Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

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5 { GRAVITATION Last Updated: July 16, 2012 Problem List 5.1 Total mass of a shell 5.2 Tunnel through the moon 5.3 Gravitational eld above the center of a thin hoop 5.4 Gravitational force near a metal-cored planet surrounded by a gaseous cloud 5.5 Sphere with linearly increasing mass density 5.6 Jumping o Vesta 5.7 Gravitational force between two massive rods 5.8 Potential energy { Check your answer! 5.9 Ways of solving gravitational problems 5.10 Rod with linearly increasing mass density 5.11 Sphere with constant internal gravitational eld 5.12 Throwing a rock o the moon These problems are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Un- ported License. Please share and/or modify. Back to Problem List 1 5 { GRAVITATION Last Updated: July 16, 2012 5.1 Total mass of a shell Given: Marino { Fall 2011 Consider a spherical shell that extends from r = R to r = 2R with a non-uniform density (r) = 0r. What is the total mass of the shell? Back to Problem List 2 5 { GRAVITATION Last Updated: July 16, 2012 5.2 Tunnel through the moon Given: Marino { Fall 2011 Imagine that NASA digs a straight tunnel through the center of the moon (see gure) to access the Moon’s 3He deposits. An astronaut places a rock in the tunnel at the surface of the moon, and releases it (from rest). Show that the rock obeys the force law for a mass connected to a spring. What is the spring constant? Find the oscillation period for this motion if you assume that Moon has a mass of 7.351022 kg and a radius of 1.74106 m. Assume the moon’s density is uniform throughout its volume, and ignore the moon’s rotation. Given: Pollock { Spring 2011 Imagine (in a parallel universe of unlimited budgets) that NASA digs a straight tunnel through the center of the moon (see gure). A robot place a rock in the tunnel at position r = r0 from the center of the moon, and releases it (from rest). Use Newton’s second law to write the equation of motion of the rock and solve for r(t). Explain in words the rock’s motion. Does the rock return to its initial position at any later time? If so, how long does it takes to return to it? (Give a formula, and a number.) Assume the moon’s density is uniform throughout its volume, and ignore the moon’s rotation. Given: Pollock { Spring 2012 Now lets consider our (real) planet Earth, with total mass M and radius R which we will approximate as a uniform mass density, (r) = 0. (a) Neglecting rotational and frictional e ects, show that a particle dropped into a hole drilled straight through the center of the earth all the way to the far side will oscillate between the two endpoints. (Hint: you will need to set up, and solve, an ODE for the motion) (b) Find the period of the oscillation of this motion. Get a number (in minutes) as a nal result, using data for the earth’s size and mass. (How does that compare to ying to Perth and back?!) Extra Credit: OK, even with unlimited budgets, digging a tunnel through the center of the earth is preposterous. But, suppose instead that the tunnel is a straight-line \chord” through the earth, say directly from New York to Los Angeles. Show that your nal answer for the time taken does not depend on the location of that chord! This is rather remarkable – look again at the time for a free-fall trip (no energy required, except perhaps to compensate for friction) How long would that trip take? Could this work?! Back to Problem List 3 5 { GRAVITATION Last Updated: July 16, 2012 5.3 Gravitational eld above the center of a thin hoop Given: Pollock { Spring 2011, Spring 2012 Consider a very (in nitesimally!) thin but massive loop, radius R (total mass M), centered around the origin, sitting in the x-y plane. Assume it has a uniform linear mass density  (which has units of kg/m) all around it. (So, it’s like a skinny donut that is mostly hole, centered around the z-axis) (a) What is  in terms of M and R? What is the direction of the gravitational eld generated by this mass distribution at a point in space a distance z above the center of the donut, i.e. at (0; 0; z) Explain your reasoning for the direction carefully, try not to simply \wave your hands.” (The answer is extremely intuitive, but can you justify that it is correct?) (b) Compute the gravitational eld, ~g, at the point (0; 0; z) by directly integrating Newton’s law of gravity, summing over all in nitesimal \chunks” of mass along the loop. (c) Compute the gravitational potential at the point (0; 0; z) by directly integrating ?Gdm=r, sum- ming over all in nitesimal \chunks” dm along the loop. Then, take the z-component of the gradient of this potential to check that you agree with your result from the previous part. (d) In the two separate limits z << R and z >> R, Taylor expand your g- eld (in the z-direction)out only to the rst non-zero term, and convince us that both limits make good physical sense. (e) Can you use Gauss’ law to gure out the gravitational potential at the point (0; 0; z)? (If so, do it and check your previous answers. If not, why not?) Extra credit: If you place a small mass a small distance z away from the center, use your Taylor limit for z << R above to write a simple ODE for the equation of motion. Solve it, and discuss the motion Back to Problem List 4 5 { GRAVITATION Last Updated: July 16, 2012 5.4 Gravitational force near a metal-cored planet surrounded by a gaseous cloud Given: Pollock { Spring 2011 Jupiter is composed of a dense spherical core (of liquid metallic hydrogen!) of radius Rc. It is sur- rounded by a spherical cloud of gaseous hydrogen of radius Rg, where Rg > Rc. Let’s assume that the core is of uniform density c and the gaseous cloud is also of uniform density g. What is the gravitational force on an object of mass m that is located at a radius r from the center of Jupiter? Note that you must consider the cases where the object is inside the core, within the gas layer, and outside of the planet. Back to Problem List 5 5 { GRAVITATION Last Updated: July 16, 2012 5.5 Sphere with linearly increasing mass density Given: Pollock { Spring 2011 A planet of mass M and radius R has a nonuniform density that varies with r, the distance from the center according to  = Ar for 0  r  R. (a) What is the constant A in terms of M and R? Does this density pro le strike you as physically plausible, or is just designed as a mathematical exercise? (Brie y, explain) (b) Determine the gravitational force on a satellite of mass m orbiting this planet. In words, please outline the method you plan to use for your solution. (Use the easiest method you can come up with!) In your calculation, you will need to argue that the magnitude of ~g(r; ; ) depends only on r. Be very explicit about this – how do you know that it doesn’t, in fact, depend on  or ? (c) Determine the gravitational force felt by a rock of mass m inside the planet, located at radius r < R. (If the method you use is di erent than in part b, explain why you switched. If not, just proceed!) Explicitly check your result for this part by considering the limits r ! 0 and r ! R. Back to Problem List 6 5 { GRAVITATION Last Updated: July 16, 2012 5.6 Jumping o Vesta Given: Pollock { Spring 2011 You are stranded on the surface of the asteroid Vesta. If the mass of the asteroid is M and its radius is R, how fast would you have to jump o its surface to be able to escape from its gravitational eld? (Your estimate should be based on parameters that characterize the asteroid, not parameters that describe your jumping ability.) Given your formula, look up the approximate mass and radius of the asteroid Vesta 3 and determine a numerical value of the escape velocity. Could you escape in this way? (Brie y, explain) If so, roughly how big in radius is the maximum the asteroid could be, for you to still escape this way? If not, estimate how much smaller an asteroid you would need, to escape from it in this way? Figure 1: Back to Problem List 7 5 { GRAVITATION Last Updated: July 16, 2012 5.7 Gravitational force between two massive rods Given: Pollock { Spring 2011 Consider two identical uniform rods of length L and mass m lying along the same line and having their closest points separated by a distance d as shown in the gure (a) Calculate the mutual force between these rods, both its direction and magnitude. (b) Now do several checks. First, make sure the units worked out (!) The, nd the magnitude of the force in the limit L ! 0. What do you expect? Brie y, discuss. Lastly, nd the magnitude of the force in the limit d ! 1 ? Again, is it what you expect? Brie y, discuss. Figure 2: Given: Pollock { Spring 2012 Determining the gravitational force between two rods: (a) Consider a thin, uniform rod of mass m and length L (and negligible other dimensions) lying on the x axis (from x=-L to 0), as shown in g 1a. Derive a formula for the gravitational eld \g" at any arbitrary point x to the right of the origin (but still on the x-axis!) due to this rod. (b) Now suppose a second rod of length L and mass m sits on the x axis as shown in g 1b, with the left edge a distance \d" away. Calculate the mutual gravitational force between these rods. (c) Let's do some checks! Show that the units work out in parts a and b. Find the magnitude of the force in part a, in the limit x >> L: What do you expect? Brie y, discuss! Finally, verify that your answer to part b gives what you expect in the limit d >> L. ( Hint: This is a bit harder! You need to consistently expand everything to second order, not just rst, because of some interesting cancellations) Fig 1a Fig 1b L m +x x=0 L x=0 x=d m Fig 1a Fig 1b L m +x x=0 L +x x=0 x=d L m m Back to Problem List 8 5 { GRAVITATION Last Updated: July 16, 2012 5.8 Potential energy { Check your answer! Given: Pollock { Spring 2011 On the last exam, we had a problem with a at ring, uniform mass per unit area of , inner radius of R, outer radius of 2R. A satellite (mass m) sat a distance z above the center of the ring. We asked for the gravitational potential energy, and the answer was U(z) = ?2Gm( p 4R2 + z2 ? p R2 + z2) (1) (a) If you are far from the disk (on the z axis), what do you expect for the formula for U(z)? (Don’t say \0″ – as usual, we want the functional form of U(z) as you move far away. Also, explicitly state what we mean by \far away”. (Please don’t compare something with units to something without units!) (b) Show explicitly that the formula above does indeed give precisely the functional dependence you expect. Back to Problem List 9 5 { GRAVITATION Last Updated: July 16, 2012 5.9 Ways of solving gravitational problems Given: Pollock { Spring 2011, Spring 2012 Infinite cylinder ρ=cr x z (a) Half-infinite line mass, uniform linear mass density, λ x (b) R z  P Figure 3: (a) An in nite cylinder of radius R centered on the z-axis, with non-uniform volume mass density  = cr, where r is the radius in cylindrical coordinates. (b) A half-in nite line of mass on the x-axis extending from x = 0 to x = +1, with uniform linear mass density . There are two general methods we use to solve gravitational problems (i.e. nd ~g given some distribution of mass). (a) Describe these two methods. We claim one of these methods is easiest to solve for ~g of mass distribution (a) above, and the other method is easiest to solve for ~g of the mass distribution (b) above. Which method goes with which mass distribution? Please justify your answer. (b) Find ~g of the mass distribution (a) above for any arbitrary point outside the cylinder. (c) Find the x component of the gravitational acceleration, gx, generated by the mass distribution labeled (b) above, at a point P a given distance z up the positive z-axis (as shown). Back to Problem List 10 5 { GRAVITATION Last Updated: July 16, 2012 5.10 Rod with linearly increasing mass density Given: Pollock { Spring 2012 Consider a very (in nitesimally!) thin but massive rod, length L (total mass M), centered around the origin, sitting along the x-axis. (So the left end is at (-L/2, 0,0) and the right end is at (+L/2,0,0) Assume the mass density  (which has units of kg/m)is not uniform, but instead varies linearly with distance from the origin, (x) = cjxj. (a) What is that constant \c” in terms of M and L? What is the direction of the gravitational eld generated by this mass distribution at a point in space a distance z above the center of the rod, i.e. at (0; 0; z) Explain your reasoning for the direction carefully, try not to simply \wave your hands.” (The answer is extremely intuitive, but can you justify that it is correct?) (b) Compute the gravitational eld, ~g, at the point (0; 0; z) by directly integrating Newton’s law of gravity, summing over all in nitesimal \chunks” of mass along the rod. (c) Compute the gravitational potential at the point (0; 0; z) by directly integrating ?Gdm=r, sum- ming over all in nitesimal \chunks” dm along the rod. Then, take the z-component of the gradient of this potential to check that you agree with your result from the previous part. (d) In the limit of large z what do you expect for the functional form for gravitational potential? (Hint: Don’t just say it goes to zero! It’s a rod of mass M, when you’re far away what does it look like? How does it go to zero?) What does \large z” mean here? Use the binomial (or Taylor) expansion to verify that your formula does indeed give exactly what you expect. (Hint: you cannot Taylor expand in something BIG, you have to Taylor expand in something small.) (e) Can you use Gauss’ law to gure out the gravitational potential at the point (0; 0; z)? (If so, do it and check your previous answers. If not, why not?) Back to Problem List 11 5 { GRAVITATION Last Updated: July 16, 2012 5.11 Sphere with constant internal gravitational eld Given: Pollock { Spring 2012 (a) Imagine a planet of total mass M and radius R which has a nonuniform mass density that varies just with r, the distance from the center. For this (admittedly very unusual!) planet, suppose the gravitational eld strength inside the planet turns out to be independent of the radial distance within the sphere. Find the function describing the mass density  = (r) of this planet. (Your nal answer should be written in terms of the given constants.) (b) Now, determine the gravitational force on a satellite of mass m orbiting this planet at distance r > R. (Use the easiest method you can come up with!) Explain your work in words as well as formulas. For instance, in your calculation, you will need to argue that the magnitude of ~g(r; ; ) depends only on r. Be explicit about this – how do you know that it doesn’t, in fact, depend on  or ? (c) As a nal check, explicitly show that your solutions inside and outside the planet (parts a and b) are consistent when r = R. Please also comment on whether this density pro le strikes you as physically plausible, or is it just designed as a mathematical exercise? Defend your reasoning. Back to Problem List 12 5 { GRAVITATION Last Updated: July 16, 2012 5.12 Throwing a rock o the moon Given: Pollock { Spring 2012 Assuming that asteroids have roughly the same mass density as the moon, make an estimate of the largest asteroid that an astronaut could be standing on, and still have a chance of throwing a small object (with their arms, no machinery!) so that it completely escapes the asteroid’s gravitational eld. (This minimum speed is called \escape velocity”) Is the size you computed typical for asteroids in our solar system? Back to Problem List 13

5 { GRAVITATION Last Updated: July 16, 2012 Problem List 5.1 Total mass of a shell 5.2 Tunnel through the moon 5.3 Gravitational eld above the center of a thin hoop 5.4 Gravitational force near a metal-cored planet surrounded by a gaseous cloud 5.5 Sphere with linearly increasing mass density 5.6 Jumping o Vesta 5.7 Gravitational force between two massive rods 5.8 Potential energy { Check your answer! 5.9 Ways of solving gravitational problems 5.10 Rod with linearly increasing mass density 5.11 Sphere with constant internal gravitational eld 5.12 Throwing a rock o the moon These problems are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Un- ported License. Please share and/or modify. Back to Problem List 1 5 { GRAVITATION Last Updated: July 16, 2012 5.1 Total mass of a shell Given: Marino { Fall 2011 Consider a spherical shell that extends from r = R to r = 2R with a non-uniform density (r) = 0r. What is the total mass of the shell? Back to Problem List 2 5 { GRAVITATION Last Updated: July 16, 2012 5.2 Tunnel through the moon Given: Marino { Fall 2011 Imagine that NASA digs a straight tunnel through the center of the moon (see gure) to access the Moon’s 3He deposits. An astronaut places a rock in the tunnel at the surface of the moon, and releases it (from rest). Show that the rock obeys the force law for a mass connected to a spring. What is the spring constant? Find the oscillation period for this motion if you assume that Moon has a mass of 7.351022 kg and a radius of 1.74106 m. Assume the moon’s density is uniform throughout its volume, and ignore the moon’s rotation. Given: Pollock { Spring 2011 Imagine (in a parallel universe of unlimited budgets) that NASA digs a straight tunnel through the center of the moon (see gure). A robot place a rock in the tunnel at position r = r0 from the center of the moon, and releases it (from rest). Use Newton’s second law to write the equation of motion of the rock and solve for r(t). Explain in words the rock’s motion. Does the rock return to its initial position at any later time? If so, how long does it takes to return to it? (Give a formula, and a number.) Assume the moon’s density is uniform throughout its volume, and ignore the moon’s rotation. Given: Pollock { Spring 2012 Now lets consider our (real) planet Earth, with total mass M and radius R which we will approximate as a uniform mass density, (r) = 0. (a) Neglecting rotational and frictional e ects, show that a particle dropped into a hole drilled straight through the center of the earth all the way to the far side will oscillate between the two endpoints. (Hint: you will need to set up, and solve, an ODE for the motion) (b) Find the period of the oscillation of this motion. Get a number (in minutes) as a nal result, using data for the earth’s size and mass. (How does that compare to ying to Perth and back?!) Extra Credit: OK, even with unlimited budgets, digging a tunnel through the center of the earth is preposterous. But, suppose instead that the tunnel is a straight-line \chord” through the earth, say directly from New York to Los Angeles. Show that your nal answer for the time taken does not depend on the location of that chord! This is rather remarkable – look again at the time for a free-fall trip (no energy required, except perhaps to compensate for friction) How long would that trip take? Could this work?! Back to Problem List 3 5 { GRAVITATION Last Updated: July 16, 2012 5.3 Gravitational eld above the center of a thin hoop Given: Pollock { Spring 2011, Spring 2012 Consider a very (in nitesimally!) thin but massive loop, radius R (total mass M), centered around the origin, sitting in the x-y plane. Assume it has a uniform linear mass density  (which has units of kg/m) all around it. (So, it’s like a skinny donut that is mostly hole, centered around the z-axis) (a) What is  in terms of M and R? What is the direction of the gravitational eld generated by this mass distribution at a point in space a distance z above the center of the donut, i.e. at (0; 0; z) Explain your reasoning for the direction carefully, try not to simply \wave your hands.” (The answer is extremely intuitive, but can you justify that it is correct?) (b) Compute the gravitational eld, ~g, at the point (0; 0; z) by directly integrating Newton’s law of gravity, summing over all in nitesimal \chunks” of mass along the loop. (c) Compute the gravitational potential at the point (0; 0; z) by directly integrating ?Gdm=r, sum- ming over all in nitesimal \chunks” dm along the loop. Then, take the z-component of the gradient of this potential to check that you agree with your result from the previous part. (d) In the two separate limits z << R and z >> R, Taylor expand your g- eld (in the z-direction)out only to the rst non-zero term, and convince us that both limits make good physical sense. (e) Can you use Gauss’ law to gure out the gravitational potential at the point (0; 0; z)? (If so, do it and check your previous answers. If not, why not?) Extra credit: If you place a small mass a small distance z away from the center, use your Taylor limit for z << R above to write a simple ODE for the equation of motion. Solve it, and discuss the motion Back to Problem List 4 5 { GRAVITATION Last Updated: July 16, 2012 5.4 Gravitational force near a metal-cored planet surrounded by a gaseous cloud Given: Pollock { Spring 2011 Jupiter is composed of a dense spherical core (of liquid metallic hydrogen!) of radius Rc. It is sur- rounded by a spherical cloud of gaseous hydrogen of radius Rg, where Rg > Rc. Let’s assume that the core is of uniform density c and the gaseous cloud is also of uniform density g. What is the gravitational force on an object of mass m that is located at a radius r from the center of Jupiter? Note that you must consider the cases where the object is inside the core, within the gas layer, and outside of the planet. Back to Problem List 5 5 { GRAVITATION Last Updated: July 16, 2012 5.5 Sphere with linearly increasing mass density Given: Pollock { Spring 2011 A planet of mass M and radius R has a nonuniform density that varies with r, the distance from the center according to  = Ar for 0  r  R. (a) What is the constant A in terms of M and R? Does this density pro le strike you as physically plausible, or is just designed as a mathematical exercise? (Brie y, explain) (b) Determine the gravitational force on a satellite of mass m orbiting this planet. In words, please outline the method you plan to use for your solution. (Use the easiest method you can come up with!) In your calculation, you will need to argue that the magnitude of ~g(r; ; ) depends only on r. Be very explicit about this – how do you know that it doesn’t, in fact, depend on  or ? (c) Determine the gravitational force felt by a rock of mass m inside the planet, located at radius r < R. (If the method you use is di erent than in part b, explain why you switched. If not, just proceed!) Explicitly check your result for this part by considering the limits r ! 0 and r ! R. Back to Problem List 6 5 { GRAVITATION Last Updated: July 16, 2012 5.6 Jumping o Vesta Given: Pollock { Spring 2011 You are stranded on the surface of the asteroid Vesta. If the mass of the asteroid is M and its radius is R, how fast would you have to jump o its surface to be able to escape from its gravitational eld? (Your estimate should be based on parameters that characterize the asteroid, not parameters that describe your jumping ability.) Given your formula, look up the approximate mass and radius of the asteroid Vesta 3 and determine a numerical value of the escape velocity. Could you escape in this way? (Brie y, explain) If so, roughly how big in radius is the maximum the asteroid could be, for you to still escape this way? If not, estimate how much smaller an asteroid you would need, to escape from it in this way? Figure 1: Back to Problem List 7 5 { GRAVITATION Last Updated: July 16, 2012 5.7 Gravitational force between two massive rods Given: Pollock { Spring 2011 Consider two identical uniform rods of length L and mass m lying along the same line and having their closest points separated by a distance d as shown in the gure (a) Calculate the mutual force between these rods, both its direction and magnitude. (b) Now do several checks. First, make sure the units worked out (!) The, nd the magnitude of the force in the limit L ! 0. What do you expect? Brie y, discuss. Lastly, nd the magnitude of the force in the limit d ! 1 ? Again, is it what you expect? Brie y, discuss. Figure 2: Given: Pollock { Spring 2012 Determining the gravitational force between two rods: (a) Consider a thin, uniform rod of mass m and length L (and negligible other dimensions) lying on the x axis (from x=-L to 0), as shown in g 1a. Derive a formula for the gravitational eld \g" at any arbitrary point x to the right of the origin (but still on the x-axis!) due to this rod. (b) Now suppose a second rod of length L and mass m sits on the x axis as shown in g 1b, with the left edge a distance \d" away. Calculate the mutual gravitational force between these rods. (c) Let's do some checks! Show that the units work out in parts a and b. Find the magnitude of the force in part a, in the limit x >> L: What do you expect? Brie y, discuss! Finally, verify that your answer to part b gives what you expect in the limit d >> L. ( Hint: This is a bit harder! You need to consistently expand everything to second order, not just rst, because of some interesting cancellations) Fig 1a Fig 1b L m +x x=0 L x=0 x=d m Fig 1a Fig 1b L m +x x=0 L +x x=0 x=d L m m Back to Problem List 8 5 { GRAVITATION Last Updated: July 16, 2012 5.8 Potential energy { Check your answer! Given: Pollock { Spring 2011 On the last exam, we had a problem with a at ring, uniform mass per unit area of , inner radius of R, outer radius of 2R. A satellite (mass m) sat a distance z above the center of the ring. We asked for the gravitational potential energy, and the answer was U(z) = ?2Gm( p 4R2 + z2 ? p R2 + z2) (1) (a) If you are far from the disk (on the z axis), what do you expect for the formula for U(z)? (Don’t say \0″ – as usual, we want the functional form of U(z) as you move far away. Also, explicitly state what we mean by \far away”. (Please don’t compare something with units to something without units!) (b) Show explicitly that the formula above does indeed give precisely the functional dependence you expect. Back to Problem List 9 5 { GRAVITATION Last Updated: July 16, 2012 5.9 Ways of solving gravitational problems Given: Pollock { Spring 2011, Spring 2012 Infinite cylinder ρ=cr x z (a) Half-infinite line mass, uniform linear mass density, λ x (b) R z  P Figure 3: (a) An in nite cylinder of radius R centered on the z-axis, with non-uniform volume mass density  = cr, where r is the radius in cylindrical coordinates. (b) A half-in nite line of mass on the x-axis extending from x = 0 to x = +1, with uniform linear mass density . There are two general methods we use to solve gravitational problems (i.e. nd ~g given some distribution of mass). (a) Describe these two methods. We claim one of these methods is easiest to solve for ~g of mass distribution (a) above, and the other method is easiest to solve for ~g of the mass distribution (b) above. Which method goes with which mass distribution? Please justify your answer. (b) Find ~g of the mass distribution (a) above for any arbitrary point outside the cylinder. (c) Find the x component of the gravitational acceleration, gx, generated by the mass distribution labeled (b) above, at a point P a given distance z up the positive z-axis (as shown). Back to Problem List 10 5 { GRAVITATION Last Updated: July 16, 2012 5.10 Rod with linearly increasing mass density Given: Pollock { Spring 2012 Consider a very (in nitesimally!) thin but massive rod, length L (total mass M), centered around the origin, sitting along the x-axis. (So the left end is at (-L/2, 0,0) and the right end is at (+L/2,0,0) Assume the mass density  (which has units of kg/m)is not uniform, but instead varies linearly with distance from the origin, (x) = cjxj. (a) What is that constant \c” in terms of M and L? What is the direction of the gravitational eld generated by this mass distribution at a point in space a distance z above the center of the rod, i.e. at (0; 0; z) Explain your reasoning for the direction carefully, try not to simply \wave your hands.” (The answer is extremely intuitive, but can you justify that it is correct?) (b) Compute the gravitational eld, ~g, at the point (0; 0; z) by directly integrating Newton’s law of gravity, summing over all in nitesimal \chunks” of mass along the rod. (c) Compute the gravitational potential at the point (0; 0; z) by directly integrating ?Gdm=r, sum- ming over all in nitesimal \chunks” dm along the rod. Then, take the z-component of the gradient of this potential to check that you agree with your result from the previous part. (d) In the limit of large z what do you expect for the functional form for gravitational potential? (Hint: Don’t just say it goes to zero! It’s a rod of mass M, when you’re far away what does it look like? How does it go to zero?) What does \large z” mean here? Use the binomial (or Taylor) expansion to verify that your formula does indeed give exactly what you expect. (Hint: you cannot Taylor expand in something BIG, you have to Taylor expand in something small.) (e) Can you use Gauss’ law to gure out the gravitational potential at the point (0; 0; z)? (If so, do it and check your previous answers. If not, why not?) Back to Problem List 11 5 { GRAVITATION Last Updated: July 16, 2012 5.11 Sphere with constant internal gravitational eld Given: Pollock { Spring 2012 (a) Imagine a planet of total mass M and radius R which has a nonuniform mass density that varies just with r, the distance from the center. For this (admittedly very unusual!) planet, suppose the gravitational eld strength inside the planet turns out to be independent of the radial distance within the sphere. Find the function describing the mass density  = (r) of this planet. (Your nal answer should be written in terms of the given constants.) (b) Now, determine the gravitational force on a satellite of mass m orbiting this planet at distance r > R. (Use the easiest method you can come up with!) Explain your work in words as well as formulas. For instance, in your calculation, you will need to argue that the magnitude of ~g(r; ; ) depends only on r. Be explicit about this – how do you know that it doesn’t, in fact, depend on  or ? (c) As a nal check, explicitly show that your solutions inside and outside the planet (parts a and b) are consistent when r = R. Please also comment on whether this density pro le strikes you as physically plausible, or is it just designed as a mathematical exercise? Defend your reasoning. Back to Problem List 12 5 { GRAVITATION Last Updated: July 16, 2012 5.12 Throwing a rock o the moon Given: Pollock { Spring 2012 Assuming that asteroids have roughly the same mass density as the moon, make an estimate of the largest asteroid that an astronaut could be standing on, and still have a chance of throwing a small object (with their arms, no machinery!) so that it completely escapes the asteroid’s gravitational eld. (This minimum speed is called \escape velocity”) Is the size you computed typical for asteroids in our solar system? Back to Problem List 13

Que 1: true of false a) Both silicon and germanium atoms have four valances electrons b) When forward-biased , a diode has a very high resistance c) A zener diode is designed to operate in the forward-bias region and has higher reverse breakdown voltage level than regular diode Write the word or phrase that best completes each statement or answers the questions: d) In semiconductor, in addition to the electron flow, there is also another kind of charge flow referred as………………. e) A silicon diode in placed in series with 2kΩresistor and a 14 V dc power supply. The current ID is: i) 6.65 mA ii) 2.2 mA iii)7.5 mA iv) 14 mA f) The series resistor that limits the forward current length through a silicon diode to 8 mA if the power supply voltage is 9.5V is : i) 1.1 kΩ ii) 2.2 kΩ iii) 9.5 mA iv) 4.7 mA FIGURE g) Determine the diode current IZ for the circuit of figure 1-2: assume VZ = 3.9 V i) 8.1 mA ii) 3.55 mA iii) 24.5 mA iv) 13.64 mA h) Determine the current through a 20 mA yellow LED when the power supply voltage is 15 V the series resistor is 2k ohm and the diode is put in backward. Assume VLED = 2V i) 20 mA ii) 0 mA iii) 10 mA iv) 6.5 mA Write the word or phrase that best completes each statement or answers the questions: i) Zener diode is a p-n junction diode that is desgined for specifc…………………voltage j) ………………………….is the process by which impurity atoms are introduced to the instrisic semiconductor in order to alter the balance between holes and electrons. 1) The average value of s full-wave rectifier with a peak vaue of 17V ia 108V 2) If the frequency of input signal of the full wave reflector is 60Hz, the output frequency is 120Hz 3) The cathode of a zener diode, when conducting is:y i) at 0.7V ii) more positive than anode iii) more negative than anode iv) -0.7V 4) A given transformer with turn ratio 12:1has an input of 115V at 60Hzthe paek output voltage v0 (p) is i) 9.58 V ii) 6.78V iii) 11.5 V iv) 13.55 V FIGURE 2-1 5) The output voltage of V0(DC)for the full wave rectifier of figure 2-1 is i) 18.07 V ii) 12.78 V iii) 8.3 V iv) 5.74 V FIGURE 2-2 6) The voltage V2(P) for the full-wavr bridge rectifier of figure 2-2 is i) 17.37 V ii)1 6.67 V iii) 12.78 V iv) 18.07 V 7) Assume the current I0(DC) in figure is 100mA and C= 2400µF .the ripple voltage vr (p-p) i) 694mV ii) 424 mV iii) 121 V iv) 347 V Use figure 2-3 for questions below: Assume that RS = 75, RL = 160 FIGURE 2-3 8) The output voltage V0 is i) 7.5 V ii) 10 V iii) 8.5 V iv) 12 V Write the word or phrase that best completes each statement or answers the questions: 9) The magnitude of the peak-to-peak ripple voltage vr (p-p) is directly proportional to the output …………………. 10) The ripple voltage at the filter section vr (p-p) can be reduced by increasing the value

Que 1: true of false a) Both silicon and germanium atoms have four valances electrons b) When forward-biased , a diode has a very high resistance c) A zener diode is designed to operate in the forward-bias region and has higher reverse breakdown voltage level than regular diode Write the word or phrase that best completes each statement or answers the questions: d) In semiconductor, in addition to the electron flow, there is also another kind of charge flow referred as………………. e) A silicon diode in placed in series with 2kΩresistor and a 14 V dc power supply. The current ID is: i) 6.65 mA ii) 2.2 mA iii)7.5 mA iv) 14 mA f) The series resistor that limits the forward current length through a silicon diode to 8 mA if the power supply voltage is 9.5V is : i) 1.1 kΩ ii) 2.2 kΩ iii) 9.5 mA iv) 4.7 mA FIGURE g) Determine the diode current IZ for the circuit of figure 1-2: assume VZ = 3.9 V i) 8.1 mA ii) 3.55 mA iii) 24.5 mA iv) 13.64 mA h) Determine the current through a 20 mA yellow LED when the power supply voltage is 15 V the series resistor is 2k ohm and the diode is put in backward. Assume VLED = 2V i) 20 mA ii) 0 mA iii) 10 mA iv) 6.5 mA Write the word or phrase that best completes each statement or answers the questions: i) Zener diode is a p-n junction diode that is desgined for specifc…………………voltage j) ………………………….is the process by which impurity atoms are introduced to the instrisic semiconductor in order to alter the balance between holes and electrons. 1) The average value of s full-wave rectifier with a peak vaue of 17V ia 108V 2) If the frequency of input signal of the full wave reflector is 60Hz, the output frequency is 120Hz 3) The cathode of a zener diode, when conducting is:y i) at 0.7V ii) more positive than anode iii) more negative than anode iv) -0.7V 4) A given transformer with turn ratio 12:1has an input of 115V at 60Hzthe paek output voltage v0 (p) is i) 9.58 V ii) 6.78V iii) 11.5 V iv) 13.55 V FIGURE 2-1 5) The output voltage of V0(DC)for the full wave rectifier of figure 2-1 is i) 18.07 V ii) 12.78 V iii) 8.3 V iv) 5.74 V FIGURE 2-2 6) The voltage V2(P) for the full-wavr bridge rectifier of figure 2-2 is i) 17.37 V ii)1 6.67 V iii) 12.78 V iv) 18.07 V 7) Assume the current I0(DC) in figure is 100mA and C= 2400µF .the ripple voltage vr (p-p) i) 694mV ii) 424 mV iii) 121 V iv) 347 V Use figure 2-3 for questions below: Assume that RS = 75, RL = 160 FIGURE 2-3 8) The output voltage V0 is i) 7.5 V ii) 10 V iii) 8.5 V iv) 12 V Write the word or phrase that best completes each statement or answers the questions: 9) The magnitude of the peak-to-peak ripple voltage vr (p-p) is directly proportional to the output …………………. 10) The ripple voltage at the filter section vr (p-p) can be reduced by increasing the value

Ch 2 Questions that might be on the test. If you cannot answer them, check your class notes or the textbook. 1. A mineral is a naturally occurring substance formed through geological processes that has: a) a characteristic chemical composition, b) a highly ordered atomic structure c) specific physical properties d) all of the above 2. There are currently more than ______ known minerals, according to the International Mineralogical Association, a) 40 b) 400 c) 4000 d) 40 000 3. Some minerals, like quartz, mica or feldspar are: a) rare b) common c) valuable d) priceless 4. Rocks from which minerals are mined for economic purposes are referred to as: a) gangue b) tailings c) ores d) granite 5. Electrons, which have a _____ charge, a size which is so small as to be currently unmeasurable, and which are the least massive of the three types of basic particles. a) positive b) negative c) neutral 6. Both protons and neutrons are themselves now thought to be composed of even more elementary particles called: a) quarks b) quakes c) parsons d) megans 7. In processes which change the number of protons in a nucleus, the atom becomes an atom of a different chemical: a) isotope b) compound c) element d) planet 8. Atoms which have either a deficit or a surplus of electrons are called: a) elements b) isotopes c) ions d) molecules 9. In the Bohr model of the atom, electrons can only orbit the nucleus in particular circular orbits with fixed angular momentum and energy, their distances from the nucleus being proportional to their respective energies. They can only make _____ leaps between the fixed energy levels. a) tiny b) quantum c) gradual 10. It is impossible to simultaneously derive precise values for both the position and momentum of a particle for any given point in time; this became known as the ______ principle. a) Bohr b) Einstein c) uncertainty d) quantum 11. The modern model of the atom describes the positions of electrons in an atom in terms of: a) quantum levels b) orbital paths c) probabilities d) GPS 12. Isotopes of an element have nuclei with the same number of protons (the same atomic number) but different numbers of: a) electrons b) neutrons c) ions d) photons 13. In helium-3 (or 3He), how many protons are present? a) 1 b) 2 c) 3 d) 4 14. In helium-3 (or 3He), how many neutrons are present? a) 1 b) 2 c) 3 d) 4 15. The relative abundance of an isotope is strongly correlated with its tendency toward nuclear _____, short-lived nuclides quickly go away, while their long-lived counterparts endure. a) fission b) fusion c) decay d) bombardment 16. The isotopic composition of elements is different on different planets. a) True b) False 17. As a general rule, the fewer electrons in an atom’s valence shell, the ____ reactive it is. Lithium, sodium, and potassium have one electron in their outer shells. a) more b) less 18. Every atom is much more stable, or less reactive, with a ____ valence shell. a) partly full b) completely full 19. A positively-charged ion, which has fewer electrons than protons, is known as a: a) anion b) cation c) fermion d) bation 20. Bonds vary widely in their strength. Generally covalent and ionic bonds are often described as “strong”, whereas ______ bonds are generally considered to be “weak”. a) van der Waals b) Faradays c) van Neumans 21. This bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared a) ionic b) covalent c) van der Waals d) metallic 22. This bond results from electrostatic attraction between atoms: a) ionic b) covalent c) van der Waals d) metallic 23. A sea of delocalized electrons causes this bonding: a) ionic b) covalent c) van der Waals d) metallic 24. The chemical composition of minerals may vary between end members of a mineral system. For example the ______ feldspars comprise a continuous series from sodiumrich albite to calcium-rich anorthite. a) plagioclase b) orthoclase c) alkaline d) acidic 25. Crystal structure is based on ____ internal atomic arrangement. a) irregular b) regular c) random d) curvilinear 26. Pyrite and marcasite are both _______, but their arrangement of atoms differs. a) iron sulfide b) lead sulfide c) copper silfide d) silver sulfide 27. The carbon atoms in ______ are arranged into sheets which can slide easily past each other, while the carbon atoms in diamond form a strong, interlocking three-dimensional network. a) sapphire b) graphite c) aluminum d) carbonate 28. TGCFAOQTCD a) Crystal habit b) Hardness scale c) Luster scale 29. Dull to metallic, submetallic, adamantine, vitreous, pearly, resinous, or silky. a) Crystal habit b) Hardness scale c) Luster scale d) Heft scale 30. The color of the powder a mineral leaves after rubbing it on unglazed porcelain. a) color b) streak c) lustre d) iridescense 31. Describes the way a mineral may split apart along various planes. a) fracture b) streak c) lustre d) cleavage 32. In modern physics, the position of electrons about a nucleus are defined in terms of: a) probabilities b) circles c) ellipses d) chromodomes 33. The symbol H+ suggests a: a) hydrogen atom b) hydrogen isotope c) hydrogen cation d) hydrogen anion 34. The tabulated atomic mass of natural carbon is not exactly 12 because carbon in nature always has multiple ________ present. a) electrons b) isotopes c) quarks d) protons 35. This type of bonding due to delocalized electrons leads to malleability, ductility, and high melting points: a) covalent b) ionic c) van der Waals d) metallic 36. The mineral ___________ is 3 on Mohs Scale whereas the mineral ___________ is 9. a) calcite, corundum b) corundum, calcite c) caliche, calcite d) chalcedony, quartz 37. In hand specimens, geologists identify most minerals based on: a) physical properties b) chemical analyses c) xray diffraction 38. This type of chemical bonding is the weakest but occurs in all substances. a) covalent b) ionic c) metallic d) none of the above 39. Quartz, feldspar, mica, chlorite, kaolin, calcite, epidote, olivine, augite, hornblende, magnetite, hematite, limonite: these minerals are: a) common in rocks b) occasionally found c) rare d) extremely rare 40. Characteristics of a mineral do NOT include: a) naturally occurring b) characteristic chemical formula c) crystalline d) organic e) all of the above 41. The chemical composition of a particular mineral may vary between end members. For example, the common mineral plagioclase feldspar varies from being _______-rich to being _________-rich. a) sodium, calcium b) potassium, sodium c) iron, magnesium d) carbon, oxygen 42. Sharing of electrons typifies the __________ bond whereas electrostatic attraction typifies the _______ bond. a) ionic, covalent b) ionic, triclinic c) covalent, ionic d) triclinic, covalent 43. If number of protons does not equal the number of electrons, the atom is a(n) : a) isotope b) ion c) quark d) simplex e) google 44. Atoms generally consist of: a) electrons b) protons c) neutrons d) all of the above 45. Not counting rare minerals, about how many mineral species are at least occasionally encountered in rocks? a) 20 b) 200 c) 2000 46. Carbon is atomic number 6. Carbon-13 has _______ protons and _______ neutrons. a) thirteen, six b) six, seven c) twelve, twenty-five d) twelve, twelve 47. Which of these particles are not nucleons? a) electrons b) neutrons c) protons 48. A mineral with visibly recognizable crystals is said to have good crystal habit; otherwise the mineral is said to be: a) massive b) granular c) compact d) any of the above 49. In chemical bonding, two atoms become linked by moving or sharing __________. a) neutrons b) protons c) electrons 50. The name of an element is determined by the number of ______ present in the ______ of an atom. a) electrons, nucleus b) neutrons, nucleus c) protons, nucleus d) protons, electron cloud e) neutrons, electron cloud 51. Generally ________ and ____________ bonds are strong whereas the ______________ bond is weak. a) covalent, ionic, van der Waals b) van der Waals, covalent, ionic c) ionic, van der Waals, covalent 52. Which of the following are held together by chemical bonds? a) molecules b) crystals c) diatomic gases 53. An ion with fewer electrons than protons is called an ______ and it carries a _________ electric charge. a) cation, positive b) anion, negative c) cation, negative d) anion, positive 54. Two or more minerals may have the same _________ composition but different _______ structure. These are called polymorphs. a) crystal, chemical b) chemical, crystal 55. Industrial minerals are: a) gem quality b) commercially valuable c) tailings d) worthless 56. All minerals are crystalline. If the crystals are too small to see, they can be detected by: a) x-ray diffraction b) cosmic rays c) sound waves d) odor 57. If two atomes have the same number of protons but different numbers of neutrons, the atoms are _______ of the same _________. a) elements, mineral b) atoms, isotope c) elements, isotope d) isotopes, element 58. Modern physics recognizes that electrons show both particle and ______ behavior. a) wave b) emotional c) thermal d) revolting 59. Sodium and potassium have one ______ electron in their outer shells and are extremely ________. a) valence, stable b) inverted, reactive c) valence, reactive d) contaminated, inactive 60. The luster of _______ would be described as ________. a) glass, vitreous b) diamond, dull c) pyrite, silky d) graphite, resinous 61. The minerals ________ and __________ are polymorphs of carbon. a) diamond, graphite b) calcite, silicate c) bonite, bronzite 62. In the ______ atom based on _______ physics, electrons were restricted to circular orbits of fixed energy levels. a) Bohr , quantum b) Rutherford, classical c) Bohr, classical d) Rutherford, quantum 63. Virtually all elements other than ______ and _______ were formed in stars and supernovae long after the Big Bang. a) hydrogen, helium b) carbon, phosphorus c) carbon, oxygen d) silica, carbon 64. Physicist Werner _________ developed the ___________ principle which means that it is impossible to know exactly the position and momentum of a particle. a) Heisenberg, certainty b) Heisenberg, uncertainty c) Bohr, uncertainty d) Bohr, certainty

Ch 2 Questions that might be on the test. If you cannot answer them, check your class notes or the textbook. 1. A mineral is a naturally occurring substance formed through geological processes that has: a) a characteristic chemical composition, b) a highly ordered atomic structure c) specific physical properties d) all of the above 2. There are currently more than ______ known minerals, according to the International Mineralogical Association, a) 40 b) 400 c) 4000 d) 40 000 3. Some minerals, like quartz, mica or feldspar are: a) rare b) common c) valuable d) priceless 4. Rocks from which minerals are mined for economic purposes are referred to as: a) gangue b) tailings c) ores d) granite 5. Electrons, which have a _____ charge, a size which is so small as to be currently unmeasurable, and which are the least massive of the three types of basic particles. a) positive b) negative c) neutral 6. Both protons and neutrons are themselves now thought to be composed of even more elementary particles called: a) quarks b) quakes c) parsons d) megans 7. In processes which change the number of protons in a nucleus, the atom becomes an atom of a different chemical: a) isotope b) compound c) element d) planet 8. Atoms which have either a deficit or a surplus of electrons are called: a) elements b) isotopes c) ions d) molecules 9. In the Bohr model of the atom, electrons can only orbit the nucleus in particular circular orbits with fixed angular momentum and energy, their distances from the nucleus being proportional to their respective energies. They can only make _____ leaps between the fixed energy levels. a) tiny b) quantum c) gradual 10. It is impossible to simultaneously derive precise values for both the position and momentum of a particle for any given point in time; this became known as the ______ principle. a) Bohr b) Einstein c) uncertainty d) quantum 11. The modern model of the atom describes the positions of electrons in an atom in terms of: a) quantum levels b) orbital paths c) probabilities d) GPS 12. Isotopes of an element have nuclei with the same number of protons (the same atomic number) but different numbers of: a) electrons b) neutrons c) ions d) photons 13. In helium-3 (or 3He), how many protons are present? a) 1 b) 2 c) 3 d) 4 14. In helium-3 (or 3He), how many neutrons are present? a) 1 b) 2 c) 3 d) 4 15. The relative abundance of an isotope is strongly correlated with its tendency toward nuclear _____, short-lived nuclides quickly go away, while their long-lived counterparts endure. a) fission b) fusion c) decay d) bombardment 16. The isotopic composition of elements is different on different planets. a) True b) False 17. As a general rule, the fewer electrons in an atom’s valence shell, the ____ reactive it is. Lithium, sodium, and potassium have one electron in their outer shells. a) more b) less 18. Every atom is much more stable, or less reactive, with a ____ valence shell. a) partly full b) completely full 19. A positively-charged ion, which has fewer electrons than protons, is known as a: a) anion b) cation c) fermion d) bation 20. Bonds vary widely in their strength. Generally covalent and ionic bonds are often described as “strong”, whereas ______ bonds are generally considered to be “weak”. a) van der Waals b) Faradays c) van Neumans 21. This bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared a) ionic b) covalent c) van der Waals d) metallic 22. This bond results from electrostatic attraction between atoms: a) ionic b) covalent c) van der Waals d) metallic 23. A sea of delocalized electrons causes this bonding: a) ionic b) covalent c) van der Waals d) metallic 24. The chemical composition of minerals may vary between end members of a mineral system. For example the ______ feldspars comprise a continuous series from sodiumrich albite to calcium-rich anorthite. a) plagioclase b) orthoclase c) alkaline d) acidic 25. Crystal structure is based on ____ internal atomic arrangement. a) irregular b) regular c) random d) curvilinear 26. Pyrite and marcasite are both _______, but their arrangement of atoms differs. a) iron sulfide b) lead sulfide c) copper silfide d) silver sulfide 27. The carbon atoms in ______ are arranged into sheets which can slide easily past each other, while the carbon atoms in diamond form a strong, interlocking three-dimensional network. a) sapphire b) graphite c) aluminum d) carbonate 28. TGCFAOQTCD a) Crystal habit b) Hardness scale c) Luster scale 29. Dull to metallic, submetallic, adamantine, vitreous, pearly, resinous, or silky. a) Crystal habit b) Hardness scale c) Luster scale d) Heft scale 30. The color of the powder a mineral leaves after rubbing it on unglazed porcelain. a) color b) streak c) lustre d) iridescense 31. Describes the way a mineral may split apart along various planes. a) fracture b) streak c) lustre d) cleavage 32. In modern physics, the position of electrons about a nucleus are defined in terms of: a) probabilities b) circles c) ellipses d) chromodomes 33. The symbol H+ suggests a: a) hydrogen atom b) hydrogen isotope c) hydrogen cation d) hydrogen anion 34. The tabulated atomic mass of natural carbon is not exactly 12 because carbon in nature always has multiple ________ present. a) electrons b) isotopes c) quarks d) protons 35. This type of bonding due to delocalized electrons leads to malleability, ductility, and high melting points: a) covalent b) ionic c) van der Waals d) metallic 36. The mineral ___________ is 3 on Mohs Scale whereas the mineral ___________ is 9. a) calcite, corundum b) corundum, calcite c) caliche, calcite d) chalcedony, quartz 37. In hand specimens, geologists identify most minerals based on: a) physical properties b) chemical analyses c) xray diffraction 38. This type of chemical bonding is the weakest but occurs in all substances. a) covalent b) ionic c) metallic d) none of the above 39. Quartz, feldspar, mica, chlorite, kaolin, calcite, epidote, olivine, augite, hornblende, magnetite, hematite, limonite: these minerals are: a) common in rocks b) occasionally found c) rare d) extremely rare 40. Characteristics of a mineral do NOT include: a) naturally occurring b) characteristic chemical formula c) crystalline d) organic e) all of the above 41. The chemical composition of a particular mineral may vary between end members. For example, the common mineral plagioclase feldspar varies from being _______-rich to being _________-rich. a) sodium, calcium b) potassium, sodium c) iron, magnesium d) carbon, oxygen 42. Sharing of electrons typifies the __________ bond whereas electrostatic attraction typifies the _______ bond. a) ionic, covalent b) ionic, triclinic c) covalent, ionic d) triclinic, covalent 43. If number of protons does not equal the number of electrons, the atom is a(n) : a) isotope b) ion c) quark d) simplex e) google 44. Atoms generally consist of: a) electrons b) protons c) neutrons d) all of the above 45. Not counting rare minerals, about how many mineral species are at least occasionally encountered in rocks? a) 20 b) 200 c) 2000 46. Carbon is atomic number 6. Carbon-13 has _______ protons and _______ neutrons. a) thirteen, six b) six, seven c) twelve, twenty-five d) twelve, twelve 47. Which of these particles are not nucleons? a) electrons b) neutrons c) protons 48. A mineral with visibly recognizable crystals is said to have good crystal habit; otherwise the mineral is said to be: a) massive b) granular c) compact d) any of the above 49. In chemical bonding, two atoms become linked by moving or sharing __________. a) neutrons b) protons c) electrons 50. The name of an element is determined by the number of ______ present in the ______ of an atom. a) electrons, nucleus b) neutrons, nucleus c) protons, nucleus d) protons, electron cloud e) neutrons, electron cloud 51. Generally ________ and ____________ bonds are strong whereas the ______________ bond is weak. a) covalent, ionic, van der Waals b) van der Waals, covalent, ionic c) ionic, van der Waals, covalent 52. Which of the following are held together by chemical bonds? a) molecules b) crystals c) diatomic gases 53. An ion with fewer electrons than protons is called an ______ and it carries a _________ electric charge. a) cation, positive b) anion, negative c) cation, negative d) anion, positive 54. Two or more minerals may have the same _________ composition but different _______ structure. These are called polymorphs. a) crystal, chemical b) chemical, crystal 55. Industrial minerals are: a) gem quality b) commercially valuable c) tailings d) worthless 56. All minerals are crystalline. If the crystals are too small to see, they can be detected by: a) x-ray diffraction b) cosmic rays c) sound waves d) odor 57. If two atomes have the same number of protons but different numbers of neutrons, the atoms are _______ of the same _________. a) elements, mineral b) atoms, isotope c) elements, isotope d) isotopes, element 58. Modern physics recognizes that electrons show both particle and ______ behavior. a) wave b) emotional c) thermal d) revolting 59. Sodium and potassium have one ______ electron in their outer shells and are extremely ________. a) valence, stable b) inverted, reactive c) valence, reactive d) contaminated, inactive 60. The luster of _______ would be described as ________. a) glass, vitreous b) diamond, dull c) pyrite, silky d) graphite, resinous 61. The minerals ________ and __________ are polymorphs of carbon. a) diamond, graphite b) calcite, silicate c) bonite, bronzite 62. In the ______ atom based on _______ physics, electrons were restricted to circular orbits of fixed energy levels. a) Bohr , quantum b) Rutherford, classical c) Bohr, classical d) Rutherford, quantum 63. Virtually all elements other than ______ and _______ were formed in stars and supernovae long after the Big Bang. a) hydrogen, helium b) carbon, phosphorus c) carbon, oxygen d) silica, carbon 64. Physicist Werner _________ developed the ___________ principle which means that it is impossible to know exactly the position and momentum of a particle. a) Heisenberg, certainty b) Heisenberg, uncertainty c) Bohr, uncertainty d) Bohr, certainty

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Question 2 0 / 1 point The formation of our solar system began when electrons settled into orbit around hydrogen nuclei water condensed into an icy body a shock wave from a nearby exploding star started a cloud of dust and gas spinning all matter and energy exploded from a tiny singularity in the big bang

Question 2 0 / 1 point The formation of our solar system began when electrons settled into orbit around hydrogen nuclei water condensed into an icy body a shock wave from a nearby exploding star started a cloud of dust and gas spinning all matter and energy exploded from a tiny singularity in the big bang

Question 1, chap 33, sect 3. part 1 of 2 10 points The compound eyes of bees and other insects are highly sensitive to light in the ultraviolet portion of the spectrum, particularly light with frequencies between 7.5 × 1014 Hz and 1.0 × 1015 Hz. The speed of light is 3 × 108 m/s. What is the largest wavelength to which these frequencies correspond? Question 3, chap 33, sect 3. part 1 of 3 10 points A plane electromagnetic sinusoidal wave of frequency 10.7 MHz travels in free space. The speed of light is 2.99792 × 108 m/s. Determine the wavelength of the wave. Question 4, chap 33, sect 3. part 2 of 3 10 points Find the period of the wave. Question 2, chap 33, sect 3. part 2 of 2 10 points What is the smallest wavelength? Question 5, chap 33, sect 3. part 3 of 3 10 points At some point and some instant, the electric field has has a value of 998 N/C. Calculate the magnitude of the magnetic field at this point and this instant. Question 6, chap 33, sect 3. part 1 of 2 10 points A plane electromagnetic sinusoidal wave of frequency 10.7 MHz travels in free space. The speed of light is 2.99792 × 108 m/s. Determine the wavelength of the wave. Question 8, chap 33, sect 3. part 1 of 1 10 points The magnetic field amplitude of an electromagnetic wave is 9.9 × 10−6 T. The speed of light is 2.99792 × 108 m/s . Calculate the amplitude of the electric field if the wave is traveling in free space. Question 7, chap 33, sect 3. part 2 of 2 10 points At some point and some instant, the electric field has has a value of 998 V/m. Calculate the magnitude of the magnetic field at this point and this instant. Question 9, chap 33, sect 5. part 1 of 1 10 points The cable is carrying the current I(t). at the surface of a long transmission cable of resistivity ρ, length ℓ and radius a, using the expression ~S = 1 μ0 ~E × ~B . Question 10, chap 33, sect 5. part 1 of 1 10 points In 1965 Penzias and Wilson discovered the cosmic microwave radiation left over from the Big Bang expansion of the universe. The energy density of this radiation is 7.64 × 10−14 J/m3. The speed of light 2.99792 × 108 m/s and the permeability of free space is 4π × 10−7 N/A2. Determine the corresponding electric field amplQuestion 11, chap 33, sect 5. part 1 of 5 10 points Consider a monochromatic electromagnetic plane wave propagating in the x direction. At a particular point in space, the magnitude of the electric field has an instantaneous value of 998 V/m in the positive y-direction. The wave is traveling in the positive x-direction. x y z E wave propagation The speed of light is 2.99792×108 m/s, the permeability of free space is 4π×10−7 T ・ N/A and the permittivity of free space 8.85419 × 10−12 C2/N ・ m2. Compute the instantaneous magnitude of the magnetic field at the same point and time.itude. Question 12, chap 33, sect 5. part 2 of 5 10 points What is the instantaneous magnitude of the Poynting vector at the same point and time? Question 13, chap 33, sect 5. part 3 of 5 10 points What are the directions of the instantaneous magnetic field and theQuestion 14, chap 33, sect 5. part 4 of 5 10 points What is the instantaneous value of the energy density of the electric field? Question 16, chap 33, sect 6. part 1 of 4 10 points Consider an electromagnetic plane wave with time average intensity 104 W/m2 . The speed of light is 2.99792 × 108 m/s and the permeability of free space is 4 π × 10−7 T・m/A. What is its maximum electric field? What is the instantaneous value of the energy density of the magnetic field? Question 17, chap 33, sect 6. part 2 of 4 10 points What is the the maximum magnetic field? Question 19, chap 33, sect 6. part 4 of 4 10 points Consider an electromagnetic wave pattern as shown in the figure below. Question 18, chap 33, sect 6. part 3 of 4 10 points What is the pressure on a surface which is perpendicular to the beam and is totally reflective? Question 20, chap 33, sect 8. part 1 of 1 10 points A coin is at the bottom of a beaker. The beaker is filled with 1.6 cm of water (n1 = 1.33) covered by 2.1 cm of liquid (n2 = 1.4) floating on the water. How deep does the coin appear to be from the upper surface of the liquid (near the top of the beaker)? An cylindrical opaque drinking glass has a diameter 3 cm and height h, as shown in the figure. An observer’s eye is placed as shown (the observer is just barely looking over the rim of the glass). When empty, the observer can just barely see the edge of the bottom of the glass. When filled to the brim with a transparent liquid, the observer can just barely see the center of the bottom of the glass. The liquid in the drinking glass has an index of refraction of 1.4 . θi h d θr eye Calculate the angle θr . Question 22, chap 33, sect 8. part 2 of 2 10 points Calculate the height h of the glass.

Question 1, chap 33, sect 3. part 1 of 2 10 points The compound eyes of bees and other insects are highly sensitive to light in the ultraviolet portion of the spectrum, particularly light with frequencies between 7.5 × 1014 Hz and 1.0 × 1015 Hz. The speed of light is 3 × 108 m/s. What is the largest wavelength to which these frequencies correspond? Question 3, chap 33, sect 3. part 1 of 3 10 points A plane electromagnetic sinusoidal wave of frequency 10.7 MHz travels in free space. The speed of light is 2.99792 × 108 m/s. Determine the wavelength of the wave. Question 4, chap 33, sect 3. part 2 of 3 10 points Find the period of the wave. Question 2, chap 33, sect 3. part 2 of 2 10 points What is the smallest wavelength? Question 5, chap 33, sect 3. part 3 of 3 10 points At some point and some instant, the electric field has has a value of 998 N/C. Calculate the magnitude of the magnetic field at this point and this instant. Question 6, chap 33, sect 3. part 1 of 2 10 points A plane electromagnetic sinusoidal wave of frequency 10.7 MHz travels in free space. The speed of light is 2.99792 × 108 m/s. Determine the wavelength of the wave. Question 8, chap 33, sect 3. part 1 of 1 10 points The magnetic field amplitude of an electromagnetic wave is 9.9 × 10−6 T. The speed of light is 2.99792 × 108 m/s . Calculate the amplitude of the electric field if the wave is traveling in free space. Question 7, chap 33, sect 3. part 2 of 2 10 points At some point and some instant, the electric field has has a value of 998 V/m. Calculate the magnitude of the magnetic field at this point and this instant. Question 9, chap 33, sect 5. part 1 of 1 10 points The cable is carrying the current I(t). at the surface of a long transmission cable of resistivity ρ, length ℓ and radius a, using the expression ~S = 1 μ0 ~E × ~B . Question 10, chap 33, sect 5. part 1 of 1 10 points In 1965 Penzias and Wilson discovered the cosmic microwave radiation left over from the Big Bang expansion of the universe. The energy density of this radiation is 7.64 × 10−14 J/m3. The speed of light 2.99792 × 108 m/s and the permeability of free space is 4π × 10−7 N/A2. Determine the corresponding electric field amplQuestion 11, chap 33, sect 5. part 1 of 5 10 points Consider a monochromatic electromagnetic plane wave propagating in the x direction. At a particular point in space, the magnitude of the electric field has an instantaneous value of 998 V/m in the positive y-direction. The wave is traveling in the positive x-direction. x y z E wave propagation The speed of light is 2.99792×108 m/s, the permeability of free space is 4π×10−7 T ・ N/A and the permittivity of free space 8.85419 × 10−12 C2/N ・ m2. Compute the instantaneous magnitude of the magnetic field at the same point and time.itude. Question 12, chap 33, sect 5. part 2 of 5 10 points What is the instantaneous magnitude of the Poynting vector at the same point and time? Question 13, chap 33, sect 5. part 3 of 5 10 points What are the directions of the instantaneous magnetic field and theQuestion 14, chap 33, sect 5. part 4 of 5 10 points What is the instantaneous value of the energy density of the electric field? Question 16, chap 33, sect 6. part 1 of 4 10 points Consider an electromagnetic plane wave with time average intensity 104 W/m2 . The speed of light is 2.99792 × 108 m/s and the permeability of free space is 4 π × 10−7 T・m/A. What is its maximum electric field? What is the instantaneous value of the energy density of the magnetic field? Question 17, chap 33, sect 6. part 2 of 4 10 points What is the the maximum magnetic field? Question 19, chap 33, sect 6. part 4 of 4 10 points Consider an electromagnetic wave pattern as shown in the figure below. Question 18, chap 33, sect 6. part 3 of 4 10 points What is the pressure on a surface which is perpendicular to the beam and is totally reflective? Question 20, chap 33, sect 8. part 1 of 1 10 points A coin is at the bottom of a beaker. The beaker is filled with 1.6 cm of water (n1 = 1.33) covered by 2.1 cm of liquid (n2 = 1.4) floating on the water. How deep does the coin appear to be from the upper surface of the liquid (near the top of the beaker)? An cylindrical opaque drinking glass has a diameter 3 cm and height h, as shown in the figure. An observer’s eye is placed as shown (the observer is just barely looking over the rim of the glass). When empty, the observer can just barely see the edge of the bottom of the glass. When filled to the brim with a transparent liquid, the observer can just barely see the center of the bottom of the glass. The liquid in the drinking glass has an index of refraction of 1.4 . θi h d θr eye Calculate the angle θr . Question 22, chap 33, sect 8. part 2 of 2 10 points Calculate the height h of the glass.

1. Discuss how the establishment of an organizational infrastructure that supports the integration of a career and succession plan competency models and value systems can help employees overcome the doom loop with respect to understanding your own career status.

1. Discuss how the establishment of an organizational infrastructure that supports the integration of a career and succession plan competency models and value systems can help employees overcome the doom loop with respect to understanding your own career status.

A number of associations or organizations are mixing up to … Read More...
Question 24 1 / 1 point Atolls form when a coral reef grows adjacent to a convergent margin. a volcanic island forms adjacent to a divergent margin. a fringing coral reef continues to grow upward after a volcanic island sinks below the sea surface. a volcanic island becomes hollowed out by wave motion.

Question 24 1 / 1 point Atolls form when a coral reef grows adjacent to a convergent margin. a volcanic island forms adjacent to a divergent margin. a fringing coral reef continues to grow upward after a volcanic island sinks below the sea surface. a volcanic island becomes hollowed out by wave motion.