How Things Work - Spring 2018

OK, so about regular circuits: The images represent SERIES CIRCUITS and PARALLEL CIRCUITS. In a  series  circuit, the current is  constant  and is set by the total resistance of the circuit (the sum of the resistors). If you remove one resistor (or light bulb, as in the first image), the current  stops . If the resistors were identical bulbs, having more bulbs would result in dimmer bulbs, since the battery voltage is distributed among them.  Note that the sum of the voltages "over" the bulbs is equal to the total voltage provided by the battery (give or take some minor losses).  Identical bulbs (or resistors) have identical voltages "over" them - 3 identical bulbs connected to a 9-V battery would have roughly 3-V each over them. In  parallel  circuits, current has multiple paths to take, so the total resistance of the circuit is actually LESS than if the resistors were alone or in series with other resistors - see details belo...

Circuits 1 Thus far, we have only discussed "static" (stationary) charges.  Static charges alone are useful, but not nearly as much as charges in motion.  As you recall, electrons are the most easily moved particles.  Recall the Galvani experiments discussed in class: https://www.youtube.com/watch?v=o8zNSzbjRLI https://www.youtube.com/watch?v=sJifWqUa2pY So, electrons are moved by the chemistry of the electrochemical/voltaic cell (originally called the "electric pile" and now simply, battery).  Here are pictures/diagrams of Volta's original batteries: There is a chemical reaction between the electrolyte paste (often an acid) and the two metals (often zinc and carbon).  Electrons are given up by one metal (zinc) and accepted by another (carbon or copper).  The motion of electrons is called "current", but we usually imagine that it is positive charge moving (to keep the numbers positive). We can't see electrons, but we can cer...

1.  What exactly *is* charge?  How do we think of it?  How does this relate to protons and electrons, etc.? 2.  Why is it that electrons are the easiest particles to manipulate? 3.  What does atomic number (Hydrogen = 1, Helium = 2, etc.) mean? 4.  What are quarks? 5.  Coulomb's law is an "inverse square law" - what does this mean exactly? 6.  Why can a charged balloon stick to a wall? 7.  What is "grounding"? 8.  Recall the demonstration where I charged up the small suspended piece - what was I showing?

What is Charge? - as fundamental to electricity & magnetism as mass is to mechanics Charge is a concept used to quantatively related "particles" to other particles, in terms of how they affect each other - do they attract or repel?  If so, with what force? Charge is represented by letter Q. The basic idea - likes charges repel (- and -, or + and +) and opposite charges attract (+ and -). Charge is measured in units called coulombs (C).  A coulomb is a huge amount of charge, but a typical particle has a tiny amount of charge: - the charge of a proton is 1.6 x 10^-19 C.  Similarly, the charge of an electron is the same number, but negative, by definition (-1.6 x 10^-19 C).  The negative sign distinguishes particles from each other, in terms of whether or not they will attract or repel.  The actual sign is arbitrarily chosen. The charge of a neutron is 0 C, or neutral. But what IS charge? Charge is difficult to define.  It is property of particles...

Center of gravity - balanced torques (T = F L, on both sides of "lever"), what makes things stable  (C/G must be supported) Energy Waves - wavelength - frequency - speed - amplitude - crests and troughs wave speed = frequency x wavelength (Note that the wave speed is the speed of light when you are talking about electromagnetic waves.) mechanical vs. electromagnetic waves music - octaves (doubling the frequency); the next note on the piano (1.0594) Doppler effect - red shift, blue shift electromagnetic spectrum - radio, micro, IR, visible (ROYGBV), UV, X, gamma light reflection light refraction lenses and mirrors (convex and concave) focal length/point predicting light paths (when light is reflected or refracted)

Optics questions - answers below Remember - no class on 4/9/18. Exam 2 on 4/16/18 1.  Review the concept of reflection, particularly the law of reflection.  Draw what happens when a light ray hits a mirror at various angles. 2.  Review the concept of refraction:  what it is, what causes it, what happens during it, under what circumstances does light bend, etc.  Draw what happens when a light ray hits a block of transparent plastic at various angles.   3.  Show how to calculate the wavelength of WTMD's signal (89.7 MHz). 4.  Some questions related to how light is affected by optics. Answers:

Lenses As shown and discussed in class, light refracts TOWARD a normal line (dotted line on the left image, perpendicular to surface of lens) when entering a more dense medium. Note in this  convex  lens that this direction of bend changes from down (with the top ray) to up with the bottom ray. This is due to the geometry of the lens. Look at the picture to make sure that this makes sense.  As a result, the rays will intersect after leaving the lens.  An image can form! The FOCAL LENGTH (f) of a lens (or curved mirror) where the light rays would intersect, but ONLY IF THEY WERE INITIALLY PARALLEL to each other. Otherwise, they intersect at some other point, or maybe not at all (if the object is too close to be focused on)! Note that your (human) eye lenses are convex - slightly thicker in the middle.  Thus, your eyes form "real" images on the retina - upside-down!  Unless, of course, the object is too close. If an image is projected onto ...

Refraction : Consider a wave hitting a new medium - one in which is travels more slowly. This would be like light going from air into water. The light has a certain frequency (which is unchangeable, since its set by whatever atomic process causes it to be emitted). The wavelength has a certain amount set by the equation, c = f l, where l is the wavelength (Greek symbol, lambda). When the wave enters the new medium it is slowed - the speed becomes lower, but the frequency is fixed. Therefore, the wavelength becomes smaller (in a more dense medium). Note also that the wave becomes "bent." Look at the image above: in order for the wave front to stay together, part of the wave front is slowed before the remaining part of it hits the surface. This necessarily results in a bend. MORE DETAIL: The general rule - if a wave is going from a lower density medium to one of higher density, the wave is refracted TOWARD the normal (perpendicular to surface) line. ...

Reflection - light "bouncing" off a reflective surface. This obeys a simple law, the law of reflection! The incident (incoming) angle equals the reflected angle. Angles are generally measured with respect to a "normal" line (line perpendicular to the surface). Note that this works for curved mirrors as well, though we must think of a the surface as a series of flat surfaces - in this way, we can see that the light can reflect in a different direction, depending on where it hits the surface of the curved mirror. So - light reflects from mirrors, according to the law of reflection.  However, if the mirrors is curved, light still obeys this rule - it just looks a bit different.  You have to visualize the curved mirror as a series of little flat mirrors. A convex mirror (top) acts reflects light rays "outward" - the light rays  seem  as though they are coming from inside the convex mirror, so it  seems  as though there is an image inside. ...

Recall that waves can be categorized into two major divisions: Mechanical waves, which require a medium. These include sound, water and waves on a (guitar, etc.) string Electromagnetic waves, which travel best where there is NO medium (vacuum), though they can typically travel through a medium as well. All electromagnetic waves can be represented on a chart, usually going from low frequency (radio waves) to high frequency (gamma rays). This translates to: long wavelength to short wavelength. All of these EM waves travel at the same speed in a vacuum: the speed of light (c). The standard wave velocity equation is still: But for light, where c is the speed of light (3 x 10^8 m/s ): c = f  l Still, f is frequency (in Hz) and  l  is wavelength (in m). (We will see during the next class that the speed of light, while constant in a vacuum, is NOT constant in other mediums.  That is, the speed of light does depend on what it travels through - and th...