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Hopper Popper

By turning the half-racquetball inside-out, energy is stored in the elastic medium. This is exactly the same process as storing energy in a rubber band by stretching it. The difference is that the energy stored in a stretched rubber band will be converted into kinetic energy (energy associated with motion) as soon as the student has found an acceptable target and releases the near end. The inverted racquetball is in a quasi-stable state, and needs the "trigger" of a collision with the floor to cause it to relax into its lowest (unstretched) energy state.

When two stacked balls are dropped, there is no simple, easy-to-follow explanation relating the reason for the upper ball to bounce higher than most people expect. Rather, this is a good opportunity to focus on the concept of energy transfer, and empirically conclude what is happening, rather than trying to explain just why. By observation, the lower ball rebounds very little from the floor and the upper ball rebounds much higher than most people expect. Evidently, the energy which would ordinarily cause rebound of the lower ball is very effectively transferred to the upper ball. The exception to this case occurs when the upper ball is a superball. Our explanation of this situation is that the superball has already begun its upward motion and has lost contact with the lower ball before any significant upward motion of the lower ball occurs.

Action and Reaction

Newton's Third Law is often stated as "If one object exerts a force (action) on a second, the second exerts an equal and opposite force (reaction) on the first". For the situation of the student holding the fire extinguisher hose, the initial action force could be considered to come from the carbon dioxide (CO2) gas molecules at high pressure. When the trigger is released, high-speed CO2 molecules are colliding with every part of the inner surface of the hose, and all these forces would cancel each other out completely if the nozzle weren't open to the atmosphere. Upon reaching the open tip, the high-speed gas molecules rush into the open air due to the lack of resistance. This means that in the direction opposite their motion, there are forces of collision on the hose to the left which just aren't being cancelled by any other forces. These forces on the hose result in an acceleration to the left.

However, since the student has a firm grasp on the hose, the student's arm and shoulder muscles will oppose the movement of the hose. As the hose moves to the left, largely involuntary muscular contractions will provide the necessary external force to bring the hose to rest. To accurately invoke Newton's Third Law, one needs to identify the objects which are interacting, and switch the subject and predicate of the sentence describing one object pushing (or pulling) on the other. Here are some examples:

The CO2 gas molecules push on the walls of the hose. (Describes an Action)

The walls of the hose push on the CO2 gas molecules. (Describes a Reaction)

The walls of the hose push on the hand. (Describes an Action)

The hand pushes on the walls of the hose. (Describes a Reaction)

The hand pulls on the arm muscles. The arm muscles pull on the hand, etc.

The most common difficulty with such situations occurs when someone raises the point that since the action and reaction are identically equal in size, none of the objects should ever go anywhere. This difficulty may be resolved by stressing that the action force (of object A on object B) is equal and opposite to the reaction force (of object B on object A). In other words, these forces are on different bodies, and thus should not be thought of as canceling one another.

There is no acceleration of the hose when its nozzle is closed because the net force (due to the sum of all internal action-reaction forces) is zero. When the nozzle is open, we may view the escaping gas as one body and the hose as the other, with the escaping gas exerting an external force on the hose. These forces between the gas and hose cause one of these objects to accelerate to the right and the other to accelerate to the left. Each experiences the same amount of force, and their relative accelerations will depend on just how massive each object is.

Inertia and Impulse

Newton's First Law (Law of Inertia, perhaps) is often stated as follows: An object in motion (or at rest) will remain in motion (or at rest), until a net, external force is applied to it. The emphasis on external forces is related in the above example. Until the CO2 can actually escape from the hose (when the nozzle is open) and be considered an external object, all molecular forces of collision are internal to the hose, and cancel out completely.

Mass is said to be a measure of inertia, and inertia is a tendency to resist acceleration, or any change in motion (or change in velocity, to be precise). The most common mistake here is to state that inertia is a tendency to resist motion, which is just not true.

To understand the FunFest demonstration of the effects of inertia, one needs to focus on the size of the involved forces and the accelerations they produce. In doing so, keep in mind that if you want to increase the acceleration of an object, the force causing the acceleration must also increase.

The force which could cause the upper bottle to tip is the force of friction between the dollar bill and the bottle. If there were no friction, the dollar bill would slide effortlessly between the two bottles. There is friction between the bill and the bottle, but it is quite limited in size. If the bill were pulled slowly from between the bottles, the resulting acceleration would be very small, and only a relatively small force is necessary to produce a small acceleration. A small frictional force between the bill and bottles can only provide a small acceleration of the bottles, but if this is over a long enough period of time, they would surely tip and spill their contents.

However, when the bill is struck sharply with the rod, the bill is forced to accelerate very rapidly. It is relatively easy to generate the amount of force necessary for this with the rod. The amount of friction between the bill and bottles does not increase commensurately under these circumstances, and once again can only produce a minor acceleration of the bottle. This frictional force has its effects further diminished since the dollar bill loses contact with the bottles so quickly. As the dollar bill is snapped from between the bottles, the upper bottle certainly does accelerate, but by an amount so small and so brief in duration as to preclude any significant motion.

Bed-of-Nails

The relevant concept here is force per unit area. If there were only a few nails, a person's weight would be great enough to cause injury if the person attempted to lie down. However, with a great many nails, the amount of force from each nail is simply not great enough to puncture the skin or even cause discomfort over short periods of time. This reasoning also explains why a cushion of some sort is needed for the person's head. In relative terms, a person's head is quite dense, and the rounded shape means that very few nails will contact the scalp. While the nails will still not puncture the skin in this case, most people would be uncomfortable without a cushion of some sort. Rather than make it appear that the person is being pampered, a block of wood is often used for this purpose.

Barrel Crunch

Standard air pressure causes a force of 1.01 x 10 to the 5th Newtons/square meter (14. 7 lb/square inch is much more familiar). Since a standard 55 gallon (208 liter) oil drum has a diameter of 55 cm and a height of 90 cm, this results in each end cap having an area of .24 m2 (368 in2), and the cylindrical side wall with an area of 1.56 m2 (2410 in2), resulting in an inward force due to air pressure of 2.05 x 10 to the 5th Newtons (46,300 lb)! This tremendous amount of force has no visible effect as long as the air pressure on the outside is the same as the pressure on the inside.

As the barrel is heated, the water inside begins to boil, producing a large volume of water vapor. As this water vapor is being continually produced, the air originally in the barrel is largely "pushed out", resulting in water vapor occupying nearly the total inner volume. To keep the air in the barrel to a minimum, the barrel is capped while the water is still boiling. Immediately after capping, the heat source is removed from the barrel.

At room temperature, only a small quantity of the water vapor filling the barrel would remain in the gaseous state. Most of the water vapor will condense into liquid water, taking up far less volume than when in the gaseous state, resulting in a very effective partial vacuum. Without forced cooling, this vacuum will form and cause the barrel to implode in approximately 15 to 20 minutes. To speed up the process for a FunFest show, the barrel is often cooled by pouring liquid nitrogen (-196 degrees C, or -321 degrees F) over the barrel. By doing this, the barrel usually collapses within just a few minutes.

Suction Cups, Magdeburg Hemispheres

The suction cups used in the FunFest show will create a partial vacuum whenever one attempts to pull the two cups apart. By attempting to pull the cups apart, the volume between the cups is increased with no increase in the number of atmospheric molecules, hence the vacuum. The size of the cups and the vacuum produced are usually sufficient to prevent younger students from pulling them apart. The cups can be rather easily pulled apart if they are "slid" past each other. In using such a shearing force, one does not significantly increase the volume between the cups, which would act to prevent them from being pulled apart.

The Magdeburg Hemispheres operate on exactly the same principle as the suction cups, except that the steel hemispheres have a fixed inner volume, and can be more effectively evacuated by the vacuum pump. With a diameter of approximately 10 cm, atmospheric pressure could provide as much as 790 Newtons (180 pounds) of compressional force on the hemispheres.

Balloons in Vacuum Chamber

The more a balloon stretches, the greater the compressional force it provides for the gas it encloses. This is the same situation as for a spring. The more a spring is stretched, the greater its restoring force. When a balloon is inflated, the compressional forces responsible for maintaining the size and shape of the balloon come from this elastic, compressional force, acting together with the compressional force from the external, atmospheric pressure. Since most people can only create pressures of 1 or 2 lb/in2 greater than atmospheric pressure with their lungs, the net effect of the balloon's stretch and external atmospheric pressure must account for about 16 lb/in2. When inflated balloons are placed in a vacuum chamber which is subsequently evacuated, the size of the balloon must increase as the atmospheric pressure is reduced. Eventually, the forces within the elastic membrane of the balloon exceed its rupture strength, and the balloon bursts.

Marshmallow Astronaut

For the purposes of this explanation, one could think of a marshmallow as consisting of a great many, leaky balloons. Since there are so many air pockets in a marshmallow, the expansion of the marshmallows should seem just as reasonable as the increase in size of the balloons in the vacuum chamber. If you closely observe the marshmallows, you will notice that while the pump is still on, there is a small decrease in size just after the marshmallows reach their largest size. This is due to the air leaking out of the air pockets, and the fact that a marshmallow is only partly elastic. That is, after all the forces causing expansion have gone, the elastic forces within the marshmallow will only cause a small reduction in size. If a marshmallow were perfectly elastic, it would return to its original size when all the air is removed.

When air is rapidly reintroduced into the chamber, there is insufficient time for air to diffuse into the pockets within the marshmallows, resulting in crushed marshmallow. In principle, before and after comparisons of the marshmallow's size should allow you to estimate what fraction of a marshmallow's original volume is air.

In general, remarks made about balloon and marshmallow behavior in a vacuum would apply to shaving cream as well, except that the bubbles comprising shaving cream are not as porous as air pockets in a marshmallow, and that there are not enough cohesive forces between the bubbles to allow them to remain intact when air is reintroduced into the chamber. This last effect results in the creation of a rather dramatic mess.

Buzzer and Light in a Vacuum

It is often observed that the sound of the balloons popping in the vacuum chamber is very faint. This is due to the fact that sound waves consist of pressure variations which travel through media of solids, liquids, or gases. The balloons tend to pop when most, but not all of the air has been removed, so the sound level is greatly diminished. By having a buzzer and a light operating simultaneously while the vacuum pump operates, the students can observe the sound level diminish in intensity. Depending upon the quality of the vacuum pump, the sound from the buzzer may not be audible at all. This demonstrates that if there is no medium of solid, liquid, or gas to transmit the vibrations, no sound will be heard. Since the light from the bulb never varies in intensity, evidently no physical medium other than space itself is necessary for the transmission of light. To relate this to more common experience, we can easily see light from our sun, but we certainly do not hear any of its explosive effects.

Pencil Shoot

This demonstration falls into the category of those whose details are difficult to explain, but the overall effect is quite obvious. Due to the dowel rod's shape and a speed between 200-300 miles per hour, it is capable of transferring its energy due to motion (kinetic energy) in a rather amazing way. When the dowel strikes a 1/2" piece of plywood, the plywood is easily penetrated by the dowel, with little or no visible damage to the dowel. Since the plywood is much thinner than the length of the dowel, and the energy transfer is focused on a very small region of the plywood, the individual layers or strata of the plywood shatter rather than breaking the dowel. Wood is very strong under compression, and since the entire dowel travels as a unit, the forces of collision act only to compress it. The nature of the collision creates a very large and sudden shearing force on the layers of plywood, and wood grains are much easier to break under shearing forces than under compression.

Vortex Generator

Whenever a fluid travels sufficiently rapidly past a barrier, smooth or laminar flow is disrupted, and turbulent flow occurs, often accompanied by eddies or whirlpool-like shapes called vortices. When the fluid is air, and the barrier is circular, vortex rings are formed. Such rings are relatively stable and can travel a considerable distance before dissipating. The fog created by pouring liquid nitrogen into water is not at all necessary for the creation of the vortex rings, but does allow them to be easily seen. The amount of energy involved with the creation of the rings has a fundamental effect on their persistence. At the speeds common to jet airliners, vortices produced by their control surfaces may travel for a few miles and present serious hazards to small airplanes. The energy needed to create such vortices comes from the energy of motion of the plane, which reduces its fuel efficiency. Therefore, considerable research has gone into studying how to diminish the turbulent flow caused by airplanes.

Laser Light Show

Children of all ages seem to be fascinated by lasers, and this demonstration is a clear favorite of the FunFest show. The centerpiece of this demonstration utilizes a mirror to effect a magnification of the motion of a loudspeaker cone. Your students are possibly familiar with the wave-forms generated when sound is processed by a microphone and displayed as a voltage (vertical) versus time (horizontal) graph on a video screen. It could be suggested to students that if a loudspeaker is to produce realistic tones, then it, too, must somehow display wave-like motion. The difference here, is that the laser beam will travel up, down, left, and right as time passes, (the previous graph only shows vertical motion for the voltage influenced by the sound waves) and one doesn't keep a record of motion in the past as a printed graph does.

Actually, a history of where the laser beam has been is stored, to a degree, by the eyes, and is the reason we see lines drawn by the laser beam, rather than just a jumpy red dot. Any time a light as intense as a reflected laser beam is focused on the retina, the perceived image will persist even if the light is turned off abruptly. This persistence of vision is also one reason we see television images as continuous, rather than 30 flickering images every second.

By mounting a lightweight mirror on the speaker cone, the mirror will move as the cone does. If one observes the mirror directly, it doesn't exhibit any obvious motion as the music plays. However, if a laser beam shines on the mirror at a sufficiently large angle, the motion can clearly be displayed. By having a viewing screen (usually the auditorium wall) at least 20 meters distant, an angular displacement of the mirror of less than 3 degrees will result in the laser beam moving more than a meter! The reflected spot of the laser beam moves along the arc length of the changing angle, which is the change in angle (in radians) times the distance from the mirror to the screen. If you have a sufficiently lightweight mirror and a laser, (always observe safety precautions when using lasers) you can stick the mirror to a person's wrist with a dab of glue and use the reflected laser beam to read their pulse. This technique is used is a wide variety of industrial and research applications to magnify small motions. If you don't have a laser, a flashlight or other light source generally will not produce acceptable results, due to the lack of a sufficiently intense, well-focused beam.

Electrostatics

Here, use of the word "static" can be a bit misleading. Charges, specifically electrons, must move in order for anything to acquire an electrostatic charge. One of the most common instances where this happens, is by walking across a carpeted floor with shoes on, and then touching a doorknob, an electric appliance, or nearly anything metallic, and ZAP!, you lose the electrostatic charge you accumulated by walking in a hurry. The word "static" refers to the behavior that when excess electrons are deposited on a non-conductor, they lose their mobility, and tend to remain relatively static, at least until the charged, non-conducting object comes in contact with something metallic. (Most metals are excellent conductors, and many non-metals are non- conductors.) Of course, the same reasoning holds true for objects with a deficiency of electrons. During the original charging process when you walk across the floor, as one object gains electrons, the other object must lose electrons. In fact, under most situations, this activity will leave the carpet with a negative charge (an excess of electrons relative to the uncharged state), and the person with a positive charge (a deficiency of electrons relative to the uncharged state).

This process is generally called Charging by Friction, and is the same mechanism used to charge the dome of the Van de Graaff generator. In this generator, friction between the rubber belt and the glass roller at the bottom cause the belt to become negatively charged. Although these charges don't move very much while on the belt, their tendency for mutual repulsion causes many of them to jump off the belt and onto the metallic teeth at the top of their ride. This metal "comb" is connected to the dome, and all the excess electrons collected by the comb travel very freely across the outer surface of the dome to give it its electrostatic charge.

Any object that now contacts the dome will share in its net, negative charge. This is called Charging by Contact. The dome builds up enough excess charge that these electrons will readily travel onto even non-conducting surfaces, such as the student or teacher who happens to have their hands on the dome. Since the person stands on a highly insulating platform while in contact with the dome, there is nowhere for the charge to go beyond spreading across the person's body. Once sufficient charge accumulates on the person's hair, the effect of mutual repulsion of like charges is nicely demonstrated.

When the aluminum pie plates are placed on the dome, they too, become charged by contact. Due to the very low mass of an aluminum pie plate, the mutual repulsion of electrons is great enough to cause levitation of the plate. This is a rather unstable condition of balance, however, and the plate falls to the ground, allowing the plate below to take its place.

Liquid Nitrogen

Liquid nitrogen boils at -321 degrees F (-196 degrees C)! This is why liquid nitrogen boils so vigorously when poured into a beaker at room temperature. Students are probably familiar with seeing what happens when a drop of water falls on a very hot skillet which is sitting on a stovetop. Let's say the surface of the skillet has a temperature about 400 F higher than room temperature. When room temperature water hits such a surface, it begins boiling nearly instantly and very vigorously. Exactly the same reasoning explains the behavior of liquid nitrogen.

For most materials, as the temperature is lowered, elasticity tends to decrease and brittleness increases. When an object such as a racquetball has its temperature lowered to the temperature of liquid nitrogen, its brittleness far exceeds its properties of elasticity, and it shatters very easily.

Laser PA System

There are several steps in this demonstration involving the change of energy from one form to another. First, the microphone changes the acoustic energy into an electric signal. This signal is then amplified by the amplifier until the voltage is high enough to affect the laser. This voltage is then applied across the resistor that carries the current operating the laser. When the voltage across a resistor is changed, the current flowing through the resistor also changes. This makes the laser beam either brighter or dimmer, depending on whether the current is increased or decreased.

The solar cell (or photovoltaic material) changes light energy directly into electrical energy. Since the intensity of the laser beam varies just as the electric current produced by the microphone, the electric current produced by the solar cell also varies just as the current produced by the microphone. This electric energy is then amplified by the amplifier and sent to the loudspeaker. The loudspeaker then changes the electrical energy back in to acoustic energy.

If you have any questions regarding Physics on the Road please contact Dr. Keith Adams, Outreach Coordinator (ktadams@purdue.edu).

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