Homework answers / question archive / The topics for the final exam are: Lenses Refraction Total internal reflection Prisms Electric charge Proton, neutron, electron, quark Particles: fundamental vs

The topics for the final exam are: Lenses Refraction Total internal reflection Prisms Electric charge Proton, neutron, electron, quark Particles: fundamental vs

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The topics for the final exam are: Lenses Refraction Total internal reflection Prisms Electric charge Proton, neutron, electron, quark Particles: fundamental vs. composite Atomic number and elements Ions and isotopes Coulomb's law (inverse square) Charging things - what happens Lightning Why are you statically shocked at times (see also: clothes dryer) Voltage (V) Current (I) Resistance (R Units of V (volts, V), I (amps, A), and R (ohms, ?) Voltages of common batteries (1.5 V) Series circuit Parallel circuit Basics of circuits - what makes a circuit Bulb brightness prediction Ohm’s Law: V = I R Basic electrical schematics (and symbols - battery, resistor, wire) Magnetism Compasses Finding north Magnetic north vs. geographic north Electromagnetism Electromagnetic induction Motors vs. generators Exam 1 Review The meter (m) is the SI standard of length. What is it? The meter was originally defined as 1 ten-millionth (1/10,000,000) of the distance from the North Pole of the Earth to its equator. What do you think of this? Proof that the Earth is “spherical”: ? ? ? ? Watching ships go away from shore Looking at the horizon from atop a mountain Lunar eclipses The classic Aristotelian argument of all things gathering toward a common center, according to relative weight: Earth, Water, Air, Fire Humanity has accepted that the Earth was round since ancient times. The Speed of Light (c) ! One meter is now defined as the distance that light will travel in 1/299,792,458 of a second. (Don’t worry, we’ll define the second shortly.) That’s approximately 1/300,000,000 seconds. One three hundred millionth of a second! This means that the speed of light (c) is equal to: c = 299,792,458 m/s = 300,000,000 m/s (approx) = 3 x 10^8 m/s (approx) By the way, the letter c comes from celeritas (speed) and constant. How fast is the speed of light, really? The speed of light is so fast that a photon of light could travel: 7 times around the Earth’s equator in 1 second To the Moon in about 1.2 seconds To the Sun in about 8.3 minutes To the nearest star system (Alpha Centauri, a 3-star system) in about 4.4 years. So, where does the second come from? ? ? Keep in mind that the second is the fundamental unit of time - it is pretty close to a human heartbeat, so it makes sense that it was adopted as a standard. The original definition of the second was: the amount of time required for a 1 meter long pendulum to swing from one side to the other (with a small “amplitude” or angle from vertical): This standard has since been changed. ? ? ? Why do you think it was changed? It was later defined as a fraction (1/86,400) of the mean solar day (24 hours). This was also changed. The current definition of the second is: ? ? the time taken by 9,192,631,770 vibrations of a specific wavelength of light emitted by a cesium-133 atom But you can think of this as the second “according to an atomic clock” What about mass? Enter the kilogram! ? ? ? The kilogram was originally defined as the mass of water that would fill a cubic decimeter container (also known as a liter). Due to the weird nature of water, and other experimental issues, the kilogram was eventually defined as the mass of a platinum-iridium cylinder kept under a double bell jar in Paris, France. Yes, the kilogram is defined by a chunk of meter. This standard changed in 2018 - it is now defined by an electrical/magnetic experiment. The brand new kilogram! Changed formally in 2019 (though approved in November 2018). The new definition of the kilogram is determined from a “Kibble Balance”, and measures the electrical power necessary to oppose the gravitational weight of a kilogram. This also requires a sensitive measure of local gravity. The major improvement is that the kilogram is no longer based on a chunk of metal (the mass of which has changed by several micrograms over the past few decades). It will now be based on a measurable, repeatable phenomenon. This equation can be useful for 3 quantities. The standard way, for finding v: Or by rearranging, to find d or t: Let’s start using the velocity equation: v=d/t Recall that this is for average (or constant) velocity. Warm-up problems: To arrive at Madison Square Garden, New York City in 3.5 hours, what should your average speed be? The distance is approximately 190 miles. v = d / t = 190 / 3.5 = 54 MPH (approx) The next problem will require a slight variation: Let’s start using the velocity equation: v=d/t Recall that this is for average (or constant) velocity. Warm-up problems: Walking at a “constant” 3 miles/hour, how long would it take you to walk to the Inner Harbor? Assume that the distance is 11 miles. t = d / v = 11 / 3 = 3.7 hours Acceleration! Acceleration, a - The rate of change of velocity, or how fast you change your velocity a = (change in velocity) / time a = (vf - vi) / t Note that the i and f are subscripts. The units here are m/s2, or m/s/s. More... Acceleration is a measure of how quickly you change your speed - that is, it's a measure of 'change in speed' per time. Imagine if you got in a car and floored it, then could watch your speedometer. Imagine now that you get up to 10 miles/hr (MPH) after 1 second, 20 MPH by the 2nd second, 30 MPH by the 3rd second, and so on. This would give you an acceleration of: 10 MPH per second. That's not a super convenient unit, but you get the idea (I hope!). Slightly more elegant form: Note that the delta symbol (triangle) means “change in”. Of course, you can use this equation to solve for any of the relevant variables: For example, with a little algebra we find that: vf = vi + a t So try this problem: A car starts from rest, accelerating at 4 m/s/s. How fast will it be traveling in 5 seconds? Remember that “from rest” means vi = 0 m/s. That will be the case with most of our problems. vf = 0 + a t = 0 + (4*5) = 20 m/s Summary of useful equations thus far: To solve for: Use: Average velocity v=d/t Acceleration a = vf / t Final velocity vf = a t Distance travelled d = ½ a t2 Falling objects... Today we discuss the acceleration due to gravity - technically, "local gravity". It has a symbol (g), and it is approximately equal to 9.8 m/s/s, or 9.8 m/s2, near the surface of the Earth. At higher altitudes, it becomes lower - a related phenomenon is that the air pressure becomes less (since the air molecules are less tightly constrained), and it becomes harder to breathe at higher altitudes (unless you're used to it). Also, the boiling point of water becomes lower - if you've ever read the "high altitude" directions for cooking Mac n Cheese, you might remember that you have to cook the noodles longer (since the temperature of the boiling water is lower). Gravity elsewhere? On the Moon, which is a smaller body (1/4 Earth radius, 1/81 Earth mass), the acceleration at the Moon's surface is roughly 1/6 of a g (or around 1.7 m/s/s). On Jupiter, which is substantially bigger than Earth, the acceleration due to gravity is around 2.2 times that of Earth. All of these things can be calculated without ever having to visit those bodies isn't that neat? Or if we approximate g as 10 m/s2... After 1 second of freefall (falling without resistance, which is not exactly the case here but...), a ball would achieve a speed of: 9.8 m/s 10 m/s After 2 seconds.... 19.6 m/s 20 m/s After 3 seconds.... 29.4 m/s 30 m/s We can calculate the speed by rearranging the acceleration equation: vf = vi + at In this case, vf is the speed at some time, a is 9.8 m/s, and t is the time in question. Note that the initial velocity vi is 0 m/s. In fact, when initial velocity is 0, the expression is really simple: vf = g t vf = 10 t Or if we approximate g as 10 m/s2... The distance is a bit trickier to figure. This formula is useful - it comes from combining the definitions of average speed and acceleration. d = vi t + ½ at2 Since the initial velocity is 0, this formula becomes a bit easier: d = ½ at2 Or: d = ½ gt2 d = ½ (10) t2 = 5 t2 After 1 second, d = 4.9 m d=5m After 2 seconds, d = 19.6 m d = 20 m After 3 seconds, d = 44.1 m d = 45 m After 4 seconds, d = 78.4 m d = 80 m Moving walkway problems The speed of the person on the moving walk, relative to the ground is: 2 m/s to the right Now, add a puppy! What is the speed of the puppy, relative to the ground? 10 m/s to the right Consider the following... If you are traveling by airplane, cruising at 600 MPH due West, and you throw a bag of airline snacks straight up into the air…. Where will they land? Ballistics cart demonstrations The ball still lands in the cart. Why? It is still moving at the same (horizontal) speed as the cart. It has NO REASON to slow down horizontally. The only force acting on it is gravity, and that is vertical. Further details So, why does the ball land back in the car? INERTIA - the ball keeps doing what it is doing (moving forward at the same speed) because there is nothing acting on it (in the horizontal direction) to make it stop. However, there IS something acting on it in the vertical direction gravity - which causes the ball to come back down once it is shot upward. The ball lands back in the car because its horizontal speed forward is never changed; only the vertical speed is affected (by the spring inside the car and by gravity). Inertia is a vital concept - its origins trace back to the Scientific Revolution, and Isaac Newton is usually given credit for it. However, Galileo also had a version of this concept, as did several other scientists of this period. Scientific Revolution: 1550 - 1700 roughly - notable for the introduction of widespread experimental (evidence-dependent) mathematical science. - also notable for the 150 years that it took for geocentrism to finally die after published in 1543 (see below) - sometimes thought of as "kick-started" by the publication of Copernicus' De Revolutionibus Orbium Celestium, in 1543 (the year of his death). This was the first major work arguing for a heliocentric (sun-centered) universe. Not initially a success of a book - its influence took decades to be realized (and very slowly) Galileo (1564 - 1642) and Newton (1642 - 1727) are often thought of as the central figures of the Sci Revolution. We shouldn’t forget many others: Copernicus, Boyle, Kepler, Hooke, Huygens, Harvey Philosophiae Naturalis Principia Mathematica, 1687 In modern language... An object will keep doing what it is doing (in a straight line), unless there is reason for it to do otherwise. This means, it will stay at rest OR it will keep moving at a constant velocity (constant speed, straight line), unless acted on by an unbalanced force. This is usually expressed as a property of matter: INERTIA In modern language... An unbalanced force (F) causes an object to accelerate (a). That means, if you apply a force to an object, and that force is unbalanced (greater than any resisting force), the object will accelerate. Symbolically: F=ma That's a linear relationship. The equation for Newton’s 2nd Law: The total (net) force equals the mass times acceleration. A new unit for force: The SI unit of Force is the newton (N): 1 N = 1 kg m / s2 A newton is approximately 0.22 lb. Sample problem Consider a 2-kg toy wind-up car with a spring inside. The spring exerts a force of 6-N, and this propels the car forward. 1. 2. 3. What is the acceleration of the car? (F = m a) 3 m/s/s What would happen to the acceleration of the car if the spring force was greater? It goes UP. What would happen to the acceleration of the car if you placed some small weights on top of the car before launching it. It goes DOWN. Weight! There is a special type of force that is important to mention now - the force due purely to gravity. It is called Weight. Since F = m a, and a is the acceleration due to gravity (or g): W=mg The SI units are still newtons. Like force, the imperial units are pounds (lb) Implications: Note that this implies that: weight can change, depending on the value of the gravitational acceleration. That is, being near the surface of the Earth (where g is approximately 9.8 m/s/s) will give you a particular weight value, the one you are most used to. However, at higher altitudes, your weight will be slightly less. And on the Moon, where g is 1/6 that of the Earth's surface, your weight will be 1/6 that of Earth. For example, if you weight 180 pounds on Earth, you'll weight 30 pounds on the Moon! (But your mass, the amount of YOU that there is, in kilogram units, will remain the same.) Weight in a moving reference frame: The elevator problem 1. 2. 3. 4. Constant v: no change Constant a up: greater Constant a down: less a = g: weightless! Falling revisited... Objects fall with the same acceleration (g) because their weight-to-mass ratios are constant. More weight means more force (W) toward earth, but ALSO more resistance to motion (m). Therefore, g is constant for a given reference frame. At the surface of the Earth, g is 9.8 m/s/s for all objects. (Assuming no air resistance, of course.) In modern language... To every action, there is opposed an equal reaction. Forces always exist in pairs. Examples: You move forward by pushing backward on the Earth - the Earth pushes YOU forward. Strange, isn't it? A rocket engine pushes hot gases out of one end - the gases push the rocket forward. Tricky thought question Fan on a sailboat - can it make the boat move? The fan provides a constant force. However, if directed toward the sail, it is acting like an “internal” force - the sail will push back on it with an equal (oppositely directed) force. In order for the fan to move the boat, it should be directed away from the fan - to the left in the images above. Because geocentrism didn’t exactly match reality... Orbits of planets didn’t quite seem to go in circular paths around the Earth. Because, well, they don’t. There are times when planets (particularly Mars) appear to go backwards - retrograde motion. We now know this is because Earth “races ahead” of Mars in its closer orbit to the Sun. (It’s like when you pass a car on the highway - at that moment, it looks like they’re going backwards, and relative to you, they are.) The ancient astronomers did not know that. So, a concept was invented by the ancient Greeks - the epicycle. Here’s what it looks like: More about epicycles... So in other words, the epicycle concept helped “save the phenomena” and square the apparent backwards (retrograde) motion with the belief that circular motion was the preferred tool of nature. After all, these were little circular orbits, semi-centered on a big circular orbit. But really, they just had it backwards (plus, the orbits weren’t exactly circular). And in some sense, they can be forgiven - after all, in no way does the Earth really feel like it is moving (rotating or revolving), so naturally, most everyone assumed that it did not. And this became the center of scientific (and religious) dogma. De Revolutionibus Orbium Coelestium, 1543 At rest, however, in the middle of everything is the sun. For, in this most beautiful temple, who would place this lamp in another or better position than that from which it can light up the whole thing at the same time? For, the sun is not inappropriately called by some people the lantern of the universe, its mind by others, and its ruler by still others. The Thrice Greatest labels it a visible god, and Sophocles' Electra, the all-seeing. Thus indeed, as though seated on a royal throne, the sun governs the family of planets revolving around it. Nicolaus Copernicus (Mikolaj Kopernik), 1543 Kepler’s Laws of Planetary Motion: Law 1 Note that these laws apply equally well to all orbiting bodies (moons, satellites, comets, etc.), as long as you reconsider the central body. Planets take elliptical orbits, with the Sun at one focus. Some details... If we were talking about satellites, the central gravitating body, such as the Earth, would be at one focus. Nothing is at the other focus. Recall that a circle is the special case of the ellipse, wherein the two focal points are coincident. Some bodies, such as the Moon, take nearly circular orbits - that is, the eccentricity is very small. Very not to scale. About ellipses... Semi-major axis, a Orbital path Other focal point, F2 (nothing there) Location of Sun (at F1) Kepler’s Laws of Planetary Motion - Law 2 The Area Law. Planets "sweep out" equal areas in equal times. This implies that in any 30 day period (for example), a planet will sweep out a sector of space - the area of this sector is the same, regardless of the particular 30 day period. Kepler’s Laws of Planetary Motion - Law 2 A major result of this is that the planet travels fastest when near the Sun. http://astro.unl.edu/naap/pos/animations/kepler.swf Seasons? So, the distance from Earth to Sun is not constant. Is this why we get seasons? No. NO! NO NO NO!!! Earth is actually closest to the Sun on or about January 4 each year. Seasons? So, the distance from Earth to Sun is not constant. Is this why we get seasons? No. NO! NO NO NO!!! Earth is actually closest to the Sun on or about January 4 each year. Seasons arise due to the tilt of Earth’s axis, about 23.5° from a line vertical to the Earth-Sun plane. During the Northern Hemisphere summer months, the Earth receives a great concentration of solar rays on the surface. During the winter months, a smaller concentration. Southern and Northern Hemispheres experience opposite timing of seasons. Tilt remains the same as location of Earth changes. Kepler’s Laws of Planetary Motion - Law 3 The Harmonic Law. Consider the semi-major axis of a planet's orbit around the Sun - that's half the longest diameter of its orbit. This distance (a) is proportional to the period of time (P) to go around the Sun in a very peculiar fashion: Units can make this easier to work with. a3 = P 2 For Earth, a is in Astronomical Units (AU) - one AU equals half the largest diameter of Earth’s orbit. It’s also close to the average distance between Earth and Sun. And P is in Earth years (yr). Here is an example of how this works. Consider an asteroid that is 4 AU in orbit size. How long will it take to orbit the Sun once? a3 = P 2 43 = P 2 64 = P2 so…… P = 8 yrs How did Newton think about Gravity? Newton's take on gravity and orbits - which is the genesis of our modern conception of it, is based on: Universal Gravitation (1687, Principia) For Newton, Kepler's laws were a manifestation of the bigger "truth" of universal gravitation. That is: All bodies have gravity unto them. Not just the Earth and Sun and planets, but ALL bodies (including YOU). Of course, the gravity for all of these is not equal. Far from it. The force of gravity can be summarized in an equation we will see shortly. Newton’s Law of Universal Gravitation Note that G (6.67 x 10-11 Nm2/kg2) is a rather tiny constant. This should suggest to you that you need large masses to yield significant gravitational forces. Large, as in planet or star-sized objects for the gravity to be significant. Gravity is an “inverse square law” - what does that mean? ? ? If the distance between the bodies is doubled, the force becomes 1/4 of its original value If the distance is tripled, the force becomes 1/9 the original amount If we're talking about an object on Earth, the force due to gravity is "weight", discussed on the next slide. Weight and g, revisited. Weight is a result of local/surface gravity. Since F = G m1 m2 / d2, and the force of gravity (weight) is equal to m g, we can come up with a simple expression for local gravity (g): g = G mplanet / r2 Using Earth numbers: mearth = 6 x 1024 kg and r = radius of earth = 6.4 x 106 m g = (6.67 x 10-11)(6 x 1024) / (6.4 x 106)2 = 9.77 m/s2 (The additional 0.03 m/s2 comes from the earth’s rotation rate.) What happens as you move away from Earth? More about local gravity, g. If you were above the surface of the earth an amount equal to the radius of the Earth, thereby doubling your distance from the center of the Earth, the value of g would be 1/4 of 9.8 m/s2. If you were 2 Earth radii above the surface, the value of g would be 1/9 of 9.8 m/s2. The value of g also depends on the mass of the planet. The Moon is 1/4 the diameter of the Earth and about 1/81 its mass. You can check this but, this gives the Moon a g value of around 1.7 m/s2. For Jupiter, it's around 25 m/s2. On the Sun, g = 274 m/s2 ! Exam 2 Review Center of Gravity Consider the see-saw. Can two people of unequal weight balance on a see-saw? If so, how? What does it take to be “balanced”? Normally, we think about forces being balanced - the forces are in equilibrium. This also means that “up” and “down” forces are equal, as well as “left” and “right” forces. For example: 50 N 25 N 25 N 50 N For rotational equilibrium, the torques must be balanced. The torques must be balanced? Yes, the torque (product of force and distance) must be the same on both sides. L1 L2 F1 F2 F1 L1 = F 2 L2 The torques must be balanced? Yes, the torque (product of force and distance) must be the same on both sides. L1 L2 F1 F2 F1 L1 = F 2 L2 For rotational equilibrium, torques must be equal on both sides of the pivot point. Sample problem. What force will make the system balance? Sample problem. What force will make the system balance? For the torques to be balanced: 20(12) = F(8) Sample problem. What force will make the system balance? For the torques to be balanced: 20(12) = F(8) F = 30 N Center of Mass (CM) The CM of an object (or system of objects) is the point where: Center of Mass (CM) The CM of an object (or system of objects) is the point where: ? ? ? ? ? ? The weighted relative positions of the distributed mass sums to zero - that means, it is the point where the torques are equal on all sides The point about which the object “balances” The point about which the object best rotates The point where, if a force is applied, the object will NOT rotate The point where we can pretend that all of the mass is located (It is sometimes outside the physical body itself.) Examples: Examples: Returning to the broom question - which end is heavier? Long or short end? To be stable, an object’s CM must be supported. What is actually balanced here? L W Wstick (L1) = Whanging (L2) stick 1 L 2 W hanging It’s as though the entire stick is located at its CM. Fluids First, a word about liquids... In general, most liquid fluids are incompressible (or very slightly compressible). As a result, pressure applied to a fluid is transferred equally everywhere in the fluid. What is pressure? The units could be psi (pounds per square inch), or (in SI units), newtons per square meter (also called a pascal, Pa). Pascal’s Principle Pressure change is transmitted without loss to every part of the fluid and walls of its container. This allows hydraulic systems to work beautifully. Pascal’s Principle Pressure change is transmitted without loss to every part of the fluid and walls of its container. This allows hydraulic systems to work beautifully. Since P is the same for both pistons: P = F 1 / A1 = F2 / A2 As A2 goes up, F2 (the lifting force) goes up. Pascal’s Principle And braking systems are similar What about flight? Flight employs nearly all of these ideas in some fashion. A plane requires an engine to build up and maintain a speed. The speed must be sufficient to provide lift, but the angle of the wing must be appropriate enough to allow the lift to happen. Flight can largely be described by Newton’s laws. Consider a wing cross-section: Flight can largely be described by Newton’s laws. Consider a wing cross-section: Air hits it at a certain speed. However, the shape of the wing forces air to rush over it and under it at different rates. The top curve creates a partial vacuum - a region "missing" a bit of air. So, the pressure (force/area) on top of the wing can become less than the pressure below. If the numbers are right, and the resulting force below the wing is greater than the weight of the plane, the plane can lift. Let’s see this animated: Let’s see this animated: This is often expressed as the Bernoulli Principle: The Bernoulli Principle Pressure in a moving stream of fluid (such as air) is less than the pressure of the surrounding fluid. Details: The previous image above shows a Newtonian way to think of flight - imagine the wing first shown, but with the front slightly inclined upward (to exacerbate the effect). There is a downward deflection of air. The reaction force from the air below provides lift and the lift is proportional to the force on the wing. Reaction force, providing lift Energy and Waves But….. IS energy a real thing? Not quite. It is a mathematical concept, completely consistent with Newton's laws and the equations of motion. It allows us to see that some number (calculated according to other manifest changes - speed, mass, temperature, position, etc.) remains constant before and after some "event" occurs. It is often easiest to think of energy as a mathematical “book-keeping” technique in science. Whatever energy we “put into” a system must be able to kept track of. In principle, we can track energy throughout all the changes in a system. Some ideas about energy ? ? ? ? ? ? ? ? Energy is quantified Energy can be stored in fuels (chemicals). Energy can be stored by lifting objects (potential energy). Moving objects carry energy (kinetic energy). Electric current carries energy. Light (and other forms of radiation) carries energy. Heat carries energy. Sound carries energy. To summarize: Energy is a mathematical way of keeping track of changes in a system. It is consistent with Newton’s laws of motion (and other agreed upon science). Therefore, we can use energy conservation as a way of solving problems: To summarize: Energy is a mathematical way of keeping track of changes in a system. It is consistent with Newton’s laws of motion (and other agreed upon science). Therefore, we can use energy conservation as a way of solving problems: We simply have to know the amount of energy in the beginning to predict what will be true at any point in time. To summarize: Energy is a mathematical way of keeping track of changes in a system. It is consistent with Newton’s laws of motion (and other agreed upon science). Therefore, we can use energy conservation as a way of solving problems: We simply have to know the amount of energy in the beginning to predict what will be true at any point in time. Likewise, we can reconstruct what things were originally like, knowing what we have now. What is a wave? Let’s ask Wikipedia. “A wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport.” There are several aspects of a wave that we should know about: ? ? ? ? ? ? Crest Trough Amplitude Wavelength (?) Frequency (f) Speed (v) Definitions Crest - peak (or high point) of a wave Trough - valley (or low point) of a wave Amplitude - height of wave, from equilibrium to a crest or trough Wavelength (?) - size of wave, from crest to crest (or trough to trough, or the distance between any 2 points that are in phase with each other) [in m] Frequency (f) - number of waves per second (in Hz) Speed (v) - how rapidly the wave energy travels (in m/s) The two main categories of waves: Mechanical waves - these waves require a medium (a physical thing that vibrates) - Examples include: sound, strings, earthquakes, water, drums Electromagnetic waves - these waves travel fastest (at the speed of light) where there is NO medium. However, they can often travel through other mediums, too. They are usually represented on an “electromagnetic spectrum”. - Examples: Radio, microwave, infrared, visible light, ultraviolet, x-rays, gamma There is a useful relationship between ?, f and v. We know that v = d/t. For a wave, consider that one wavelength (?) passes a given point in one period. v=?/T Since f = 1/T v = ? (1/T) = ? f Strange harmonic patterns on flat (Chladni) plates Sound Wave speed equation Remember, sound is a longitudinal wave. This metal tube has tiny holes in it and it is filled with propane and lit - it acts long a long gas burner. However, there is a speaker at one end playing various frequencies. You can see how the flame height changes with tone. This demonstrates that the pressure of propane gas molecules inside the tube varies with pressure of the sound - that’s a longitudinal wave. https://www.youtube.com/watch?v=cqilJNsiqig&t=22s Remember, sound is a longitudinal wave. This metal tube has tiny holes in it and it is filled with propane and lit - it acts long a long gas burner. However, there is a speaker at one end playing various frequencies. You can see how the flame height changes with tone. This demonstrates that the pressure of propane gas molecules inside the tube varies with pressure of the sound - that’s a longitudinal wave. Human Hearing Range The frequency range of average human hearing is approximately: 20 Hz - 20,000 Hz This changes with age and repeated exposure to loud sounds. Dogs can hear up to 45,000 Hz. Mice, bats, and cats are even higher. http://www.szynalski.com/tone-generator/ Octaves http://www.szynalski.com/tone-generator/ In music, doubling the frequency is defined as an octave. An octave is the same note, but in a higher register. An octave lower is the same note, but half the frequency - in a lower register. To find the frequency of a note 2 octaves higher, you double the frequency again. Octaves are also the difference between the low “DO” and the high “DO” on a DO-RE-ME major scale. Another image: The Equal-Tempered Scale The equal tempered scale is the common musical scale for the tuning of pianos and other instruments of fixed scale. It divides the octave into 12 equal semi-tones (or “half-steps”). But what is a semi-tone? The semi-tone is the next note on the piano keyboard. It’s the next official note that follows. Start with any note – to get its octave, we multiply the frequency by 2. There are 12 recognized notes from the first note to the octave of that note. In equal temperament, we multiply a note by the same factor each time to get the next note. What does that mean? It means that to get the next octave, we’re multiplying by the same factor 12 times. OK, but what number multiplied by itself 12 times is 2 - the 12th root of 2. What is the 12th root of 2? On a calculator, you can take the 12th root of 2. It works out to be: 1.05945455 Or approximately 1.059 So, to get to the very next note on the piano, multiply that note’s frequency by 1.059 (approx). Doppler Effect The Doppler Effect - what is it? The Doppler Effect is the phenomenon wherein a sound or light emitter is moving. The person or thing that detects the sound or light will notice or measure a different frequency than that one that was original emitted. Based on the difference between emitted frequency and detected frequency, the speed of the emitter can be calculated. Imagine that you are tapping your finger in a pool of water. It will make concentric circles around your finger. The outermost circular ripple is actually from the first time your finger tapped the water. All of the ripples are the same distance apart – this is actually the wavelength of the water waves you’ve made. Consider the ripples from your finger Now move your finger to the left, as you tap. What does this mean? You are moving your finger to the left while you tap. Since it is moving AND emitting pulses at the same time, the waves are getting closer on the left resulting in a shorter wavelength (or higher frequency) on the left. And it is the complete opposite on the right – the wavelength is longer, because the pulses are getting farther apart. This is the heart of the Doppler Effect. The Doppler Effect is the phenomenon wherein a sound or light emitter is moving. The person or thing that detects the sound or light will notice or measure a different frequency than that one that was original emitted. Now move your finger to the right, as you tap. So, while the sound-source is in motion (to the right): Person on the right measures/detects a higher frequency (and shorter wavelength) than the person on the left (who gets a lower frequency, longer wavelengh). Car horns! Does this work for light (and other EM waves)? Oh my…. Yes! If a light source is moving toward you, you detect/measure a higher frequency this is called a BLUE SHIFT. If a light source is moving away from you, you detect/measure a lower frequency this is called a RED SHIFT. Implications Distant galaxies in the universe are moving away from us, as determined by their red shifts. This indicates that the universe is indeed expanding (first shown by E. Hubble). Implications The 2011 Nobel Prize in Physics went to local physicist Adam Riess (and 2 others) for the discovery of the accelerating expansion of the universe. Awesome stuff! EM Spectrum Recall that waves can be divided into 2 types: Mechanical - which require a medium of some sort And… Electromagnetic - which do NOT require a medium, and travel fastest when there is nothing in their way (ie., in a vacuum) Furthermore, all EM waves travel at the same speed (in a vacuum) - the speed of light: c = 3 x 108 m/s Remember: The only difference from before is that the speed is the speed of light. Otherwise, everything is the same. The EM Spectrum All electromagnetic waves can be represented on a chart, usually going from low frequency (radio waves) to high frequency (gamma rays). You can also think of this as: long wavelength to short wavelength. Let’s take a closer look: Some details... General breakdown of e/m waves from low frequency (and long wavelength) to high frequency (and short wavelength): Radio Microwave IR (infrared) Visible (ROYGBV) UV (ultraviolet) X-rays Gamma rays The Sun emits all forms of EM radiation, Reflection of Light What is reflection of light? Reflection is light "bouncing" off a reflective surface. This obeys a simple law, the Law of reflection! Angle IN equals Angle OUT. But the idea is always the same. Angle of “incidence” (IN) equals angle of “reflection” (OUT). The Details…. The light ray is hitting the upper surface of the concave mirror. At that point of impact, we draw a short line that is tangent to the surface. Imagine that that short line represents the mirror AT THAT POINT. Then, see how that light ray reflects off the surface at that point. The Details…. Now, the light ray is hitting the lower surface of the concave mirror. At this point of impact, we draw another short line that is tangent to the surface. Imagine that that short line represents the mirror AT THAT POINT. Then, see how that light ray reflects off the surface at that point. Note that the ray is reflecting “up” from the bottom. Rays reverse direction from top to bottom. And if you have many rays of light….. In a well-designed concave mirror, the parallel light rays coming in from the left hit the mirror and all reflect back to a point: the focal point. Since light rays converge (meet), we can get images to form when many light rays from all over an object meet. We call this type of image, when light rays converge, a real image. What is a focal point? ? ? ? ? ? ? ? ? ? The focal point is where parallel light rays converge (meet) after hitting the mirror. It is related to the curvature of the mirror. Only curved mirrors have focal points. The distance from the center of the mirror to the focal point is called focal length, f. Images ONLY form at the focal point, if the rays are initially parallel, or the object is very far from the mirror. Usually, images form at other locations. If the object is placed at f, no image forms. If the object is placed within f, no real image forms. When the object is within f, only virtual images form. What is a focal point? ? The focal point is where parallel light rays converge (meet) after hitting the mirror. Curved mirrors? Case 2: Convex. As you might expect, the reflection of rays happen in the opposite direction. They don’t converge (meet), but the rays seem to be coming from back inside the mirror. The focal point is defined as negative, but is still related to the curvature of the mirror. Only images inside the mirror (virtual images) form. More about real images Real images can be projected onto a screen (or just into the air). They are generally upside-down. They can be bigger, smaller, or the same size as the original object, depending on the distance between the mirror and the object. This can be calculated, of course. As the distance between mirror and object (o) decreases, the distance between mirror and image (i) increases. Types of images - Virtual ? ? ? ? ? In some cases, no real images form. However, if an image appears “inside” of the mirror, we refer to it as a virtual image. A virtual image appears to be inside the mirror and can NOT be projected onto a screen. The distance that that the image seems to be from the front surface of the mirror is still called the image distance, but is recorded as negative. Flat/plane mirrors always give virtual images. Think about how bathroom mirrors work - your image seems to be “behind” the mirror. Convex mirrors (like convenience store mirrors) always give virtual images. How tall does a “full-length” mirror need to be? Just about half your height! Law of reflection in action! You can easily see yourself in a plane mirror. But you have to be looking into the mirror, within the left and right edges of the mirror. (This is an overhead view.) YOU. You can see yourself by looking into the mirror while standing within the dotted lines. On the other hand…. Another person can see you anywhere the Law of Reflection allows it. (This is an overhead view.) YOU. This is a MUCH bigger range - they can see you by looking into the mirror from any of the points within the outer arrow regions (or along the dotted line). Exam 3 Review 11. Refraction of Light What is refraction? Refraction is the phenomenon that happens when light (or any EM wave) enters a NEW medium. Remember that light travels at the speed of light (c) in a vacuum - but NOT in any other medium. It gets slowed down by any medium other than a vacuum. Think of this analogy: Imagine going to the beach. You get out of the car and then start running. What happens when you hit sand? You SLOW DOWN - light exhibits similar behavior. Consider how a change in medium affects light: When light passes from one medium to another that is more dense, it slows down. Since the frequency has no reason to change, the wavelength must get smaller. Light waves do the same! Note that the wavelength gets smaller (shorter) as they go through the glass. The light slows since the waves are getting closer together. The reverse happens as they light waves leave the glass - they speed up again. But doesn’t light also bend during refraction? It can! Consider this analogy: Details: Normal line Θ1 Initial angle Θ2 Refracted angle Let’s see this with lasers! ΘI ΘR Note that the refracted angle (ΘI) is smaller than the initial angle (ΘR). Another way to think about it... Another analogy - imagine soldiers marching together. As they enter sand (from concrete) at an angle (not straight through), soldiers reaching sand will slow first. Examples: Initial angle “New” initial angle Refracted angle* Initial angle Refracted angle* New refracted angle** (Dotted lines are “normal” lines - perpendicular to the surface.) *Smaller: new medium is more dense **Larger: new medium is less dense The details... Refracted angle 1 Initial angle Angle onto right wall of prism Refracted angle 2 (back outside) Light hits left side of prism and is refracted toward first normal line. Then it hits right inside wall of prism and is then refracted away from normal line to outside. However, if the light entering the path is “white” light: Things are a bit trickier when the light isn’t just one color, but rather a mixture of colors (like white light). Remember, the index of refraction is a way of expressing how optically dense a medium is. The actual optical density of a medium (other than in a vacuum) depends on the incoming wavelength. Different wavelengths have slightly different speeds in (non-vacuum) mediums. For example, red slows down by a certain amount, but violet slows down by a slightly lower amount - meaning that red light goes through a material (glass, for example) a bit faster than violet light. Red light exits first. However, if the light entering the path is “white” light: In addition, different wavelengths of light are "bent" by slightly different amounts. This is trickier to see, but it causes rainbows and prismatic effects. And refraction is how lenses work! Lenses Refraction in action! What is really happening? When a light ray hits the top of the lens, we draw a normal (perpendicular) line at that point. The ray, upon entering the lens, bends toward the normal line, for all the reasons we have seen before - this creates the first refraction of the beam. Then after it leaves, it refracts again - bending away from the normal line. See how this changes the direction of the light ray? What is really happening? And if the ray enters from the bottom, the exact opposite thing happens. Now you have to imagine this happening millions of times, with many rays hitting the lens. As a result, light rays from an object can be made to form an image after they go through a lens - since they meet again. Also note that the rays have been redirected, so that now they are upside-down compared to their initial direction. With lasers... And with many rays through a convex lens….. Much like with mirrors, the place where parallel rays meet is called the focal point and the distance to it is the focal distance, f. There will be a real image at f. That’s true for parallel rays. If the rays are NOT parallel, which is usually the case, they will meet somewhere else (or maybe not at all). Lasers! Convex lenses are a lot like concave mirrors They have a focal point, where the light rays focus IF THEY ARE INITIALLY PARALLEL - when the object is very far away. If the rays are not initially parallel, which is when the object is not very far away, a real image forms elsewhere (or maybe not at all). Play around with this and see how the image location changes, depending on where the object is: https://phet.colorado.edu/en/simulation/geometric-optics Image formation? Where (or if) a real (or virtual) image forms depends entirely on the object location relative to the lens focal length. Note how changing the object location (on the left) makes the image size and formation location change. How about concave lenses? A light ray enters from the left, hits the concave lens, and is refracted TOWARD a normal line (the dotted line, which is perpendicular to the surface). When the ray leaves the concave lens, it is refracted again. This time it bends away from the second normal line. How about concave lenses? A light ray enters from the left, hits the concave lens, and is refracted TOWARD a normal line (the dotted line, which is perpendicular to the surface). When the ray leaves the concave lens, it is refracted again. This time it bends away from the second normal line. And the process is upside-down for a bottom ray. Image formation….. …. depends on the object location here as well. Lasered! Multiple beams! Optical Instruments Here’s something we all (ideally) have: eyes Common problems: myopia Treated with a concave (-f) lens to “pre-spread out” the light before it hits the lens. Now, with a concave (-f) lens: Common problems: hyperopia Treated with a convex (+f) lens to “pre-converge” the light before it hits the lens. Now, with a convex (+f) lens: Electricity! Part 1 - Electrostatics What is electrical charge? Charge is: - as fundamental to electricity & magnetism as mass is to mechanics - a concept used to quantitatively relate "charged particles" to other such particles, in terms of how they affect each other. Basically, do they attract or repel? If so, with how much force? - represented by letter q (or Q). - based on the charge possessed by the electron and proton. The Fundamental Laws of Electrostatics There are 2 types of electrical charge: positive and negative. Like charges repel. Opposite charges attract. Let’s recall the basics of the atom. So, atoms have 2-3 basic components: A nucleus containing: Protons - particles with positive charge Neutrons - particles with NO charge And surrounding the nucleus in “orbital clouds” are: Electrons - particles with negative charge Atomic number The nucleus of any atom contains protons and (usually) neutrons (which carry no charge). The number of protons in the nucleus is called the atomic number, and it defines the element (H = 1, He = 2, Li = 3). Atoms with different numbers of neutrons are still the same element, but represent different isotopes of the atom. For example: Hydrogen normally has 1 proton in its nucleus. If it also has a neutron, we call it deuterium. If it has 2 neutrons, we call it tritium. All of these are still hydrogen. Ions In a normal balanced (neutral) atom, the number of protons and electrons is the same. However, if electrons are gained or lost, we say that the atom has become charged: - Positively, if electrons are lost Negatively, if electrons are gained We call these charged atoms: ions More atomic details: Each proton is around 2000 times the mass of the electron and makes up (along with any neutrons) the bulk of the atom. This mass difference also explains why the electron orbits the proton, and not the other way around. Protons in the nucleus of an atom should, one would imagine, repel each other greatly. As it happens, the nucleus of an atom is held together by the strong nuclear force (particles which are spring-like, called gluons, keep it together). This also provides what chemists called binding energy, which can be released in nuclear reactions. Electrons determines negative or positive charge. If an object has more electrons than protons - that is, electrons have been added somehow - the net charge is negative (-). If an object has more protons than electrons - that is, if electrons have been removed somehow - the net charge is positive (+). However, we can NOT easily move protons. That usually takes a particle accelerator. Almost always, things are charged positively by REMOVING electrons, leaving a net positive charge. Chemistry deals with charge pretty differently. Rather than saying that the charge of a proton is +1.6 x 10-19 C, and the charge of an electron is -1.6 x 10-19 C, they define the charges in simpler terms: Qproton = +1 Qelectron = -1 Qneutron = 0 And every other charge in an atom is defined in those terms. Neutral matter contains an equal number of protons and electrons. In general, electrons are easy to move around. Being “outside” the tightly-knit nucleus, electrons are significantly easier to move than protons. In fact, nearly all of chemistry is devoted to what happens when electrons are moved around and/or shared - this causes chemical “reactions” between atoms. In the demos, when I used friction to “charge” things, I was moving electrons removing them from one object and adding them to another. This left both objects charged: one negatively (due to the extra electrons), and one positively (because of the missing electrons). A word about scale: It is impossible to accurately represent the relative sizes of particles on simple atomic drawings. The space between the nucleus and the nearest electrons is (relatively) vast. For example, in the image to the right: If the protons and neutrons were “actual size,” the nearest electrons would be several miles away and the entire atom would at least 10 miles in diameter! Atoms are mostly empty space. What about the force between charged objects? How particles interact with each other is governed by a physical relationship called Coulomb's Law: Coulomb’s Law Coulomb’s law tells us that the force (of attraction or repulsion) is given by a physical constant (k) times the product of the charges, divided by their distance of separation squared. The proportionality constant (k) is used to make the units work out to measurable amounts. The most important thing to see in Coulomb’s law is that it is an inverse square law that tells us how charges interact with each other. What’s so important about an inverse square law? This is an INVERSE SQUARE law, meaning that the force gets substantially weaker as the distance grows greater - by the square of the distance apart. - If the distance between the bodies is doubled, the force becomes 1/4 of its original value - If the distance is tripled, the force becomes 1/9 the original amount. And so forth. That is the effect of force depending on 1 over the distance squared. Inverse square laws are common in physics. The graphs always resemble this type of curve: Particles - the big 3 Up to now, you’ve probably thought about 3 main particles associated with atoms: - Protons Neutrons Electrons As it happens, only one of these is fundamental. The other two can actually be broken up further. Fundamental particles: electrons and quarks Electrons are fundamental particles - they cannot be broken up further. Protons and neutrons are composite, however. They CAN be further broken up into fundamental particles called quarks. Protons contain two “up” quarks and one “down” quark. Neutrons contain two “down” quarks and one “up” quark. Voltage, Current and Circuits! Voltage is a way of measuring electric potential. The definition of Voltage: - Amount of available energy (in joules) per coulomb of charge. V = Energy / charge = E / Q There is a new unit for voltage: the joule/coulomb, called the volt (V). What can cause voltage? Galvani is credited with the discovery of “bioelectricity” (or electrophysiology). Upon extensive study by Volta, it was determined that 2 different metals and an acidic solution would create an electric potential difference later called a voltage. The chemical reaction with acid causes one electrode (Zn) to be negative and the other (Cu) to be positive. What is happening in the wet cell? The acid is reacting with the metals. Electrons are traveling from one to the other. What is voltage good for? Voltage is good for moving charges (electrons). Let’s find out what it takes to make charges move. Take a battery, bulb, and piece of wire. How can we make the light bulb light? What works? Battery has 2 critical parts: + and Bulb has 2 conductive parts: base & barrel A complete “path” for charge has to happen. And in a circuit, electrons “flow”. How fast does charge travel? Current! Current (I) - the rate at which positive charge "flows" I = Q/t The unit is the coulomb per second, defined as an ampere (A). Just as one coulomb is a huge amount of charge (nearly 6.3 billion billion protons), one ampere (or amp) is a tremendous amount of current - more than enough to kill a person. In fact, you can feel as little as 0.01 A. Typical currents in a circuit are on the order of mA (milliamperes). So, what exactly IS a circuit? An electrical circuit can be thought of as a complete "loop" through which charge can travel. Therefore, it actually has to be physically complete - there can be no openings. The current actually has to have a complete path to take. We use special (internationally recognized) pictures called schematics to represent the circuit. This circuit represents a battery, wire, and something called a resistor (the jagged line). Battery Wire Wire Resistor Other electrical symbols: Resistance, R We also quantify how much a device reduces current. This is called resistance. Resistance (R) - the ratio of voltage applied to an electrical device to the current that results through the device. Alternately: the amount by which the voltage is "dropped" per ampere of current. R = V/I We have a new unit for resistance: volt/ampere, which is called an ohm (Ω). Voltage provides “push” for current through the circuit. V = Voltage (in V) I = Current (in A) R = Resistance (in Ω) Ohm’s Law (in equation form): So, voltage equals current times resistance. We could also say that: current equals voltage divided by resistance Or: resistance equals voltage divided by current (which we have seen already) Working with Ohm’s law, mathematically: Series and Parallel Circuits The Building Blocks of Complex Circuits Types of circuits: Series and Parallel Types of circuits: Series and Parallel SERIES: PARALLEL: Equal brightness bulbs, but dimmer than 1 bulb alone Voltage is the same over both bulbs, and is the same as the battery voltage Voltage is distributed between the bulbs Current is the same in each Remove 1 bulb and both go out - how many holidays lights work Bulbs are of equal brightness, and are just as bright as 1 bulb alone Remove 1 bulb and the other stays lit at the same brightness Parallel circuits generally draw more current (more $) Houses (outlets) are wired in parallel Bulb brightness comparison Series: 1 bulb alone is brighter than 2 (or more) in series: the total resistance of the circuit is greater, so the current is less. Parallel: 1 bulb alone has the same brightness as 2 (or more) bulbs. Bulbs have the same brightness and therefore, the same current. Furthermore... Two identical bulbs in series will be dimmer than the same bulbs in parallel. Again, the total resistance is greater (in series), making the current less. Magnetism! How was magnetism “discovered?” There are naturally occurring magnetic minerals - a very common one is called magnetite (Fe3 O4), also known as iron oxide. Thousands of years ago, folks discovered that little slivers of this mineral, when floated on water (thanks to surface tension), would always align in a particular line. This line was very close to the “known” North-South axis. More about North To find True/Geographic north, it is easiest to find Polaris (the current north star). Polaris is actually not all that bright, though in the top 50 brightest stars in the night sky. You need to find the Big Dipper (asterism at the rear end of Ursa Major). Follow the “pointer stars” at the end of the dipper. These visually lead you to Polaris. You can find North pretty easily at night: Celestial North Polaris is close to, but not quite at, Celestial North. Some more details... ? ? ? ? ? Magnetic north on the Earth is near Ellesmere Island in Northern Canada, several hundred miles from true (geographic) North (the North Pole). It is moving toward Russia at several miles per year. Like poles repel Opposite poles attract Each magnet must have at least one North and one South pole (though they may have more than one of each). There is NO such thing as a magnetic monopole. Magnetic fields are real, but the lines are imaginary - Field lines indicate the direction that a compass needle would take in the vicinity of the magnetic field. Some more details... ? ? Similar to the case of charge, magnetic poles are divided into North and South poles. A North magnetic pole on a compass is one that points toward the Earth's magnetic north pole. This means that the Earth's magnetic north is ACTUALLY A SOUTH POLE (magnetically speaking). How do we get magnetism? Magnetic fields are related to electrons spins. Electrons act like tiny magnetic spinning tops. There is a tiny magnetic element associated with each electron spin. If the spins align, more or less, the object is said to be somewhat magnetic. More spin alignments (domains) means more magnetism. Materials that do this easily are generally said to be ferromagnetic. As it happens, metals do this best (free electrons). In the core of the Earth, molten metal convects (rises and falls), giving the Earth a good magnetic field – measurable from the surface and beyond. Several planets have magnetic fields. Electromagnetism: Enter H. C. Oersted! In general, the motion of charges leads to magnetic fields. If you have charge traveling through a wire, electrons can be thought of as moving together – this causes a magnetic field, also known as electromagnetism. The magnetic field caused by a current passing through a wire is often small, but if you coil the wire upon itself, the magnetic fields “add up”. Several hundred turns of wire (with current running through it) can produced quite a strong electromagnet. Electromagnets and Telegraphs Since current can cause magnetism, electromagnets were a natural device to invent soon after its discovery. Electromagnets and Telegraphs Since current can cause magnetism, electromagnets were a natural device to invent soon after its discovery. And not long after that, telegraphs were invented (1830s-1840s, by Morse and others - this was nearly instantaneous communication! The Motor Principle If you watch the animation carefully, you’ll see that there is a split in the copper-colored ring: this split-ring is called a commutator, and it causes the current to switch directions every half a rotation (or more frequently, if there are more splits). This means that half of the time, the coil is repelled and half of the time it is attracted. Thus, it never stops. Another electromagnetic device - the speaker Attached to the speaker cone is a coil. A current comes into the coil - a current that is changing with the incoming music. Since the current changes repeatedly, the magnetic field around the speaker coil also changes. It attracts and repels the permanent magnet in a fashion proportional to the incoming music. Electromagnetic Induction Current causes magnetism – this was shown in the early 19th century by Hans Oersted. As it happens, the reverse is also true – magnetism can cause current, as Michael Faraday discovered (around 1831). It’s about relative motion between coil and magnet. The Generator Principle This is the basis of modern power production. 1. What does this represent? Ω volt, the unit of voltage ohm, the unit for resistance watt, the unit for power farad, the unit of capacitance 2. In this picture, the light bulbs are connected: in series O in parallel in a combination circuit O in a wheatstone circuit 3. This is a symbol for: resistor capacitor battery diode switch 4. Which of these things can NOT be broken up further? 1 point proton neutron electron atom all of these are unbreakable 1 point 5. Consider this circuit. If the first (top) bulb is unscrewed from its socket, what happens to the rest of the bulbs? (The red block is a battery.) they get brighter they go out they get dimmer, but don't go out O they flash on and off O Option 5 1 point 6. Lithium is element number 3 on the Periodic Table. What does this number represent? the number of protons in the nucleus of a Lithium atom the number of neutrons in the nucleus of a Lithium atom the historical order in which it was discovered O the number of quarks in a Lithium atom O none of these 7. Which light bulb will light up? 4 first one second one O third one O all of them O none of them 8. Following the 2 "pointer stars" (Merak, Dubhe) of the Big Dipper will help 1 point you find: Merak Dubhe Big Dipper Geographic south O Arcturus Sirius (brightest star in the night sky) Polaris (North Star) the Milky Way 1 point 9. Which circuit will have the brighter bulbs? Assume that the bulbs are identical. (The red block is a battery.) The one on the left The one on the right O They will be of equal brightness 10. What will happen if the first bulb is unscrewed/removed? (Again, the red 1 point box is a battery.) The other two will get brighter The other two will stay at the same brightness The other two will go out as well The second one will go out, but not the third one O The third one will go out, but not the second one 11. Which statement is true regarding Magnetic North (on Earth)? 1 point O It is located at the geographic North Pole O It is located at the geographic South Pole O It is actually a magnetic south pole O It doesn't exist O It is located in Alaska 1 point 12. Most elements have several isotopes. Each isotope has a different number of: neutrons protons electrons O neutrinos 13. Consider a 12-V battery connected directly to a 6-ohm bulb. How much 1 point current (in appropriate units) flows through the bulb? O 1/2 O 2 72 18 O 6 14. What is the appropriate unit for current? ampere (or amp) watt volt ohm O joule 15. The image that forms on the retina of your eye is: O upside-down and virtual O upside-down and real O right-side up and virtual O right-side up and real 16. Is this an expected set of light paths for this type of lens? 1 point 11111 O Yes, this is typical for this type of lens. O No, this is not possible for this type of lens. O There is not enough information - the shape does not affect the light path 17. What exactly is the focal point of a lens? 1 point the place where light rays always cross the place where light rays never cross the place where light rays cross only if they are originally parallel to each other O the place where the image always forms O the 1st and the 4th options are both correct 18. What type of lens do we have in our eyes? 1 point concave convex no lens - only a retina no lens - only an opening (iris) 1 point 19. If a coil of wire is connected to a battery and a compass needle is nearby, what will happen? the compass needle will spin repeatedly nothing signficant will happen the compass needle will line up in a specific direction O the coil will spin around and around 1 point 20. What is the common theme between motors, telegraphs, and speakers? electromagnetism electromagnetic induction electrostatic charging series and parallel circuits 21. What makes an atom neutral (with no net charge)? more protons than electrons equal number of protons and neutrons equal number of protons and electrons more electrons than protons O equal number of electrons and neutrons 22. Electrical current is really all about the motion of what particle in a circuit? protons quarks O electrons O neutrons O Option 5 1 point 23. A magnet sits still inside a coil of wire. Will this cause electrical current to travel through the coil? N S O Yes Ο Νο 24. What is the voltage of AA, AAA, C and D batteries? 1 point O 3 v O 1.5 V 9V O 12 V O They are all different. 25. Consider two circuits with identical bulbs and batteries. One circuit has 1 point 2 bulbs in parallel, and one circuit has 3 bulbs in parallel. Which will "kill" the battery sooner? 2 bulbs 3 bulbs same time for each O We have no way to predict this. 26. Which side is more optically dense? 1 point normal light of incidence mcdium 1 interface 0 medium 2 light of refraction top O bottom they are the same Othere is not enough information to tell 27. What do these symbols represent? 1 point capacitor diode switch resistor transformer 28. The rate at which charge travels (in a circuit) is called: 1 point O voltage O current O resistance O power 29. On a correctly polarized compass, the red (or darker) end of the needle 1 point is: O North South Neither North nor South - North and South are in the middle of the needle O There is no standard for a compass. 30. Magnetite is: 1 point a plastic material that has been magnetized a naturally occuring magnetic mineral an electromagnetic coil another name for electron 31. What has a greater total resistance, two bulbs in series or the same two 1 point bulbs in parallel? series O parallel O they have the same total resistance 1 point 32. Two charges are separated by a small distance and experience a force of attraction. What will happen to the force if the distance between them is doubled? it will become 1/2 as much O it will become 1/4 as much it will become twice as great it will become 4 times as great O it will switch from attractive to repulsive 33. Opposite charges: 1 point always attract always repel O always orbit around each other 34. What device operates via electromagnetic induction? 1 point O battery O speaker O light bulb O generator resistor 35. What exactly causes refraction of light? 1 point hitting a mirror hitting electrons change of medium (such as going from air to water) O light going through small openings such as tiny slits Submit