About Me Introduction – About me This webfolio provides you with a template for the construction of your portfolio for the module. Construct this portfolio as you go along and it will provide the content for the assignment . There are resources at the end of the portfolio to help you. You can also find some of the material on WOLF. If you are unsure of anything please ASK your tutor. You must attend classes to ensure that you can work on the exercises that will form part of this portfolio. The purpose of this section is to help your tutors to understand the context of your answers and your understanding of strategic issues. Welcome to (put your name here) webfolio. I am currently a student at the University of Wolverhampton Business School, studying (put your degree course in here). I have chosen to come on this particular course because (reasons for joining here). Write a short piece about yourself and what you have studied before

About Me Introduction – About me This webfolio provides you with a template for the construction of your portfolio for the module. Construct this portfolio as you go along and it will provide the content for the assignment . There are resources at the end of the portfolio to help you. You can also find some of the material on WOLF. If you are unsure of anything please ASK your tutor. You must attend classes to ensure that you can work on the exercises that will form part of this portfolio. The purpose of this section is to help your tutors to understand the context of your answers and your understanding of strategic issues. Welcome to (put your name here) webfolio. I am currently a student at the University of Wolverhampton Business School, studying (put your degree course in here). I have chosen to come on this particular course because (reasons for joining here). Write a short piece about yourself and what you have studied before

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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

Consider the following linear equations: 5x 2y 4z 12 x 3y 13 4x 3y 2z 13 + + = + = + + = a) Write these equations in matrix form b) Find the determinant of the matrix of coefficients c) Solve the equations using the matrix inversion method

Consider the following linear equations: 5x 2y 4z 12 x 3y 13 4x 3y 2z 13 + + = + = + + = a) Write these equations in matrix form b) Find the determinant of the matrix of coefficients c) Solve the equations using the matrix inversion method

a) 5 2 4 x 12 1 3 0 y … Read More...
Module Overview Summary of Module Description For full details, go to Module Descriptor. Aims The aim of this module is to: • Develop individuals for a career in business and management • Enhance and develop employability , professional and lifelong learning skills and personal development Learning Outcomes Learners will be able to critically evaluate the acquisition of a range of academic and professional skills using a number of theoretical frameworks. Assessment – Summary Category Assessment Description Duration Word Count Weight (%) Written Assignment Essay 1 Reflective Essay N/A 3000 45 For full details, go to Assessment. Additional Information Remember that a variety of Resources is available to support your learning materials.Skills and character audit This document provides an initial picture of your skills and character. It will also provide the basis of further documents that make up the first assignment on the module. It is based on the skills statements that form a fundamental part of your Masters programme which were approved by a validation panel that consisted of members of staff in the Business School, academic staff from other higher education institutions and employers. The statements in the form are there for you and you will not be judged on whether your responses are positive or negative. The responses should enable you to identify what you are good or bad at from which you can create a personal SLOT analysis (Strengths, Limitations, Opportunities, Threats). From this SLOT analysis you can then concentrate on developing certain areas that will enhance your academic and professional development. We would very much like to” get to know” you through this document and would encourage you to also complete the notes section. In this you could give us a rationale for your responses to the questions. As a guide to how you should gauge your response consider the following: Strongly agree – I have a wide range of experience in this area and have been commended by a tutor or employer for my efforts in this area Agree – I am comfortable with this aspect and have been able to demonstrate my ability Disagree – I am Ok with this but realise that I do need to improve Strongly disagree – I know I am weak in this area and need to focus on this as I could fine this weakness to be detrimental to my progression Explain why – please take the room to consider the reasons for your answer as this is the reflection that is of most value. Do not worry if your section spills onto the next page.   Intellectual (thinking) skills Strongly Agree Agree Disagree Strongly Disagree I am a creative person who can adapt my thinking to circumstances I am able to organise my thoughts, analyse, synthesise and critically appraise situations I can identify assumptions, evaluate statements in terms of evidence, detect false logic or reasoning, identify implicit values, define terms adequately and generalise appropriately Explain why: Professional/Vocational skills Strongly Agree Agree Disagree Strongly Disagree I use a wide range of techniques in approaching and solving problems. I am comfortable with a range of research techniques I am able to analyse and interpret quantitative data I am able to analyse and interpret qualitative data My leadership skills are well developed and I can adapt them to different situations I am able to manage people effectively Motivating myself and others comes easy to me I am aware of my responsibilities to myself, the organisation and other people I treat people with respect and consideration Explain why:   Key/Common skills Strongly Agree Agree Disagree Strongly Disagree I am able to use mathematical techniques to analyse data I can effectively interpret numerical data including tables and charts I am able to use a wide range of software on a PC I use a range Information Technology devices to communicate and access information I am a good listener I am able to communicate my ideas well in a face-to-face situation I can adapt my written style to suit an audiences needs I am comfortable presenting my ideas to an audience Whenever I have completed a task I always reflect on the experience with a view to seeking continuous improvement I manage my time effectively I am always prompt when asked to complete a task I am aware of the need to be sensitive to the cultural differences to which I have been exposed I am keen to learn about other people and their country and culture I enjoy working with others to complete a task I know my own character and am sensitive of this in a group situation I understand that a group is made of individuals and I am sensitive to the needs and preferences of others I will always ensure that I get my views across in a meeting I am willing to accept the viewpoint of others I always give 100% in a group task Explain why: SLOT Analysis Having responded to the statements above you should now be in a position to look forward and recognise those areas on which your development will be based. The SLOT analysis can help you to arrange this. Strengths – can be those skills and characteristics to which you have responded positively to in the previous section. It is worth noting that whilst you may be strong in these areas that does not mean you ignore their development. Indeed you may be able to utilise these strengths in the development of areas identified as weaknesses or to overcome strengths, this will enhance those skills and characteristics. Limitations – All of us can identify some sort of limitation to our skills. None of us should be afraid of doing this as this is the first stage on the improvement and development of these weaknesses. Opportunities – These arise or can be created. When thinking of this look ahead at opportunities that will arise in a professional, academic or social context within which your development can take place. Threats – Many threats from your development can come from within – your own characteristics e.g. poor time management can lead to missing deadlines. However we could equally identify a busy lifestyle as a threat to our development. Once again think widely in terms of where the threat will come from. Do not worry if you find that a strength can also be a limitation. This is often true as a characteristic you have may be strength in one situation but a limitation in another. E.g. you may be an assertive person, which is positive, but this could be negative in a group situation. Please try and elaborate this in the notes section at the foot of the table. SLOT Analysis (you may need to use two pages to set out this analysis) Strengths Limitations Opportunities Threats Analysis of the Bullet points in the SLOT table Objectives Having undertaken some analysis of your skills and characteristics the aim of this next section is to identify various aspects of your development during the course of this module, other modules on your course, and extra-curricular activities. Make sure the objectives are SMART:- S – Specific. Clearly identified from the exercises undertaken M – Measurable. The outcomes can be easily demonstrated (to yourself, and where possible others) A – Achievable. They can be done given the opportunities available to you R – Relevant. They form part of your development either on this award, in your employability prospects or in your current job role T – Timebound. They can be achieved within a given timescale Whilst there are 5 rows in the table below, please feel free to add more. However be sure that you need to do this development and that they fit within the scope of the above criteria. Area What I am going to do. How I am going to do it When I am going to do it by Force Field Analysis This technique was designed by Kurt Lewin (1947 and 1953). In the business world it is used for decision making, looking at forces that need to be considered when implementing change – it can be said to be a specialised method of weighing up the pros and cons of a decision. Having looked at your personal strengths and weaknesses we would like you to use this technique to become aware of those factors that will help/hinder, give you motivation for or may act against, your personal development. Whilst you could do this for each of your objectives we want you to think in terms of where you would like to be at the end of your Masters programme. In the central pillar, put in a statement of where you want to be at the end of the course. Then in the arrows either side look at those factors/forces that may work in your favour. Be realistic and please add as many arrows that you think may be necessary; use a separate page for the module if it makes it easier to structure your thoughts. Forces or factors working for achieving your desired outcome Where I want to be Forces or factors against working against you achieving your desired outcome

Module Overview Summary of Module Description For full details, go to Module Descriptor. Aims The aim of this module is to: • Develop individuals for a career in business and management • Enhance and develop employability , professional and lifelong learning skills and personal development Learning Outcomes Learners will be able to critically evaluate the acquisition of a range of academic and professional skills using a number of theoretical frameworks. Assessment – Summary Category Assessment Description Duration Word Count Weight (%) Written Assignment Essay 1 Reflective Essay N/A 3000 45 For full details, go to Assessment. Additional Information Remember that a variety of Resources is available to support your learning materials.Skills and character audit This document provides an initial picture of your skills and character. It will also provide the basis of further documents that make up the first assignment on the module. It is based on the skills statements that form a fundamental part of your Masters programme which were approved by a validation panel that consisted of members of staff in the Business School, academic staff from other higher education institutions and employers. The statements in the form are there for you and you will not be judged on whether your responses are positive or negative. The responses should enable you to identify what you are good or bad at from which you can create a personal SLOT analysis (Strengths, Limitations, Opportunities, Threats). From this SLOT analysis you can then concentrate on developing certain areas that will enhance your academic and professional development. We would very much like to” get to know” you through this document and would encourage you to also complete the notes section. In this you could give us a rationale for your responses to the questions. As a guide to how you should gauge your response consider the following: Strongly agree – I have a wide range of experience in this area and have been commended by a tutor or employer for my efforts in this area Agree – I am comfortable with this aspect and have been able to demonstrate my ability Disagree – I am Ok with this but realise that I do need to improve Strongly disagree – I know I am weak in this area and need to focus on this as I could fine this weakness to be detrimental to my progression Explain why – please take the room to consider the reasons for your answer as this is the reflection that is of most value. Do not worry if your section spills onto the next page.   Intellectual (thinking) skills Strongly Agree Agree Disagree Strongly Disagree I am a creative person who can adapt my thinking to circumstances I am able to organise my thoughts, analyse, synthesise and critically appraise situations I can identify assumptions, evaluate statements in terms of evidence, detect false logic or reasoning, identify implicit values, define terms adequately and generalise appropriately Explain why: Professional/Vocational skills Strongly Agree Agree Disagree Strongly Disagree I use a wide range of techniques in approaching and solving problems. I am comfortable with a range of research techniques I am able to analyse and interpret quantitative data I am able to analyse and interpret qualitative data My leadership skills are well developed and I can adapt them to different situations I am able to manage people effectively Motivating myself and others comes easy to me I am aware of my responsibilities to myself, the organisation and other people I treat people with respect and consideration Explain why:   Key/Common skills Strongly Agree Agree Disagree Strongly Disagree I am able to use mathematical techniques to analyse data I can effectively interpret numerical data including tables and charts I am able to use a wide range of software on a PC I use a range Information Technology devices to communicate and access information I am a good listener I am able to communicate my ideas well in a face-to-face situation I can adapt my written style to suit an audiences needs I am comfortable presenting my ideas to an audience Whenever I have completed a task I always reflect on the experience with a view to seeking continuous improvement I manage my time effectively I am always prompt when asked to complete a task I am aware of the need to be sensitive to the cultural differences to which I have been exposed I am keen to learn about other people and their country and culture I enjoy working with others to complete a task I know my own character and am sensitive of this in a group situation I understand that a group is made of individuals and I am sensitive to the needs and preferences of others I will always ensure that I get my views across in a meeting I am willing to accept the viewpoint of others I always give 100% in a group task Explain why: SLOT Analysis Having responded to the statements above you should now be in a position to look forward and recognise those areas on which your development will be based. The SLOT analysis can help you to arrange this. Strengths – can be those skills and characteristics to which you have responded positively to in the previous section. It is worth noting that whilst you may be strong in these areas that does not mean you ignore their development. Indeed you may be able to utilise these strengths in the development of areas identified as weaknesses or to overcome strengths, this will enhance those skills and characteristics. Limitations – All of us can identify some sort of limitation to our skills. None of us should be afraid of doing this as this is the first stage on the improvement and development of these weaknesses. Opportunities – These arise or can be created. When thinking of this look ahead at opportunities that will arise in a professional, academic or social context within which your development can take place. Threats – Many threats from your development can come from within – your own characteristics e.g. poor time management can lead to missing deadlines. However we could equally identify a busy lifestyle as a threat to our development. Once again think widely in terms of where the threat will come from. Do not worry if you find that a strength can also be a limitation. This is often true as a characteristic you have may be strength in one situation but a limitation in another. E.g. you may be an assertive person, which is positive, but this could be negative in a group situation. Please try and elaborate this in the notes section at the foot of the table. SLOT Analysis (you may need to use two pages to set out this analysis) Strengths Limitations Opportunities Threats Analysis of the Bullet points in the SLOT table Objectives Having undertaken some analysis of your skills and characteristics the aim of this next section is to identify various aspects of your development during the course of this module, other modules on your course, and extra-curricular activities. Make sure the objectives are SMART:- S – Specific. Clearly identified from the exercises undertaken M – Measurable. The outcomes can be easily demonstrated (to yourself, and where possible others) A – Achievable. They can be done given the opportunities available to you R – Relevant. They form part of your development either on this award, in your employability prospects or in your current job role T – Timebound. They can be achieved within a given timescale Whilst there are 5 rows in the table below, please feel free to add more. However be sure that you need to do this development and that they fit within the scope of the above criteria. Area What I am going to do. How I am going to do it When I am going to do it by Force Field Analysis This technique was designed by Kurt Lewin (1947 and 1953). In the business world it is used for decision making, looking at forces that need to be considered when implementing change – it can be said to be a specialised method of weighing up the pros and cons of a decision. Having looked at your personal strengths and weaknesses we would like you to use this technique to become aware of those factors that will help/hinder, give you motivation for or may act against, your personal development. Whilst you could do this for each of your objectives we want you to think in terms of where you would like to be at the end of your Masters programme. In the central pillar, put in a statement of where you want to be at the end of the course. Then in the arrows either side look at those factors/forces that may work in your favour. Be realistic and please add as many arrows that you think may be necessary; use a separate page for the module if it makes it easier to structure your thoughts. Forces or factors working for achieving your desired outcome Where I want to be Forces or factors against working against you achieving your desired outcome

  Intellectual (thinking) skills   Strongly Agree Agree Disagree Strongly … Read More...
Chapter 07 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy BioFlix Quiz: The Carbon Cycle Watch the animation at left before answering the questions below. Part A An organism gets carbon by using carbon dioxide in the atmosphere to make sugar molecules. This organism is a Hint 1. Review the animation or your Study Sheet for The Carbon Cycle. ANSWER: Correct During photosynthesis, producers use carbon dioxide to make sugar molecules. Part B Which organisms play a role in returning carbon to the atmosphere? Hint 1. Review the animation or your Study Sheet for The Carbon Cycle. ANSWER: higher-level consumer. producer. primary consumer. decomposer. None of the above Consumers and decomposers, but not producers. Producers only. Decomposers only. Consumers only. Producers, consumers, and decomposers. Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 7 5/21/2014 8:02 PM Correct Producers, consumers, and decomposers all return carbon dioxide to the atmosphere during cellular respiration. Part C Every carbon atom in the organic molecules that make up your body MUST recently have been part of Hint 1. Review the animation or your Study Sheet for The Carbon Cycle. ANSWER: Correct You are a consumer, and all your carbon comes ultimately from plants and other producers. Part D Imagine following a single carbon atom through the carbon cycle. Which of the following is a possible path for the carbon atom to take? Hint 1. Review the animation or your Study Sheet for The Carbon Cycle. ANSWER: Correct Carbon moves from the atmosphere into a producer (such as a plant), up the food chain, and then back to the atmosphere during cellular respiration. Part E Which process or processes return carbon to the atmosphere? Hint 1. Review the animation. ANSWER: Correct Cellular respiration results in the release of carbon dioxide to the atmosphere. a higher-level consumer. a primary consumer. a decomposer. a producer. a sugar molecule made in one of your chloroplasts. The atmosphere; a plant; a higher-level consumer; then back to the atmosphere. The atmosphere; a plant; an herbivore; another plant; then back to the atmosphere. The atmosphere, a plant, a herbivore, a decomposer, then back to the atmosphere The atmosphere; a decomposer; a higher-level consumer; then back to the atmosphere. The atmosphere; a decomposer; then back to the atmosphere. Cellular respiration only Photosynthesis only Cellular respiration and photosynthesis Breakdown of large organic molecules into smaller organic molecules Cellular respiration and the breakdown of large organic molecules into smaller organic molecules Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 7 5/21/2014 8:02 PM Activity: The Nitrogen Cycle Click here to complete this activity. Then answer the questions. Part A Nitrifying bacteria convert _____ to _____. ANSWER: Correct Nitrifying bacteria convert ammonium to nitrites. Part B _____ removes nitrogen from the atmosphere. ANSWER: Correct Nitrogen fixation is the conversion of nitrogen gas to a form that can be used by plants (and other organisms). Part C Assimilation is indicated by the letter(s) _____. nitrogen gas … ammonium nitrogen gas … nitrates ammonium … nitrites nitrates … nitrogen gas ammonium … nitrogen gas Denitrification Nitrification Mineralization Nitrogen fixation Assimilation Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 7 5/21/2014 8:02 PM ANSWER: Correct Assimilation is the uptake of nutrients into an organism. Part D Nitrogen-fixing bacteria is(are) indicated by the letter(s) _____. ANSWER: Correct Both of these pointers are indicating nitrogen-fixing bacteria. Nitrogen fixation is the conversion of nitrogen to a form that plants can use. Part E Nitrification is indicated by the letter(s) _____. ANSWER: C B A D and E C and D B and C A and B D and E C and D A Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 7 5/21/2014 8:02 PM Correct Nitrification is the conversion of organic nitrogen-containing compounds to nitrites and nitrates. Part F Denitrifying bacteria convert _____ to _____. ANSWER: Correct Denitrifying bacteria convert nitrates to nitrogen gas. Part G Which one of these is a nitrate? ANSWER: Correct NO3 – is a nitrate. Part H Which one of these is a nitrite? ANSWER: Correct This is a nitrite. GeoScience: Earth’s Water and the Hydrologic Cycle A B B and C D and E B and E nitrogen gas … nitrites nitrogen gas … ammonium nitrates … nitrogen gas ammonium … nitrogen gas nitrogen gas … nitrates NO2 – NH4 – NH2 SH NO3 – PO4 – NH2 NH4 – NO2 – NO3 – Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 7 5/21/2014 8:02 PM When you have finished, answer the questions. Part A The largest percentage of fresh water today is located in: ANSWER: Correct Ice sheets and glaciers are the greatest single repository of fresh water: they contain 77.3% of all Earth’s fresh water and 99.357% of all Earth’s surface fresh water. Part B Earth’s oceans hold: ANSWER: Correct The oceans contain 97.22% of all water, comprising about 1.321 billion cubic kilometers of salt water. This leaves only 2.78% of all of Earth’s water as fresh water (non-oceanic). Part C Which of the following is true of the hydrologic cycle? ANSWER: Correct About 20% of the moisture evaporated from the ocean combines with 2% of land-derived moisture to produce 22% of all precipitation that falls over land. Clearly, the bulk of continental precipitation comes from the oceanic portion of the cycle. Concept Review: Eutrophication Can you sequence the steps in the eutrophication process that occurs in a body of water? Part A Drag each statement to the appropriate location in the flowchart of the eutrophication process. ANSWER: soil. ice sheets and glaciers. the rivers and lakes of the world. groundwater resources. about the same amount of water as all groundwater sources combined. most of the fresh water on Earth. the bulk of all of the water found on Earth. about the same amount of water as all Earth’s rivers and lakes combined. Atmospheric water and surface water do not mix. Most evaporation on Earth occurs over the continents. The bulk of the precipitation occurs over land. Most of the water that falls on the continents is derived from the oceans. Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 7 5/21/2014 8:02 PM Concept Review: Biogeochemical Cycles Can you sort the items by which biogeochemical cycle they apply to? Part A Drag each description to the appropriate bin. ANSWER: Score Summary: Your score on this assignment is 62.3%. You received 12.45 out of a possible total of 20 points. Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 7 5/21/2014 8:02 PM

Chapter 07 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy BioFlix Quiz: The Carbon Cycle Watch the animation at left before answering the questions below. Part A An organism gets carbon by using carbon dioxide in the atmosphere to make sugar molecules. This organism is a Hint 1. Review the animation or your Study Sheet for The Carbon Cycle. ANSWER: Correct During photosynthesis, producers use carbon dioxide to make sugar molecules. Part B Which organisms play a role in returning carbon to the atmosphere? Hint 1. Review the animation or your Study Sheet for The Carbon Cycle. ANSWER: higher-level consumer. producer. primary consumer. decomposer. None of the above Consumers and decomposers, but not producers. Producers only. Decomposers only. Consumers only. Producers, consumers, and decomposers. Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 7 5/21/2014 8:02 PM Correct Producers, consumers, and decomposers all return carbon dioxide to the atmosphere during cellular respiration. Part C Every carbon atom in the organic molecules that make up your body MUST recently have been part of Hint 1. Review the animation or your Study Sheet for The Carbon Cycle. ANSWER: Correct You are a consumer, and all your carbon comes ultimately from plants and other producers. Part D Imagine following a single carbon atom through the carbon cycle. Which of the following is a possible path for the carbon atom to take? Hint 1. Review the animation or your Study Sheet for The Carbon Cycle. ANSWER: Correct Carbon moves from the atmosphere into a producer (such as a plant), up the food chain, and then back to the atmosphere during cellular respiration. Part E Which process or processes return carbon to the atmosphere? Hint 1. Review the animation. ANSWER: Correct Cellular respiration results in the release of carbon dioxide to the atmosphere. a higher-level consumer. a primary consumer. a decomposer. a producer. a sugar molecule made in one of your chloroplasts. The atmosphere; a plant; a higher-level consumer; then back to the atmosphere. The atmosphere; a plant; an herbivore; another plant; then back to the atmosphere. The atmosphere, a plant, a herbivore, a decomposer, then back to the atmosphere The atmosphere; a decomposer; a higher-level consumer; then back to the atmosphere. The atmosphere; a decomposer; then back to the atmosphere. Cellular respiration only Photosynthesis only Cellular respiration and photosynthesis Breakdown of large organic molecules into smaller organic molecules Cellular respiration and the breakdown of large organic molecules into smaller organic molecules Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 7 5/21/2014 8:02 PM Activity: The Nitrogen Cycle Click here to complete this activity. Then answer the questions. Part A Nitrifying bacteria convert _____ to _____. ANSWER: Correct Nitrifying bacteria convert ammonium to nitrites. Part B _____ removes nitrogen from the atmosphere. ANSWER: Correct Nitrogen fixation is the conversion of nitrogen gas to a form that can be used by plants (and other organisms). Part C Assimilation is indicated by the letter(s) _____. nitrogen gas … ammonium nitrogen gas … nitrates ammonium … nitrites nitrates … nitrogen gas ammonium … nitrogen gas Denitrification Nitrification Mineralization Nitrogen fixation Assimilation Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 7 5/21/2014 8:02 PM ANSWER: Correct Assimilation is the uptake of nutrients into an organism. Part D Nitrogen-fixing bacteria is(are) indicated by the letter(s) _____. ANSWER: Correct Both of these pointers are indicating nitrogen-fixing bacteria. Nitrogen fixation is the conversion of nitrogen to a form that plants can use. Part E Nitrification is indicated by the letter(s) _____. ANSWER: C B A D and E C and D B and C A and B D and E C and D A Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 7 5/21/2014 8:02 PM Correct Nitrification is the conversion of organic nitrogen-containing compounds to nitrites and nitrates. Part F Denitrifying bacteria convert _____ to _____. ANSWER: Correct Denitrifying bacteria convert nitrates to nitrogen gas. Part G Which one of these is a nitrate? ANSWER: Correct NO3 – is a nitrate. Part H Which one of these is a nitrite? ANSWER: Correct This is a nitrite. GeoScience: Earth’s Water and the Hydrologic Cycle A B B and C D and E B and E nitrogen gas … nitrites nitrogen gas … ammonium nitrates … nitrogen gas ammonium … nitrogen gas nitrogen gas … nitrates NO2 – NH4 – NH2 SH NO3 – PO4 – NH2 NH4 – NO2 – NO3 – Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 7 5/21/2014 8:02 PM When you have finished, answer the questions. Part A The largest percentage of fresh water today is located in: ANSWER: Correct Ice sheets and glaciers are the greatest single repository of fresh water: they contain 77.3% of all Earth’s fresh water and 99.357% of all Earth’s surface fresh water. Part B Earth’s oceans hold: ANSWER: Correct The oceans contain 97.22% of all water, comprising about 1.321 billion cubic kilometers of salt water. This leaves only 2.78% of all of Earth’s water as fresh water (non-oceanic). Part C Which of the following is true of the hydrologic cycle? ANSWER: Correct About 20% of the moisture evaporated from the ocean combines with 2% of land-derived moisture to produce 22% of all precipitation that falls over land. Clearly, the bulk of continental precipitation comes from the oceanic portion of the cycle. Concept Review: Eutrophication Can you sequence the steps in the eutrophication process that occurs in a body of water? Part A Drag each statement to the appropriate location in the flowchart of the eutrophication process. ANSWER: soil. ice sheets and glaciers. the rivers and lakes of the world. groundwater resources. about the same amount of water as all groundwater sources combined. most of the fresh water on Earth. the bulk of all of the water found on Earth. about the same amount of water as all Earth’s rivers and lakes combined. Atmospheric water and surface water do not mix. Most evaporation on Earth occurs over the continents. The bulk of the precipitation occurs over land. Most of the water that falls on the continents is derived from the oceans. Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 7 5/21/2014 8:02 PM Concept Review: Biogeochemical Cycles Can you sort the items by which biogeochemical cycle they apply to? Part A Drag each description to the appropriate bin. ANSWER: Score Summary: Your score on this assignment is 62.3%. You received 12.45 out of a possible total of 20 points. Chapter 07 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 7 5/21/2014 8:02 PM

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