#$&* course Phy 121 9:30 July 23 If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
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Given Solution: `a** You have an inverse square force. Square the ratio of Earth radius to orbital radius and multiply by 9.8 m/s^2: Field strength=(Re/r)^2*9.8m/s^2 ** STUDENT COMMENT I used G M_earth / r^2. Wonder if they get the same result. INSTRUCTOR RESPONSE For r > Re, the expressions G M_earth / r^2 and (Re/r)^2*9.8m/s^2 give the same results, to the number of significant figures dictated by the known quantities. The first formula is inherently more accurate, because the radius of the Earth is not the same at the poles as at the equator, with the result that Re is not known as precisely as G and the mass of the Earth. STUDENT QUESTION: ???? I don't think I understand the answer. Is mine correct? ????? INSTRUCTOR RESPONSE: Your method is completely equivalent to this one, though you didn't actually show the expressions you would get: • a_grav = k / r^2, and a_grav = g =9.8 m/s^2 when R = R_e, the radius of the Earth. Thus • 9.8 m/s^2 = k / R_e^2 and • k = 9.8 m/s^2 * R_e^2. The proportionality becomes • a_grav = 9.8 m/s^2 * R_e^2 / r^2 = 9.8 m/s^2 * (R_e / r)^2. Any proportionality of the form • y = k x^p implies that if y1 = k x1^p and y2 = k x2^p, we have • y2 / y1 = k x1^p / (k x2^p) = (x1 / x2)^p. In the current case p = -2, the y quantity would be the acceleration of gravity and the x quantity would be the distance from the center of the Earth. Using y1 = g and x1 = R_e, with y2 = a_grav and x2 = r, we have • a_grav / g = (r / R_e)^(-2) so that • a_grav = g * (R_e / r)^2. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qIf we double our distance from the center of the Earth, what happens to the gravitational field strength we experience? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Around 1/4 the gravitational field confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** We have an inverse square force so if r2 = 2 * r1 the ratio of the gravitational field will be g2 / g1 = (1 / r2^2) / (1 / r1^2) = r1^2 / r2^2 = (r1 / r2)^2 = (r1 / (2 * r1))^2 = r1^2 / 4 r1^2 = 1/4. In a nutshell double the radius gives us 1 / 2^2 = 1/4 the gravitational field. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ********************************************* Question: `qQuery class notes #24 Describe the paths of various particles 'shot' parallel to the surface of the Earth from the top of a very high tower, starting with a very small velocity and gradually increasing to a velocity sufficient to completely escape the gravitational field of the Earth. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I’m not too sure how to answer this…. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aGOOD STUDENT ANSWER: Each particle sets out to follow an orbit around the center of mass of the earth. But for particles shot at slower speeds, this path is interupted by the surface of the eath and simply stops there. The faster it is shot, the further x distance becomes before the particle lands. However, if it given a great enough velocity, it will fall around the curviture of the earth. If is shot even faster than that, it will follow an eliptical oribit with varying speeds and distances from center of earth. GOOD STUDENT ANSWER: With a very low velocity the projectile will not traveled as far. It will fall to earth in a nearly parabolic fashion since it gains vertical velocity as it travels horizontally at a steady pace. If the projectile is fired at a very strong velocity it will leave the earths vacinity but will still be pulled by the forces acting on it from the earths center. This will cause it to go only so far at which point it has slowed down considerabley, since it has lost most of its kinetic energy. It turns and begins to gain energy as it approaches the earths area, using the potential energy it gained on the trip out. (Causing it to speed up). The path that this projectile will take will be eliptical, and it will continue to loop around the earth. If the projectile is fired at the correct velocity to form a circular orbit, it will also fall at a parabolic fashion, although the earth's surface will also be descending at the same rate so that the object will appear to be 'not falling'. It is falling but at the same rate the earth is 'falling' under it. It will circle the earth until something causes it to stop. INSTRUCTOR RESPONSE: The path of the projectile will always be an ellipse with the center of the Earth at one focus. For low velocities and low altitude this path is very nearly parabolic before being interrupted by the surface of the Earth. One of these ellipses is a perfect circle and gives us the circular orbit we use frequently in this section. ** STUDENT COMMENT: I thought this object left the earths force...if not i understand it will fall back to earth as a normal projectile because of a small velocity and have a parabolic path because gravity will take over
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Given Solution: `a** For a given distance from the center of the Earth, there is only one velocity for which centripetal acceleration is equal to gravitational acceleration, so there is only one possible velocity for a circular orbit of given orbital radius. The orbital radius is determined by the height of the 'tower', so for a given tower there is only one velocity which will achieve a circular orbit. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qIs it necessary in order to achieve a circular orbit to start the object out in a direction parallel to the surface of the Earth? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If you have only one shot than it would definitely seem to be necessary… confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** If you have just one 'shot' then you must start out parallel to the surface of the Earth. The reason is that any circle about the center must be perpendicular at every point to a radial line--a line drawn from the center to the circle. Any radial line will intercept the surface of the Earth and must be perpendicular to it, and the circular orbit must also be perpendicular to this line. Therefore the orbit and the surface are perpendicular to the same line and are therefore parallel. ** STUDENT COMMENT: im now seeing the idea of a launch paralell to earth. the tower needs to be pretty tall then. the velocity needs to be headed in the direction of the orbit it will take. INSTRUCTOR REPSONSE: The main reason it has to be very tall is because of the atmosphere. If you shoot the projectile with sufficient speed while it's in the atmosphere, it will quickly lose most of its kinetic energy to air resistance; the energy goes mostly into heating the object, which as a result proceeds to melt as its orbit decays. Whether it melts before hitting the ground or not depends on how quickly the orbit decays and how high it was in the first place. If there was no atmosphere, you still would need to be careful about the flattening of the Earth at the equator (the radius at the equator is about 20 km greater than the radius at the poles, which means that if you wanted an orbit that took you over the equator, then even in the absence of atmosphere a tower at the pole would have to be at least 20 km high. STUDENT QUESTION When a rocket is launched why is it pointed straight up, isnt this perpendicular to the earth surface, would it be more effective to have it pointed at an angle to be shot parallel with the orbit and the surface of the earth? INSTRUCTOR RESPONSE Excellent question. You want to get out of the atmosphere as quickly as possible, to minimize the work you need to do against air resistance. A vertical launch position is much more stable than one at an angle away from vertical. Same reason we build towers vertical rather than leaning. The launch starts out vertical, and gradually curves toward the tangential direction. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qPrinciples of Physics and General College Physics Problem 5.2: A jet traveling at 525 m/s moves in an arc of radius 6.00 km. What is the acceleration of the jet? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: (525 m/s)^2 / (6000 m) = 45.9 m/s^2 (45.9 m/s^2) / (9.8 m/s^2) = 4.68 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aThe jet will have centripetal acceleration a_cent = v^2 / r, where v is its speed and r the radius of the circle on which it is traveling. In this case we have v = 525 m/s and r = 6.00 km = 6000 meters. The centripetal acceleration is therefore a_cent = v^2 / r = (525 m/s)^2 / (6000 m) = 45 m/s^2, approx.. One 'g' is 9.8 m/s^2, so this is about (45 m/s^2) / (9.8 m/s^2) = 4.6 'g's'. STUDENT QUESTION: there are roughly 1600m in a mile I believe, so 45m/s would be 2700m a minute and 162,000m/hr. so that would be roughly 100mi/hour, am I making a math error here or is that speed really 4.6g’s??? INSTRUCTOR RESPONSE: That speed would be about 100 mph. However 100 mph is not an acceleration, but as you say, a speed. g's measure acceleration, not speed. Nothing here is moving at 45 m/s. There is a centripetal acceleration of 45 m/s^2. One 'g' is 9.8 m/s^2. So 45 m/s^2 is somewhat more than 4 'g's'. It is in fact 4.6 g's. STUDENT QUESTION What does g stand for? INSTRUCTOR RESPONSE g stands for the acceleration of gravity. One 'g' is 9.8 m/s^2. Two 'g's' would be 19.6 m/s^2. etc. At 10 g's you pass out; if you continue this acceleration for more than a couple of minutes you die. A fighter jet in a turn can withstand 10 g's; the pilot can't. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `qPrinciples of Physics and General College Physics Problem 5.2: A jet traveling at 525 m/s moves in an arc of radius 6.00 km. What is the acceleration of the jet? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: (525 m/s)^2 / (6000 m) = 45.9 m/s^2 (45.9 m/s^2) / (9.8 m/s^2) = 4.68 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aThe jet will have centripetal acceleration a_cent = v^2 / r, where v is its speed and r the radius of the circle on which it is traveling. In this case we have v = 525 m/s and r = 6.00 km = 6000 meters. The centripetal acceleration is therefore a_cent = v^2 / r = (525 m/s)^2 / (6000 m) = 45 m/s^2, approx.. One 'g' is 9.8 m/s^2, so this is about (45 m/s^2) / (9.8 m/s^2) = 4.6 'g's'. STUDENT QUESTION: there are roughly 1600m in a mile I believe, so 45m/s would be 2700m a minute and 162,000m/hr. so that would be roughly 100mi/hour, am I making a math error here or is that speed really 4.6g’s??? INSTRUCTOR RESPONSE: That speed would be about 100 mph. However 100 mph is not an acceleration, but as you say, a speed. g's measure acceleration, not speed. Nothing here is moving at 45 m/s. There is a centripetal acceleration of 45 m/s^2. One 'g' is 9.8 m/s^2. So 45 m/s^2 is somewhat more than 4 'g's'. It is in fact 4.6 g's. STUDENT QUESTION What does g stand for? INSTRUCTOR RESPONSE g stands for the acceleration of gravity. One 'g' is 9.8 m/s^2. Two 'g's' would be 19.6 m/s^2. etc. At 10 g's you pass out; if you continue this acceleration for more than a couple of minutes you die. A fighter jet in a turn can withstand 10 g's; the pilot can't. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!