on how much light is available. Light then passes through the crystalline lens, a membrane capable of changing shape with the help of ciliary muscles as a mechanism to focus the image on the retina, where all the sensory cells are located. This muscle action also serves to make slight changes in the bulge-shape of the cornea changing the focal length. While the cornea does most of the refracting, the role of the lens is to make small alterations thanks to its flexibility. Generally, the focal length (or length from the lens to the point at which the light rays converge) is approximately 1.8 cm. The anatomy of the eye ensures that at this length, the image produced is focused on the retina in a reduced, inverted form (the brain reverts the image such that we perceive everything right side up). The eye adjusts its focal length via the mechanisms described earlier in a process called accommodation, which allows us to focus on images both close up and far away. Close up objects require a shorter focal length so that the image will focus on the retina. Conversely, far objects require a longer focal length. This means that for distant objects, the ciliary muscles relax, and contract for close objects. To apply this further, nearsightedness (or the inability to focus on objects far away) is caused by a bulging cornea or elongated eyeball which causes a shortening of the focal length. Corrective lenses are shaped divergently (concave in the middle) to spread out the light rays before they enter the eye, thus moving the focal point back to the retina. Farsightedness is the exact opposite; the focal length is lengthened such that convergent lenses are necessary. - written by Keith Casey

The Physics of Waterskiing

Ever wonder about the physics of water skiing?

Well, when you are water skiing physics comes into play quite a bit.  When you try to get up on a ski, it’s important to keep your ski at a fairly precise angle to the water so that as you’re pulled forward the water hitting your ski creates a downward force, enabling you to stand up.  When the upward force of the water on your ski is equal to the downward force of gravity, you can effectively stay afloat.

When you are being pulled behind the boat, the force of tension in the rope is also acting on you.  When there is constant tension in the rope, you will travel at the same speed as the boat that is towing you.  However, if you’ve ever been water skiing you know that the skier is often traveling at a speed faster than the boat.  How is this possible? Well, this is where centripetal forces come into play. The rope keeps the skier in a circular path around the boat.  Because of this circular motion, the skier experiences acceleration toward the center of the circular path, just as we saw in lab with the swinging mass.  This centripetal acceleration means that the skier can be skiing at speeds quite a bit faster than the boat is traveling-- making wipe outs that much more painful!

Finally, Bernoulli's principle factors in as well.  As the velocity of fluid flow increases, the pressure decreases.  Therefore, the speed of the boat must increase when the skis have less surface area (so, if you're doubling skiing, the boat can pull you significantly slower than if you are single skiing).  If you've ever tried to barefoot ski, this makes complete sense and explains why the boat has to pull you a such a fast speed in order to keep you going-- because after all, your feet are much, much smaller in surface area than a ski.  And this is why when you fall while barefoot skiing, it can be pretty painful!

Will It Float!

If you watched David Letterman growing up, you will remember Will It Float. Mixed in with the top 10 and the opening monologue, an entire segment was dedicated to physics. The idea of the game is simple. An object is announced and David Letterman and Paul Shaffer guess if the object will float in a bucket of water.

Whether the object floats or not is dependent on two forces. The force of gravity acts downward on the object, while an upward buoyant force is exerted by the liquid. If the force of gravity is greater than the buoyant force, the object will sink. If the buoyant force is greater the object will sink. When the forces are equal the object will hover in the water. The buoyant force is always upwards since the pressure in a fluid increases with depth. As a result the upward force on the bottom of an object is greater than the downward force on the top of an object. Another way to look at buoyancy is Archimedes' principle, which states, "the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by that object" (263 Giancoli).

So will the cheese log float or sink? That depends on whether or not the weight of water displaced by the cheese log is greater than the weight of the cheese log. Click on the link to find out.

http://www.youtube.com/watch?v=zm-AkvwPdZ4

Here's another link that explains buoyancy in more detail.

http://www.pbs.org/wgbh/nova/lasalle/buoybasics.html

Up!

Much like movie romance, movie physics often push the boundaries of what is real and possible. A fun example of this comes from the 2009 Pixar movie "Up". In the proud tradition of unreal movie physics, this film depicts an old man's house being torn from its foundation and lifted off the ground by an enormous bunch of helium balloons.

Now, is it possible for such a thing to occur without the magic of animation? This is the question asked by the team on National Geographic's "How Hard Can It Be?".

The answer? No, impossible.

In order for balloons to lift a house, the upward force of the balloons must exceed the force due to gravity keeping the house planted firmly on the ground. The upward motion of the balloons is due to buoyancy. The helium balloon is lighter than the air it displaces, so it moves upward. Unfortunately, the gathering the quantity of balloons needed exceed the force due to gravity is simply not feasible.

But that's no fun. So the folks over at "How Hard Can It Be?" scaled it down and did it anyway. They constructed a light weight replica home and gathered approximately 300 high capacity weather balloons. With this set-up, they were able to lift the house, with people inside, creating a real-life re-enactment of the movie. And that's still pretty cool.

http://www.youtube.com/watch?v=rV6rNqin4P8