Destroy The wall 2
Cargo Bridge
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A Classic Propellor Toy
This classic toy was well known before Leonardo da Vinci was a boy, and may have influenced some of his aerodynamic ideas. There are also stories about Orville and Wilbur Wright playing with this toy as kids.
The toy is easy to make, being nothing more than a propellor on a stick, but the physics behind its stability in flight are not so simple.
To make the toy, we need the following:
- A block of soft pine, 8 inches long, 2 inches wide, and 1/2 inch thick. The dimensions are not critical.
- A 10 inch dowel, 1/4 inch in diameter.
- A drill or auger with a 1/4 inch bit.
- A wood file or shaping tool, or a whittling knife. Power tools like a drum sander or belt sander make the job go much faster.
- A drop of white glue.
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We start by drilling a 1/4 inch wide hole through the 8 inch block of soft pine.
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Next, we remove the wood from the corners of the block.
If you are using a knife, hold the block in your left hand, and shave away the wood on the right side of the block. To make the propellor shape, we are removing only the wood on the top right side. The left side is untouched, and the right side is shaved down to a sharp edge.
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Now turn the block over, and repeat, shaving off the right side only, so the propellor blade is a thin piece of wood, at a pronounced angle to the hole.
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Now hold the wood block by the blade you have just made, and carve the other end of the propellor in just the same way as the first. Again, only the right side is shaved down to the bottom, and the left side is unshaved.
A knife, while traditional, is not the fastest, easiest, or safest way to remove the wood. Using a wood file or a shaving tool or planer is better. Power sanders are even faster.
The wood can be left in its rough whittled form, or it can be sanded smooth. You can paint the blades, or draw designs on them with felt tipped markers.
Click on image for a larger picture
Now we glue the dowel into the hole. In the photo, I am using a dowel that is 9½ inches long. The dowel can be a little shorter or a little longer, but a shorter dowel will make a less stable flight, and a longer dowel adds unneeded weight. The optimum length is something you will want to experiment with, since each hand carved toy will be slightly different.
How to fly it
Hold the dowel against your left palm using your right fingertips.
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Now quickly slide your right hand forward and your left hand back, so your left fingertips are against your right palm. The propellor toy will fly away, and land a short walk away.
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Click on image for a larger picture
The photo above shows some toys made by hand in Africa. We support the artisans there by offering these hand painted toys in our catalog.
Destroy The Wall
Swinging Ball (theory)
We want the ball pass through the nail. Determine the minimum speed of v in order to doing this! (It's not necessary to get the string in tension at all time).
WORK, ENERGY & POWER
Work is a very normal term, usually one we dislike; "clean up your room !", "mow the lawn !" etc.
This word of "work" brings to mind pushing, pulling, walking back and forth. The very unusual thing about the day-to-day usage is that it is almost identical to the Physics usage of the term.
"The WORK done on an object, is the product of the average force on it and the distance travelled in the direction of the force."
Notice; the work is done on an object, like a lump of wood during wood stacking, by something which exerts a force ( you on the wood ). This force must then proceed to move it through a distance in its direction.
You are stacking wood.
In section A, lifting the wood, you are doing work on the log as the force you exert is in the same direction as the distance travelled.
In section B, apart from a slight amount of force to start moving it along the dotted line, you are doing very little work on the log as the lifting force you exert is not in the direction of travel.
In section C, gravity does work on the log.
In VERY simplistic terms
The unit of work in the modern system is the joule J . ( Very old units include the calorie, BTU and the erg. )
GRAPHICALLY
Work has no sense of direction. We do not ascribe arrows to work or energy.
Distance is used rather than displacement in the simple definition because the force acting may take a windy path. You are literally doing work on the pen when you push it writing. The total path taken which is important is the distance rather than the displacement.
"ENERGY is the ABILITY of an object to do work for whatever reason."
This again sounds like common sense, but stored energy in whatever form has the same units as work and can do, numerically, that amount of work.
Energy comes in various forms;
- chemical eg nitroglycerine, or food - indeed the amount of energy involved in exothermic reactions is measured in joules as is nutritional energy values of foods.
- heat - both the heat associated with water and the radiation heat associated with the warm sunlight.
- motion - a ball thrown hard onto your flesh certainly exerts a force into your skin through a distance. This particular energy is easy to measure and is called kinetic energy.
- "hidden" energies called potential energies. A spring in a set mouse trap has one such energy, as has an old tree limb waiting to fall down on someone's head.
Interchangeability of the energies ;
Like momentum, the work-energy idea turns out to be a conservation law. Whenever a process occurs, energy does work and turns into a new form of energy or energies.
When all the forms of energy before and after any process are added we find exactly the same number.
PRINCIPLE OF CONSERVATION OF ENERGY; " In any closed system, the total amount of energy remains constant regardless of any process which takes place."
Again, physicists would like to know why, - it is linked to momentum and mass is also a form of energy. ( OK - what is energy ? )
GRAVITATIONAL POTENTIAL ENERGY;
In falling through a height "h" which is in the same direction as the force, the work done by gravity is
work done = force.dist = Mg.h
thus Grav. Pot. Energy Ep = Mgh
This is a stored energy available to be converted into movement energy on release. The Hydro uses this energy in the form of stored water which is released, converts first to kinetic energy then to electrical energy which is distributed around the State.
KINETIC ENERGY; " Energy available because of the object's motion".
Consider a mass, m, which is moving with a speed , v, and does work which brings it to rest.
The unbalanced force, F, which it exerts in doing the work is, by Newton's Third Law also exerted on it , bringing it to a halt.
Funbal = ma
so, Work done = Funbal . dist = mas
( we are assuming all of this takes place in a straight line so that distance and displacement are essentially the same )
Using 2as = v2 - vo2
we get mas = 1/2 .mv2 = Work done
Ek = Kinetic energy = 1/2 mv2
All forms of energy can have such formulae worked out for them !
Eg 1; A swing oscillates through a height of 3m. How fast is the little girl going at the bottom of the swing ?
Soln; This movement is not in a straight line so we must rely on conservation of energy to see how fast the girl is going. We must assume that no energy is turned into heat or other less easily calculated forms.
In swinging, the energy changes from Grav. Pot . Energy to Kinetic Energy. So
Ep lost = Ek gained ( cons of energy )
mgh lost = 1/2 .mv2 gained
thus, gh = 1/2 v2 ( as the mass is common )
9.8 . 3 = 0.5 v2
v2 = 58.7
v = 7.65 ms-1
Eg 2; A 4 kg stone is thrown from the top of a hill which is 20m high. It is thrown at 30 ms-1 at angle such that its maximum height reached is 15m.
a) How fast is it travelling at the top ?
b) How fast is travelling when it reaches the bottom ?
Soln; a) We could do this problem by the conventional projectile motion but because it only involves energy changes, that is a far simpler method.
The total energy of the stone at the start of the journey is composed of Kinetic Energy if we start by ignoring that it is above the sea.
Total Energy at start = Ek
= 1/2 mv2
= 0.5 . 4 . 900 = 1800 J
When it rises, 15m it loses kinetic energy but gains pot energy.
Ep gained = mgh' = 4 . 9.8 . 15 = 588 J
At the top we have a mixture of energies = starting energy
thus 1800 = 588 + new Ek
new Ek = 1800 - 588 = 1212 J = 1/2 m(vnew)2
thus vnew = 24.6 ms-1 = speed at the top.
b) At the bottom of the cliff, it has lost additional Ep which is converted into Ek
Additional Ek = mgh" = 4 . 9.8 . 20 = 784 J
new total energy is now = 1800 + 784 = 2584 J
This is now all kinetic energy, so 2584 = 1/2 m(vbottom)2
vbottom = 36 ms-1 near enough.
In every such operation, however, we usually lose some energy in undesirable forms, usually heat generated by friction or some such process.
Heat is not easily turned back into "useful" forms of energy. All of a car's petrol energy eventually turns into heat; much of in the first place out of the exhaust system, some into warming the surrounding air through drag, some in warming the oil in the various parts through friction and lastly in the brakes through friction.
Energy efficient buses try to avoid the latter loss by using some form of energy storage device for example a gyro ( storing kinetic energy ) or electrical generators for converting the vehicle's kinetic energy back to electrical energy.
Ironically, in our houses, we generate heat in stoves, hot water tanks and heaters from the Gravitational Pot. Energy of the stored water. Better insulation lessens the loss of such energy to the outside. Many other techniques exist for decreasing a home's reliance on Hydro energy. We pay, of course, for the Hydro energy we use. The electrical companies use a variant of the joule called a kilowatt-hour.
Most of our food energy is used to generate heat. This provides the conditions for our body cells to flourish in. Spare energy from this is available for doing our day-to-day activities and any left over goes into stored chemical energy called fat.
POWER
"Power is the rate of doing work or changing energy."
P = Work Done = ΔEnergy
t t
A powerful person is capable of doing the same work as a less powerful person in a shorter time.
The unit of power is the watt, W which is the Js-1.
Eg ; If Poatina generates 500 MW at 90% efficiency from a head of water 1000m above the generator, how much water is needed each second ?
Soln; The water clearly loses Grav Pot Energy so that this is the energy change we need.
P = Work done = Δenergy
t t
500 x 106 = mgh = m . 9.8 . 1000
t t
thus, m / t = 5.1 x 104 kg s-1 = 51 tonnes s-1
But the station is only 90% efficient, so the required amount of water is
= 51 x 100 / 90 = 56.7 tonnes s-1
PROBLEMS
1. You push a table through 3m with a force of 30N. How much work have you done on the table? The table fails to accelerate continuously due to friction. What form of energy is created? ( 90 J)
2. In lifting a 20kg bucket of water through 2m from a hole, work has been done and energy transformed. What work have you done, where have you obtained the energy from and what form of energy has the water and bucket now got? (392J)
3. You are writing an English essay of total length 3 pages. Estimate how far the pen moves in your script and how much force you apply to the pen on average. Hence estimate how much work you do on the pen. Where does the physical (not mental! ) energy go that you expend? (Is there such a quantity as mental energy?) ( ~ 4J)
4. A major environmental push is for "energy conservation" in the house, work place etc. How does this conception differ from the pure physicists' conception of energy conservation?
5. Comets, in their highly elliptical orbits, travel fastest near the Sun and slowest out beyond Jupiter. Discuss the energy changes in such an orbit.
Building a radio in 10 minutes.
For our 10 minute radio, we will need these parts:
- A ferrite loop antenna coil In our other crystal radios we wound the coil by hand. In this project we use a much smaller coil with a ferrite rod inside, from our catalog. The ferrite rod allows the coil to be smaller, and it can be moved in and out of the coil for coarse tuning.
- A variable capacitor (30 to 160 picofarads) We carry this in our catalog. You can also find them in old broken or discarded radios.
- A Germanium diode (1N34A) We carry this in our catalog.
- A piezoelectric earphone Also in our catalog.
- Two alligator jumper wires We use alligator jumper wires here for convenience. They are used to connect the ground and antenna wires to a good ground and a long wire antenna. We carry these in our catalog.
- About 50 to 100 feet of stranded insulated wire for an antenna. This is actually optional, since you can use a TV antenna or FM radio antenna by connecting our radio to one of the lead-in wires. But it's fun to throw your own wire up over a tree or on top of a house, and it makes the radio a little more portable.
- A block of wood or something similar for a base
Click on photo for a larger picture
You can see from the photo how simple this radio is, and why it can be put together in a very short time.
The black painted wire from the ferrite loop is soldered to the center lead of the variable capacitor. The unpainted wire is soldered to the rightmost lead of the variable capacitor.
The germanium diode is soldered to the rightmost lead of the variable capacitor.
One of the piezoelectric earphone wires is soldered to the free end of the germanium diode. The other is soldered to the center lead of the variable capacitor.
The red painted wire of the coil is attached to the long wire antenna with an alligator clip lead.
The green painted wire of the coil is attached to a good ground (such as a cold water pipe) using another alligator clip lead.
That's it -- you're done!
Click on photo for a larger picture
How does it work?
We will start the tuning with the variable capacitor set in the middle of its range, neither all the way clockwise, nor all the way counter clockwise.
With the earphone in your ear, slowly move the ferrite rod into the coil, listening for radio stations.
With a long antenna, you can tune several radio stations. In some areas, one or two stations will be so close or so powerful that they overwhelm all the others, and you will only hear those one or two stations.
How does the ferrite change the frequency?
The ferrite rod increases the inductance of the coil. In our other (hand-wound) coils, we increased the inductance by winding some more loops, or by using a "tapped" coil, and selecting a tap that was farther down the coil.
As the ferrite rod is inserted into the coil, more of the coil is affected by the ferrite, and so the inductance increases. Increasing the inductance moves the frequency lower. This allows us to hear stations "lower on the radio dial".
Ferrite is used because it is magnetic, like iron or steel, but it is not a conductor of electricity. If it were conductive, the coil would induce "eddy currents" in it, and some of the energy would be lost heating up the core. Because ferrite is not a conductor, we can use its magnetic properties to change the inductance of the coil, without losing volume.
If you have a long antenna, a good ground, and you are not too close to a strong station, the variable capacitor will help in fine tuning the stations.
There are actually two coils of wire wound around the ferrite rod. The large coil is connected to the variable capacitor. The small coil is connected to the antenna and ground.
This arrangement allows the radio to be more selective, so that strong stations don't drown out the weak ones. Really strong local stations will still overwhelm the more distant stations, however.
If you have no strong local stations, you can make the stations you receive sound louder by connecting the antenna and ground directly to the large coil. Connect the antenna to the center lead of the variable capacitor, and the ground to the rightmost lead of the variable capacitor. The stations will be louder, but they will most likely all be heard at once, since you radio will be less selective in tuning out adjacent stations.
Wave Motion
Superposition
The first, and most profound, difference between wave motion and the motion of objects is that waves do not display any repulsion of each other analogous to the normal forces between objects that come in contact. Two wave patterns can therefore overlap in the same region of space, as shown in the figure at the top of the page. Where the two waves coincide, they add together. For instance, suppose that at a certain location in at a certain moment in time, each wave would have had a crest 3 cm above the normal water level. The waves combine at this point to make a 6-cm crest. We use negative numbers to represent depressions in the water. If both waves would have had a troughs measuring -3 cm, then they combine to make an extradeep -6 cm trough. A +3 cm crest and a -3 cm trough result in a height of zero, i.e. the waves momentarily cancel each other out at that point. This additive rule is referred to as the principle of superposition, "superposition" being merely a fancy word for "adding."
Superposition can occur not just with sinusoidal waves like the ones in the figure above but with waves of any shape. The figures on the following page show superposition of wave pulses. A pulse is simply a wave of very short duration. These pulses consist only of a single hump or trough. If you hit a clothesline sharply, you will observe pulses heading off in both directions. This is analogous to the way ripples spread out in all directions when you make a disturbance at one point on water. The same occurs when the hammer on a piano comes up and hits a string.
Experiments to date have not shown any deviation from the principle of superposition in the case of light waves. For other types of waves, it is typically a very good approximation for low-energy waves.
Discussion Questions
| A | In figure (c) below, the fifth frame shows the spring just about perfectly flat. If the two pulses have essentially canceled each other out perfectly, then why does the motion pick up again? Why doesn't the spring just stay flat?
|
The medium is not transported with the wave.
 |
| As the wave pattern passes the rubber duck, the duck stays put. The water isn't moving with the wave. |
The sequence of three photos above shows a series of water waves before it has reached a rubber duck (left), having just passed the duck (middle) and having progressed about a meter beyond the duck (right). The duck bobs around its initial position, but is not carried along with the wave. This shows that the water itself does not flow outward with the wave. If it did, we could empty one end of a swimming pool simply by kicking up waves! We must distinguish between the motion of the medium (water in this case) and the motion of the wave pattern through the medium. The medium vibrates; the wave progresses through space.
| Self-Check |
In the photos above, you can detect the side-to-side motion of the spring because the spring appears blurry. At a certain instant, represented by a single photo, how would you describe the motion of the different parts of the spring? Other than the flat parts, do any parts of the spring have zero velocity? | ||
| Answer | The leading edge is moving up, the trailing edge is moving down, and the top of the hump is motionless for one instant. |
The incorrect belief that the medium moves with the wave is often reinforced by garbled secondhand knowledge of surfing. Anyone who has actually surfed knows that the front of the board pushes the water to the sides, creating a wake. If the water was moving along with the wave and the surfer, this wouldn't happen. The surfer is carried forward because forward is downhill, not because of any forward flow of the water. If the water was flowing forward, then a person floating in the water up to her neck would be carried along just as quickly as someone on a surfboard. In fact, it is even possible to surf down the back side of a wave, although the ride wouldn't last very long because the surfer and the wave would quickly part company.
A wave's velocity depends on the medium.
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| The wave pattern moves to the left while the earthworm moves to the right. The medium - the worm's body segments - does not move along with the wave pattern. |
A material object can move with any velocity, and can be sped up or slowed down by a force that increases or decreases its kinetic energy. Not so with waves. The magnitude of a wave's velocity depends on the properties of the medium (and perhaps also on the shape of the wave, for certain types of waves). Sound waves travel at about 340 m/s in air, 1000 m/s in helium. If you kick up water waves in a pool, you will find that kicking harder makes waves that are taller (and therefore carry more energy), not faster. The sound waves from an exploding stick of dynamite carry a lot of energy, but are no faster than any other waves. In the following section we will give an example of the physical relationship between the wave speed and the properties of the medium.
Once a wave is created, the only reason its speed will change is if it enters a different medium or if the properties of the medium change. It is not so surprising that a change in medium can slow down a wave, but the reverse can also happen. A sound wave traveling through a helium balloon will slow down when it emerges into the air, but if it enters another balloon it will speed back up again! Similarly, water waves travel more quickly over deeper water, so a wave will slow down as it passes over an underwater ridge, but speed up again as it emerges into deeper water.
 | Hull speed. |
Wave patterns
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| Circular and linear wave patterns, with velocity vectors shown at selected points. |
If the magnitude of a wave's velocity vector is preordained, what about its direction? Waves spread out in all directions from every point on the disturbance that created them. If the disturbance is small, we may consider it as a single point, and in the case of water waves the resulting wave pattern is the familiar circular ripple. If, on the other hand, we lay a pole on the surface of the water and wiggle it up and down, we create a linear wave pattern. For a three-dimensional wave such as a sound wave, the analogous patterns would be spherical waves (visualize concentric spheres) and plane waves (visualize a series of pieces of paper, each separated from the next by the same gap).
Infinitely many patterns are possible, but linear or plane waves are often the simplest to analyze, because the velocity vector is in the same direction no matter what part of the wave we look at. Since all the velocity vectors are parallel to one another, the problem is effectively one-dimensional. Throughout this chapter and the next, we will restrict ourselves mainly to wave motion in one dimension, while not hesitating to broaden our horizons when it can be done without too much complication.
Discussion Questions
| A | [see above] |
| B | Sketch two positive wave pulses on a string that are overlapping but not right on top of each other, and draw their superposition. Do the same for a positive pulse running into a negative pulse. |
| C | A traveling wave pulse is moving to the right on a string. Sketch the velocity vectors of the various parts of the string. Now do the same for a pulse moving to the left. |
| D | In a spherical sound wave spreading out from a point, how would the energy of the wave fall off with distance? |
