course PHy 121
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22:16:04 `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 --> Volume of a cube = length ^3 V = 10cm^3 = 1000cm^3
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22:16:14 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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22:21:22 `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 --> There are 100 centimeters in one meter. So ten 10cm cubes would make the 1 meter side. If the cubes are 10cm on each side, they are 1000cm^3 in volume. The bigger cube is 1m or 100cm on each side, so they are 10^6 cm^3 in volume. If we divide 10^6 cm^3 by 1000cm^3 we see that there must be 1000 of the smaller cubes.
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22:21:33 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 --> I understand this problem.
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22:23:57 `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 --> There are 1000 meters in one kilometer. So it would take 1000 of the one meter tiles to cover one side of the the square. So the area of the bigger square would be 1000m x 1000m. This means there are 10^6 of the small squares in the bigger square.
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22:24:12 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 --> I understand.
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22:26:07 `q004. How many cubic centimeters are there in a liter?
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RESPONSE --> One cubic centimeter is equal to one milliliter. There are 1000 milliliters in one liter. Therefore, there are 1000 cubic centimeters in one liter.
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22:29:16 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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22:30:01 `q005. How many liters are there in a cubic meter?
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RESPONSE --> There are 1000 milliliters in one liter. Since 1 mL = 1 cm^3, there are 1000 cubic centimeters in one liter. A cubic meter is 10^6 cm^3 in volume. so there are 1000 liters in one cubic meter: One cubic meter, 10^6 cm^3, divided by one liter, 1000cm^3, gives us 1000.
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22:32:31 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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22:33:59 `q006. How many cm^3 are there in a cubic meter?
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RESPONSE --> There are 100 centimeters in one meter. So there are (100cm)^3 in one cubic meter. This means 1 m^3 = 10^6 cm^3.
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22:36:56 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 --> Ok.
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22:37:19 `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 --> 1000 L = 1m^3 1cm^3 of water = 1kg 1m^3 of water = 1000kg
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22:38:28 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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22:39:23 `q008. What is the mass of a cubic km of water?
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RESPONSE --> 1km^3 = (1000m)^3 =10^9 m^3 1m^3 = 1000kg 1km^3 = (10^9 m^3)(1000kg/m^3) = 10^12 kg
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22:42:08 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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22:44:48 `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 --> (2L)(5 x 10^9) = 10^10 L/day 1000 L = 1 m^3 1km = 10^3m 1km^3 = (10^3m)^3 = 10^9 m^3 1km^3 = (10^9 m^3)(1000L/m^3) = 10^12 L (10^12L)/(10^10 L/d) = 100 days
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22:47:35 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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22:49:24 `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 --> Surface area of a sphere: A = 4pi(r^2) A = 4pi(6400km^2) = 163840000pi km^2 Volume = Area x depth V = (163840000pi km^2)(2km) = approx 1.03 x 10^9 km^3
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22:49:30 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
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22:49:41 `q011. Summary Question 1: How can we visualize the number of cubic centimeters in a liter?
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RESPONSE --> We visualize cubic centimeters in a liter as 10 layers of 10 rows of 10 cubes that are 10cm on a side.
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22:49:52 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 --> OK
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22:50:38 `q012. Summary Question 2: How can we visualize the number of liters in a cubic meter?
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RESPONSE --> We can visulize the number of liters in a cubic meter as 10 layers of 10 rows of 10 cubes that are 10 cm on each side. Since 1 ten centimeter cube is a liter, there are 1000 liters in one cubic meter.
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22:50:48 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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22:51:44 `q013. Summary Question 3: How can we calculate the number of cubic centimeters in a cubic meter?
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RESPONSE --> We know that there are 100 cm in one meter. Since 1 m^3 = (1m)^3, we can say that 1m^3 = (100cm)^3. So there are 100^3 cm^3 or 10^6 cm^3 in one cubic meter.
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22:52:02 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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22:54:17 `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 --> Because you have to say that one cubic km is 1km x 1km x 1km. Which is the same as 1000m x 1000m x 1000m because 1000 meters equals 1 kilometer. so there are actually 10^9 cubic meters in one cubic kilometer.
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22:54:22 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
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22:55:54 `q015. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> I added these knew formulas for volume to my notes.
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22:55:59 This ends the fourth assignment.
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RESPONSE -->
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ǒkxԎaʷ¡ÁwP assignment #004 ۶mSۥ} Physics I 06-11-2006
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16:33:49 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 --> `dv = a x `dt vf = `dv + vo (vf + vo) / 2 = vAve `ds = vAve x `dt
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16:35:38 **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.
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16:37:18 What is the displacement `ds associated with uniform acceleration from velocity v0 to velocity vf in clock time `dt?
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RESPONSE --> `ds = (vf + vo)/2 x `dt Displacement equals the average velocity multiplied by the time interval.
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16:37:26 ** 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
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16:41:56 Describe the flow diagram we obtain for the situation in which we know v0, vf and `dt.
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RESPONSE --> The flow diagram shows from left to right as you move down: Top:`dt, a, vo Next: `dv, vf Bottom: vAve, `ds This diagram represents the process in which first we calculate velocity change (`dv) from acceleration (a) and time interval (`dt). Next it shows that we ontain the final velocity (vf) by adding the velocity change (`dv) and the intial velocity (vo). Then we add the final and intitial velocities together and get the average velocity, vAve: (vf + vo) / 2. Finally, we use the average velocity (vAve) and the time interval (`dt) to find displacement (`ds): `ds = vAve x `dt.
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16:42:20 ** 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
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16:42:49 Query Add any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I don't really know how to find force. I was a little confused with the Rubber Band Calibration experiment. Have we touched on force yet or is it a subject that will be discussed later on?
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16:43:45 ** 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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