course Phy 202 ݽé¬Ïú‘·Ý®ñ–ð¡“‹®åŽÊщƒª]yÜkƒ÷assignment #003
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19:48:12 `q003. What is surface area of a sphere of diameter three cm?
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RESPONSE --> skip confidence assessment: 0
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19:48:21 The surface area of a sphere of radius r is A = 4 pi r^2. This sphere has radius 3 cm / 2, and therefore has surface area A = 4 pi r^2 = 4 pi * (3/2 cm)^2 = 9 pi cm^2.
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RESPONSE --> self critique assessment: 3
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19:48:44 `q005. If the hypotenuse of a right triangle has length 6 meters and one of its legs has length 4 meters what is the length of the other leg?
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RESPONSE --> skip confidence assessment: 0
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19:48:52 If c is the hypotenuse and a and b the legs, we know by the Pythagorean Theorem that c^2 = a^2 + b^2, so that a^2 = c^2 - b^2. Knowing the hypotenuse c = 6 m and the side b = 4 m we therefore find the unknown leg: a = sqrt( c^2 - b^2) = sqrt( (6 m)^2 - (4 m)^2 ) = sqrt(36 m^2 - 16 m^2) = sqrt(20 m^2) = sqrt(20) * sqrt(m^2) = 2 sqrt(5) m, or approximately 4.4 m.
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RESPONSE --> self critique assessment: 3
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19:51:41 `q006. If a rectangular solid made of a uniform, homogeneous material has dimensions 4 cm by 7 cm by 12 cm and if its mass is 700 grams then what is its density in grams per cubic cm?
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RESPONSE --> D = m/v V= A * h V = 4 cm * 7 cm * 12 cm V = 336 cm^3 D = 700 g / 336 cm^3 D = 25/12 g/cm^3 or about 2.083 g/cm^3 confidence assessment: 3
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19:52:18 The volume of this solid is 4 cm * 7 cm * 12 cm = 336 cm^3. Its density in grams per cm^3 is the number of grams in each cm^3. We find this quantity by dividing the number of grams by the number of cm^3. We find that density = 700 grams / (336 cm^3) = 2.06 grams / cm^3. Note that the solid was said to be uniform and homogeneous, meaning that it's all made of the same material, which is uniformly distributed. So each cm^3 does indeed have a mass of 2.06 grams. Had we not known that the material was uniform and homogeneous we could have said that the average density is 2.06 grams / cm^3, but not that the density is 2.06 grams / cm^3 (the object could be made of two separate substances, one with density less than 2.06 grams / cm^3 and the other with density greater than 2.06 g / cm^3, in appropriate proportions; neither substance would have density 2.06 g / cm^3, but the average density could be 2.06 g / cm^3).
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RESPONSE --> Ok self critique assessment: 3
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19:56:12 `q007. What is the mass of a sphere of radius 4 meters if its average density is 3,000 kg/cubic meter?
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RESPONSE --> V = 4/3 pi r^3 V = 4/3 pi (4m)^3 V = 268.1 m^3 (approx) D = M/V D * V = M M = (3,000 kg/m^3) * 268.1 m^3 M = 804,247.7 kg confidence assessment: 2
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19:57:02 A average density of 3000 kg / cubic meter implies that, at least on the average, every cubic meter has a mass of 3000 kg. So to find the mass of the sphere we multiply the number of cubic meters by 3000 kg. The volume of a sphere of radius 4 meters is 4/3 pi r^3 = 4/3 * pi (4m)^3 = 256/3 * pi m^3. So the mass of this sphere is mass = density * volume = 256 / 3 * pi m^3 * 3000 kg / m^3 = 256,000 * pi kg. This result can be approximated to an appropriate number of significant figures.
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RESPONSE --> It would have been a more exact answer if I had left it in units of pi however it is still correct. self critique assessment: 2
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20:00:03 `q008. If we build a an object out of two pieces of material, one having a volume of 6 cm^3 at a density of 4 grams per cm^3 and another with a volume of 10 cm^3 at a density of 2 grams per cm^3 then what is the average density of this object?
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RESPONSE --> Object 1 Density = 4 g/cm^3 Object 2 Denisty = 2 g/cm^3 Average density = (4 g/cm^3 + 2 g/cm^3)/2 = 3 g/cm^3 confidence assessment: 2
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20:01:29 The first piece has a mass of 4 grams / cm^3 * 6 cm^3 = 24 grams. The second has a mass of 2 grams / cm^3 * 10 cm^3 = 20 grams. So the total mass is 24 grams + 20 grams = 44 grams. The average density of this object is average density = total mass / total volume = (24 grams + 20 grams) / (6 cm^3 + 10 cm^3) = 44 grams / (16 cm^3) = 2.75 grams / cm^3.
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RESPONSE --> I only averaged the two densities. I should have found the mass of both objects and then divided the total mass by the total volue to find the density of the created object. self critique assessment: 2
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20:26:52 `q009. In a large box of dimension 2 meters by 3 meters by 5 meters we place 27 cubic meters of sand whose density is 2100 kg/cubic meter, surrounding a total of three cubic meters of cannon balls whose density is 8,000 kg per cubic meter. What is the average density of the material in the box?
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RESPONSE --> M = D*V M = (3 m^3) * (8,000 kg/m^3) M = 24,000 kg M = D*V M = (2100 kg/m^3) * (27m^3) M = 56,700 kg ave mass = 80,700 kg/2 = 40350 kg ave vol = 30 m^3/ 2 = 15 m^3 ave D = ave M/ ave V ave D = 40, 350 kg / 15 m^3 ave D = 2,690 kg/m^3 confidence assessment: 2
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20:27:06 We find the average density from the total mass and the total volume. The mass of the sand is 27 m^3 * 2100 kg / m^3 = 56,700 kg. The mass of the cannonballs is 3 m^3 * 8,000 kg / m^3 = 24,000 kg. The average density is therefore average density = total mass / total volume = (56,700 kg + 24,000 kg) / (27 m^3 + 3 m^3) = 80,700 kg / (30 m^3) = 2,700 kg / m^3, approx..
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RESPONSE --> Ok self critique assessment: 3
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20:46:24 `q010. How many cubic meters of oil are there in an oil slick which covers 1,700,000 square meters (between 1/2 and 1 square mile) to an average depth of .015 meters? If the density of the oil is 860 kg/cubic meter the what is the mass of the oil slick?
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RESPONSE --> V = A * h V = 1,700,000 m^2 * .015 m V = 25500 m^3 D = M/V M = D * V M = 860 kg/m^3 * 25500 m^3 M = 21,930,000 kg confidence assessment: 3
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20:46:41 The volume of the slick is V = A * h, where A is the area of the slick and h the thickness. This is the same principle used to find the volume of a cylinder or a rectangular solid. We see that the volume is V = A * h = 1,700,000 m^2 * .015 m = 25,500 m^3. The mass of the slick is therefore mass = density * volume = 860 kg / m^3 * 24,400 m^3 = 2,193,000 kg. This result should be rounded according to the number of significant figures in the given information.
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RESPONSE --> Ok self critique assessment: 3
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20:48:50 `q011. Summary Question 1: How do we find the surface area of a cylinder?
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RESPONSE --> SA = (2 pi r l) + ( 2 pi r^2) confidence assessment: 2
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20:50:06 The curved surface of the cylinder can be 'unrolled' to form a rectangle whose dimensions are equal to the circumference and the altitude of the cylinder, so the curved surface has volume Acurved = circumference * altitude = 2 pi r * h, where r is the radius and h the altitude. The top and bottom of the cylinder are both circles of radius r, each with resulting area pi r^2. {]The total surface area is therefore Acylinder = 2 pi r h + 2 pi r^2.
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RESPONSE --> I should have explained that you can ""unroll"" it to form 1 rectangle and 2 circles thus you find the SA of the rectangle and that of the 2 circles. self critique assessment: 2
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20:50:37 `q012. Summary Question 2: What is the formula for the surface area of a sphere?
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RESPONSE --> SA = 4 pi r^2 confidence assessment: 3
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20:50:47 The surface area of a sphere is A = 4 pi r^2, where r is the radius of the sphere.
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RESPONSE --> Ok self critique assessment: 3
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20:53:21 `q013. Summary Question 3: What is the meaning of the term 'density'.
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RESPONSE --> Density a property of matter that can be used to identify different materials. It is the ratio of mass to volume. It can be used to identify all the elements. confidence assessment: 2
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20:54:50 The average density of an object is its mass per unit of volume, calculated by dividing its total mass by its total volume. If the object is uniform and homogeneous then its density is constant and we can speak of its 'density' as opposed to its 'average density'
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RESPONSE --> I did not distinguish between average density and density. Density is for a constant homogeneous material and average density is not. As well I should have stated the formula Density = mass/volume self critique assessment: 2
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20:55:24 `q014. Summary Question 4: If we know average density and mass, how can we find volume?
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RESPONSE --> You can multiply the average density and the mass and find the average volume confidence assessment: 3
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20:55:37 Since mass = ave density * volume, it follows by simple algebra that volume = mass / ave density.
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RESPONSE --> Ok self critique assessment: 3
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20:58:15 `q015. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
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RESPONSE --> I have organized the information into 1) Knowing the SA formulas 2) understanding the Pythagorem Theorem 3) Understanding Density and how to use it to find both mass and volume and intergrating the volume formulas into finding density. confidence assessment: 2
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