course Phy121 Included here is the q_a_area_volumes_misc.exe asst 4 and also the query for assignment 4.
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01:55:48 `q001. There are 10 questions and 5 summary questions in this assignment. How many cubic centimeters of fluid would require to fill a cubic container 10 cm on a side?
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RESPONSE --> We need to find the volume of the cube. Since V = A *h, the A = 10*10 = 100 h = 10 100 * 10 = 1000 cm^3 or 1 Liter
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01:55:56 The volume of the container is 10 cm * 10 cm * 10 cm = 1000 cm^3. So it would take 1000 cubic centimeters of fluid to fill the container.
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RESPONSE --> ok
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01:56:52 `q002. How many cubes each 10 cm on a side would it take to build a solid cube one meter on a side?
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RESPONSE --> If each cube is 10 cm, and 10 cm = .10 M We would need 10 cubes. 10 cubes & 10 cm = 100 cm which = 1 meter.
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01:58:06 It takes ten 10 cm cubes laid side by side to make a row 1 meter long or a tower 1 meter high. It should therefore be clear that the large cube could be built using 10 layers, each consisting of 10 rows of 10 small cubes. This would require 10 * 10 * 10 = 1000 of the smaller cubes.
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RESPONSE --> For some reason I thought it was 1 meter high, not an entire cube measuring 1 meter on each side.
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02:01:27 `q003. How many square tiles each one meter on each side would it take to cover a square one km on the side?
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RESPONSE --> 1 km = 1000 meters so it would take 1000 squares per side. A = l x w or 1000 x 1000 = 1,000,000 squares
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02:01:47 It takes 1000 meters to make a kilometer (km). To cover a square 1 km on a side would take 1000 rows each with 1000 such tiles to cover 1 square km. It therefore would take 1000 * 1000 = 1,000,000 squares each 1 m on a side to cover a square one km on a side. We can also calculate this formally. Since 1 km = 1000 meters, a square km is (1 km)^2 = (1000 m)^2 = 1,000,000 m^2.
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RESPONSE --> Ok.
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02:02:02 `q004. How many cubic centimeters are there in a liter?
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RESPONSE --> There are 1000 cm^3 in a liter.
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02:02:17 A liter is the volume of a cube 10 cm on a side. Such a cube has volume 10 cm * 10 cm * 10 cm = 1000 cm^3. There are thus 1000 cubic centimeters in a liter.
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RESPONSE --> ok.
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02:04:59 `q005. How many liters are there in a cubic meter?
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RESPONSE --> If it takes 1000 10cm cubes to make a cube 1 meter on a side, that is 1,000,000 cm^3 in volume. If it takes 1000 cm^3 per Liter, there are 1000 liters in 1 m^3.
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02:15:13 A liter is the volume of a cube 10 cm on a side. It would take 10 layers each of 10 rows each of 10 such cubes to fill a cube 1 meter on a side. There are thus 10 * 10 * 10 = 1000 liters in a cubic meter.
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RESPONSE --> ok
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02:15:35 `q006. How many cm^3 are there in a cubic meter?
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RESPONSE --> Based on the last question, there are 1,000,000 cm^3 in 1 m^3
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02:16:53 There are 1000 cm^3 in a liter and 1000 liters in a m^3, so there are 1000 * 1000 = 1,000,000 cm^3 in a m^3. It's important to understand the 'chain' of units in the previous problem, from cm^3 to liters to m^3. However another way to get the desired result is also important: There are 100 cm in a meter, so 1 m^3 = (1 m)^3 = (100 cm)^3 = 1,000,000 cm^3.
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RESPONSE --> I figured there was another way to convert, but I was not sure because of the ^3.
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02:18:03 `q007. If a liter of water has a mass of 1 kg the what is the mass of a cubic meter of water?
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RESPONSE --> 1 m^3 = 1000 liters, if 1 L = 1kg, then 1000 L = 1000 kg, therefore 1m^3 of water weights 1000 kg.
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02:18:11 Since there are 1000 liters in a cubic meter, the mass of a cubic meter of water will be 1000 kg. This is a little over a ton.
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RESPONSE --> ok.
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02:23:19 `q008. What is the mass of a cubic km of water?
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RESPONSE --> 1m^3 = 1000 kg (1km)^3 = (1000m)^3 = 1,000,000,000 m^3 * 1000 = 1.0 x 10^12 kg.
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02:26:50 A cubic meter of water has a mass of 1000 kg. A cubic km is (1000 m)^3 = 1,000,000,000 m^3, so a cubic km will have a mass of 1,000,000,000 m^3 * 1000 kg / m^3 = 1,000,000,000,000 kg. In scientific notation we would say that 1 m^3 has a mass of 10^3 kg, a cubic km is (10^3 m)^3 = 10^9 m^3, so a cubic km has mass (10^9 m^3) * 1000 kg / m^3 = 10^12 kg.
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RESPONSE --> ok.
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02:35:57 `q009. If each of 5 billion people drink two liters of water per day then how long would it take these people to drink a cubic km of water?
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RESPONSE --> If 5 billion people drank 2 liters per day, this would total 10,000,000,000 liters per day or 1.0 x 10^10 Since 1m^3 = 1000L and 1km^3 = 1,000,000,000 m^3 or 1 x10^9m^3 We would then multiply 1 x 10^9 * 1000 = 1 x 10^12 L, which represents the total amount of liters in 1 km^3 We then divide the total number of L in 1km^3, by the amount that the people are drinking daily. 1x10^12/1x10^10 = 100 days
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02:36:21 5 billion people drinking 2 liters per day would consume 10 billion, or 10,000,000,000, or 10^10 liters per day. A cubic km is (10^3 m)^3 = 10^9 m^3 and each m^3 is 1000 liters, so a cubic km is 10^9 m^3 * 10^3 liters / m^3 = 10^12 liters, or 1,000,000,000,000 liters. At 10^10 liters per day the time required to consume a cubic km would be time to consume 1 km^3 = 10^12 liters / (10^10 liters / day) = 10^2 days, or 100 days. This calculation could also be written out: 1,000,000,000,000 liters / (10,000,000,000 liters / day) = 100 days.
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RESPONSE --> ok
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02:42:51 `q010. The radius of the Earth is approximately 6400 kilometers. What is the surface area of the Earth? If the surface of the Earth was covered to a depth of 2 km with water that what would be the approximate volume of all this water?
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RESPONSE --> SA = 4 Pi r^2 SA = 163,840,000Pikm^2 I know it's late and perhaps I am tired, but I want to say we would multiply the surface area by the 2km to get the approximate volume of all this water, since the water covers the entire surface area of the earth, and then we need to multiply that by its depth of 2km. 327,680,000 Pi km^2 ???
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02:45:08 The surface area would be A = 4 pi r^2 = 4 pi ( 6400 km)^2 = 510,000,000 km^2. A flat area of 510,000,000 km^2 covered to a depth of 2 km would indicate a volume of V = A * h = 510,000,000 km^2 * 2 km = 1,020,000,000 km^3. However the Earth's surface is curved, not flat. The outside of the 2 km covering of water would have a radius 2 km greater than that of the Earth, and therefore a greater surface area. However a difference of 2 km in 6400 km will change the area by only a fraction of one percent, so the rounded result 1,020,000,000,000 km^3 would still be accurate.
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RESPONSE --> Ok, so I was correct. I did not calculate out with Pi, but my answer would be close to the one you have.
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02:46:04 `q011. Summary Question 1: How can we visualize the number of cubic centimeters in a liter?
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RESPONSE --> we can envision the number of layers and rows and cubes required to fill a Liter volume.
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02:47:08 Since a liter is a cube 10 cm on a side, we visualize 10 layers each of 10 rows each of 10 one-centimeter cubes, for a total of 1000 1-cm cubes. There are 1000 cubic cm in a liter.
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RESPONSE --> I did not provide specific measurements. I envision sugar cubes when trying to set this up.
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02:48:16 `q012. Summary Question 2: How can we visualize the number of liters in a cubic meter?
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RESPONSE --> Since we know that 10cm cubes in 10 layers of 10 rows of 10 cubes each represent 1 m^3, and we know that a cube cm on each side represents a liter, we can exchange these 10cm cubes for liters.
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02:48:32 Since a liter is a cube 10 cm on a side, we need 10 such cubes to span 1 meter. So we visualize 10 layers each of 10 rows each of 10 ten-centimeter cubes, for a total of 1000 10-cm cubes. Again each 10-cm cube is a liter, so there are 1000 liters in a cubic meter.
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RESPONSE --> ok.
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02:49:55 `q013. Summary Question 3: How can we calculate the number of cubic centimeters in a cubic meter?
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RESPONSE --> Since (1m)^3 = (100cm)^3 (100cm)^3 = 1,000,000 cm^3 = 1m^3
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02:50:09 One way is to know that there are 1000 liters in a cubic meters, and 1000 cubic centimeters in a cubic meter, giving us 1000 * 1000 = 1,000,000 cubic centimeters in a cubic meter. Another is to know that it takes 100 cm to make a meter, so that a cubic meter is (100 cm)^3 = 1,000,000 cm^3.
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RESPONSE --> ok.
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02:53:39 `q014. Summary Question 4: There are 1000 meters in a kilometer. So why aren't there 1000 cubic meters in a cubic kilometer? Or are there?
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RESPONSE --> 1000 meters per kilometer is a length on a flat or one dimensional plane. This amount can represent a side of a cube, but it does not represent the entire volume of that cube, which has more than one side. cubic m and cubic km are measurements of volume, not length, so we cannot use the same conversions as we do when converting different lengths. There are 1000 cubic meters in a cubic kilometer, but the 1000 makes up a part of the total volume of the cubic kilometer.
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02:54:48 A cubic kilometer is a cube 1000 meters on a side, which would require 1000 layers each of 1000 rows each of 1000 one-meter cubes to fill. So there are 1000 * 1000 * 1000 = 1,000,000,000 cubic meters in a cubic kilometer. Alternatively, (1 km)^3 = (10^3 m)^3 = 10^9 m^3, not 1000 m^3.
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RESPONSE --> Ok. I'm sorry, I'm not doing a very good job with the explanations. I do understand the conversions, and also the visualizations but for some reason I'm pushing through this quicker than I should.
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02:57:17 `q015. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> As stated earlier, I envision a lot of sugar cubes, stacked to form the larger solid cubes of varying volumes (1m^3, 1km^3). As you can tell, I would have to envision a lot! This exercise has definitely assisted with organizing the differences between area and volume, both in how they are related and also how they differ. The area represents the surface, whereas the volume looks at the entire object, all the lengths, the amount required to fill, etc. etc.
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y Ս assignment #004 004. `Query 4 Physics I 02-10-2006
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03:03:02 Intro Prob 6 given init vel, accel, `dt find final vel, dist If initial velocity is v0, acceleration is a and time interval is `dt, then in symbols what are the final velocity vf and the displacement `ds?
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RESPONSE --> v) a `dt a=(vf-v0)/'dt from this we can solve for vf a*`dt = vf-v0 a*`dt-v0 = vf a*`dt = `ds
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03:05:42 **You would use accel. and `dt to find `dv: a * `dt = `dv. Adding `dv to initial vel. vo you get final vel. Then average initial vel. and final vel. to get ave. vel.: (v0 + vf) / 2 = ave. vel. You would then multiply ave. vel. and `dt together to get the distance. For example if a = 3 m/s^2, `dt = 5 s and v0 = 3 m/s: 3 m/s^2 * 5 s = 15 m/s = `dv 15 m/s + 3 m/s = 18 m/s = fin. vel. (18 m/s + 3 m/s) / 2 = 10.5 m/s = vAve 10.5 m/s * 5 s = 52.5 m = dist. In more abbreviated form: a * `dt = `dv v0 + `dv = vf (vf + v0) /2 = vAve vAve * `dt = `ds so `ds = (vf + v0) / 2 * `dt. **
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RESPONSE --> Ok, I for some reason was thinking from acceleration we could find displacement, but obviously that cannot be. Average accleration can help me find intial and final velocity, but does not tell me displacement. From `dv we can find vAve. This would assume uniform acceleration, correct?
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03:09:27 What is the displacement `ds associated with uniform acceleration from velocity v0 to velocity vf in clock time `dt?
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RESPONSE --> vAve = (vf-v0)/2 and since vAve = `ds/`dt then `ds = vAve * `dt which = (v0 + vf) / 2 * `dt
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03:50:01 ** Since accel is uniform vAve = (v0 + vf) / 2. Thus displacement is `ds = vAve * `dt = (v0 + vf) / 2 * `dt, which is the first equation of uniformly accelerated motion. **
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RESPONSE --> ok. i did not see it stated that the acceleration was uniform, so I assumed it was.
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03:59:12 Describe the flow diagram we obtain for the situation in which we know v0, vf and `dt.
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RESPONSE --> We typically start with the `dt at top, then that feeds into `dv, which we know from vf-v0. From the `dv and `dt, we can also figure out a (acceleration). Then from the vf-v0 we can next calculate vAve. Then when you multiply vAve *`dt, we can find `ds.
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04:00:09 ** The first level in the diagram would contain `dt, v0 and vf. Then v0 and vf would connect to `dv in the second level. The second level would also contain vAve, connected from vf in the first level to v0 in the first level. The third level would contain an a, connected to `dv in the second level and `dt in the first level. The third level would also contain `ds, connected to vAve in the fourth level and `dt in the first level. **
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RESPONSE --> ok, I think I tried to make it fit to the example we were shown in the notes. We can create a flow chart beginning with the variables we know and work our way from that start.
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04:00:38 Query Add any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> As stated, that rather than fitting in the pieces we knew into the flow chart we reviewed in class, I should have created one based on these variables.
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04:00:56 ** Student Response: I think I really confused what information stood for what in the Force and Pendulum Experiment. However, I enjoy doing the flow diagrams. They make you think in a different way than you are used to. INSTRUCTOR NOTE: These diagrams are valuable for most people. Not all--it depends on learning style--but most. **
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RESPONSE --> ok
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