course MTH 174 }E胫{{xassignment #009
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23:04:27 query problem 8.4.3 (8.3.4 3d edition) was 8.2.6) moment of 2 meter rod with density `rho(x) = 2 + 6x g/m
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RESPONSE --> (a) The sum of 2 + 6x * `dx approximates the mass (b) The integral from 0 to 2 of (2 + 6x) dx = (3(2)^2 - 3(0)^2) = 12 g
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23:56:27 what is the moment of the rod?
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RESPONSE --> The integral from 0 to 2 of x(2 + 6x) dx = 20
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23:56:58 What integral did you evaluate to get a moment?
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RESPONSE --> The integral from 0 to 2 of x(2 + 6x) dx
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21:43:29 query problem 8.4.12 (was 8.2.12) mass between graph of f(x) and g(x), f > g, density `rho(x)
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RESPONSE --> [ The integral from a to b of (f(x) - g(x) dx ] * [ (1/(b - a)) * the integral from a to b of `rho(x) dx ] = mass
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21:43:47 what is the total mass of the region?
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RESPONSE --> [ The integral from a to b of (f(x) - g(x) dx ] * [ (1/(b - a)) * the integral from a to b of `rho(x) dx ] = mass
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21:44:28 What integral did you evaluate to obtain this mass?
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RESPONSE --> [ The integral from a to b of (f(x) - g(x) dx ] * [ (1/(b - a)) * the integral from a to b of `rho(x) dx ] = mass
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23:02:05 What is the mass of an increment at x coordinate x with width `dx?
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RESPONSE --> [ The integral from x to (x+`dx) of (f(x) - g(x) dx ] * [ (1/(b - a)) * the integral from x to (x+`dx) of `rho(x) dx ] = mass
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23:04:32 What is the area of the increment, and how do we obtain the expression for the mass from this area?
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RESPONSE --> [ The integral from x to (x+`dx) of (f(x) - g(x) dx ] = area (cm^2) cm^2 * g/cm^2 = g = mass
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23:07:16 How to we use the mass of the increment to obtain the integral for the total mass?
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RESPONSE --> Plug in the increment of the total mass (from a to b).
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assignment #009 Ճ߉mְWb Physics II 12-01-2007
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10:41:11 query problem 8.4.3 (8.3.4 3d edition) was 8.2.6) moment of 2 meter rod with density `rho(x) = 2 + 6x g/m
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RESPONSE -->
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10:41:27 what is the moment of the rod?
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RESPONSE -->
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10:41:58 what is the moment of the rod?
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RESPONSE -->
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10:42:02 What integral did you evaluate to get a moment?
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RESPONSE -->
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10:42:04 query problem 8.4.12 (was 8.2.12) mass between graph of f(x) and g(x), f > g, density `rho(x)
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RESPONSE -->
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10:42:06 what is the total mass of the region?
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RESPONSE -->
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10:42:08 What integral did you evaluate to obtain this mass?
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RESPONSE -->
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10:42:10 What is the mass of an increment at x coordinate x with width `dx?
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RESPONSE -->
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10:42:16 What is the area of the increment, and how do we obtain the expression for the mass from this area?
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RESPONSE -->
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10:42:20 How to we use the mass of the increment to obtain the integral for the total mass?
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RESPONSE -->
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22:25:06 query problem 8.5.13 (8.4.10 3d edition; was 8.3.6) cylinder 20 ft high rad 6 ft full of water
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RESPONSE --> The water at the top of the tank will not have to be pumped as far as the water at the bottom of the tank. The total distance over which the water will be pumped is a function of the height of the water. The density of water at STP is 62.4 lb/ft^3. The area of the tank is `pi * (6 ft.)^2 * 20 ft = 2261.95 ft^3. It the tank is full, the water weighs 141,146 lb Work = Force * Distance Work = 2,822,909.50 ft-lb
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22:42:25 how much work is required to pump all the water to a height of 10 ft?
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RESPONSE --> approximately 2,822,910 ft-lbs.
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22:48:21 What integral did you evaluate to determine this work?
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RESPONSE --> [The integral from 0 to 20 of 36 `pi (x + 10) dx]ft^3 * ft * 62.4 lb/ft^3 = lb * ft = lb-ft.
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22:55:03 Approximately how much work is required to pump the water in a slice of thickness `dy near y coordinate y? Describe where y = 0 in relation to the tank.
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RESPONSE --> 62.4 * (36 `pi * `dy)((20-y) + 10) = Work (lb-ft.) The bottom of the tank is at y = 0.
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22:55:35 12-01-2007 22:55:35 Explain how your answer to the previous question leads to your integral.
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NOTES ------->
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assignment #009 Ճ߉mְWb Physics II 12-01-2007
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22:56:17 query problem 8.4.3 (8.3.4 3d edition) was 8.2.6) moment of 2 meter rod with density `rho(x) = 2 + 6x g/m
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RESPONSE -->
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22:56:19 what is the moment of the rod?
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RESPONSE -->
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22:56:21 What integral did you evaluate to get a moment?
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RESPONSE -->
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22:56:22 query problem 8.4.12 (was 8.2.12) mass between graph of f(x) and g(x), f > g, density `rho(x)
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RESPONSE -->
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22:56:23 what is the total mass of the region?
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RESPONSE -->
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22:56:25 What integral did you evaluate to obtain this mass?
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RESPONSE -->
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22:56:26 What is the mass of an increment at x coordinate x with width `dx?
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RESPONSE -->
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22:56:28 What is the area of the increment, and how do we obtain the expression for the mass from this area?
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RESPONSE -->
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22:56:29 How to we use the mass of the increment to obtain the integral for the total mass?
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RESPONSE -->
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22:56:31 query problem 8.5.13 (8.4.10 3d edition; was 8.3.6) cylinder 20 ft high rad 6 ft full of water
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RESPONSE -->
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22:56:33 how much work is required to pump all the water to a height of 10 ft?
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RESPONSE -->
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22:56:35 What integral did you evaluate to determine this work?
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RESPONSE -->
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22:58:03 Approximately how much work is required to pump the water in a slice of thickness `dy near y coordinate y? Describe where y = 0 in relation to the tank.
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RESPONSE -->
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23:24:47 Explain how your answer to the previous question leads to your integral.
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RESPONSE --> 62.4 * (36 `pi * `dy)((20-y) + 10) = 62.4 * 36 `pi (y + 10) `dy = 62.4 * [The integral from 0 to 20 of 36 `pi (y + 10) dy]
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00:05:25 query problem 8.3.18 CHANGE TO 8.5.15 work to empty glass (ht 15 cm from apex of cone 10 cm high, top width 10 cm)
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RESPONSE --> Problem 8.5.15 on page 407, fuel oil tank cylinder burried 10 ft. beneath the surface with radius 5 ft, 15 ft high, with current oil level at 6 ft. Work required to pump all oil to the surface: oil weighs 50 lb/ft^3 Oil level begins at depth 10 + (15 - 6) = 19ft. 50 * 25 `pi `dy ((6 - y) + 19) 50 * the integral from 0 to 6 of 25 `pi (25 - y) dy = 518,363 lb-ft
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00:05:34 how much work is required to raise all the drink to a height of 15 cm?
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RESPONSE --> 518,363 lb-ft
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00:05:51 What integral did you evaluate to determine this work?
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RESPONSE --> 50 * the integral from 0 to 6 of 25 `pi (25 - y) dy
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00:06:08 Approximately how much work is required to raise the drink in a slice of thickness `dy near y coordinate y? Describe where y = 0 in relation to the tank.
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RESPONSE --> 50 * 25 `pi `dy ((6 - y) + 19)
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00:06:31 How much drink is contained in the slice described above?
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RESPONSE -->
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00:06:35 What are the cross-sectional area and volume of the slice?
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RESPONSE -->
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00:06:38 Explain how your answer to the previous questions lead to your integral.
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RESPONSE -->
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00:07:10 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I'm not sure which problem you wanted for that last one.
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