course Phy 241
......!!!!!!!!...................................
20:52:12 `q001. There are 10 questions and 5 summary questions in this assignment. What is surface area of a rectangular solid whose dimensions are 3 meters by 4 meters by 6 meters?
......!!!!!!!!...................................
RESPONSE --> There are six surfaces on the rectangular solid. 2 with the dimensions of 3x4 2 with 4x6 and the last 2 with 6x3. The surface area is calculated by taking the area of each side and then adding them together. This turns out to be 108 m^2.
.................................................
......!!!!!!!!...................................
20:52:28 A rectangular solid has six faces (top, bottom, front, back, left side, right side if you're facing it). The pairs top and bottom, right and left sides, and front-back have identical areas. This solid therefore has two faces with each of the following dimensions: 3 m by 4 m, 3 m by 6 m and 4 m by 6 m, areas 12 m^2, 18 m^2 and 24 m^2. Total area is 2 * 12 m^2 + 2 * 18 m^2 + 2 * 24 m^2 = 108 m^2.
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
20:56:51 `q002. What is the surface area of the curved sides of a cylinder whose radius is five meters and whose altitude is 12 meters? If the cylinder is closed what is its total surface area?
......!!!!!!!!...................................
RESPONSE --> The surface area of a cylinder is 2 pi*r*h. Therefore we can calculate the total SA as 2*5*12*pi=120pi m^2. To find the SA of only the sides we can subtract the area of the two circular bases. The area of the circles is 2pi(r^2)=50 pi. Now the sides only have an area of 70 pi m^2.
.................................................
......!!!!!!!!...................................
21:05:13 The circumference of this cylinder is 2 pi r = 2 pi * 5 m = 10 pi m. If the cylinder was cut by a straight line running up its curved face then unrolled it would form a rectangle whose length and width would be the altitude and the circumference. The area of the curved side is therefore A = circumference * altitude = 10 pi m * 12 m = 120 pi m^2. If the cylinder is closed then it has a top and a bottom, each a circle of radius 5 m with resulting area A = pi r^2 = pi * (5 m)^2 = 25 pi m^2. The total area would then be total area = area of sides + 2 * area of base = 120 pi m^2 + 2 * 25 pi m^2 = 170 pi m^2.
......!!!!!!!!...................................
RESPONSE --> I took the formula from a website that did not specify that the 2pi*r*h only represented the sides. I understand the process, I just worked it backwards from a misguided equation. The actual equation should read 2 pi r^ 2 + 2 pi r h.
.................................................
......!!!!!!!!...................................
21:06:30 `q003. What is surface area of a sphere of diameter three cm?
......!!!!!!!!...................................
RESPONSE --> The surface are of a sphere is represented by the equation 4 pi r ^2, which would yield 9 pi cm^2.
.................................................
......!!!!!!!!...................................
21:06:35 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.
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
21:07:54 `q004. What is hypotenuse of a right triangle whose legs are 5 meters and 9 meters?
......!!!!!!!!...................................
RESPONSE --> For this problem we can use a^2+b^2=c^2. This yields about 10.3 m.
.................................................
......!!!!!!!!...................................
21:08:17 The Pythagorean Theorem says that the hypotenuse c of a right triangle with legs a and b satisfies the equation c^2 = a^2 + b^2. So, since all lengths are positive, we know that c = sqrt(a^2 + b^2) = sqrt( (5 m)^2 + (9 m)^2 ) = sqrt( 25 m^2 + 81 m^2) = sqrt( 106 m^2 ) = 10.3 m, approx.. Note that this is not what we would get if we made the common error of assuming that sqrt(a^2 + b^2) = a + b; this would tell us that the hypotenuse is 14 m, which is emphatically not so. There is no justification whatsoever for applying a distributive law (like x * ( y + z) = x * y + x * z ) to the square root operator.
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
21:10:04 `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?
......!!!!!!!!...................................
RESPONSE --> First square 6 to yield 36, then square 4 to yield 16. Next subtract 16 from 36 to get 20. Finally take the square root of 20 to yield an answer of about 4.5 m.
.................................................
......!!!!!!!!...................................
21:11:41 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.
......!!!!!!!!...................................
RESPONSE --> I got an answer of 4.4721 and rounded off to 4.5m.
.................................................
......!!!!!!!!...................................
21:13:58 `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?
......!!!!!!!!...................................
RESPONSE --> Density =mass/volume. Volume can be calculated by multiplying 4*7*12 to equal 336cm. Then divide the 700 grams by the 336cm to get a density of approximately 2.1 g/cm.
.................................................
......!!!!!!!!...................................
21:15:12 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).
......!!!!!!!!...................................
RESPONSE --> yes volume is cubed, cm*cm*cm...I left out the ^3. I got that 700/336 = 2.083333 with the 3 repeating.
.................................................
......!!!!!!!!...................................
21:18:13 `q007. What is the mass of a sphere of radius 4 meters if its average density is 3,000 kg/cubic meter?
......!!!!!!!!...................................
RESPONSE --> D=m/v, therefore mass = density*volume. First we can calculate the volume with the equation 4/3 pi r^3. This yields about 85.3 pi m^3. Now just multiply by the 3,000 to get a mass of about 256,000 kg.
.................................................
......!!!!!!!!...................................
21:18:42 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.
......!!!!!!!!...................................
RESPONSE --> I left out the pi when typing the answer.
.................................................
......!!!!!!!!...................................
21:24:57 `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?
......!!!!!!!!...................................
RESPONSE --> To calculate an average density, we can take the total volume and figure out the percentage volume of each object. The first object is 6/16 and the second is 10/16. Now we can multiply the fraction by each corresponding density and add them together. 1.25 + 1.5 = 2.75 g/cm^3.
.................................................
......!!!!!!!!...................................
21:26:59 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.
......!!!!!!!!...................................
RESPONSE --> I had a different approach, but achieved the same answer. I now know that it is easier to remember that the ave density is simply the total mass divided by the total volume.
.................................................
......!!!!!!!!...................................
21:33:09 `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?
......!!!!!!!!...................................
RESPONSE --> average density= total mass/total volume. First we can calculate mass by multiplying the densities by the volume. To find total mass we add them both together. 56700kg + 24000kg=80700kg. The total volume can be found by multiplying the dimensions of the box or adding the volumes of the individual materials, either way we come up with 30 m^3. Now we can take the total mass 80700kg/ total volume 30 m^3 to yield an average density of 2690 kg/m^3.
.................................................
......!!!!!!!!...................................
21:33:50 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..
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
21:37:22 `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?
......!!!!!!!!...................................
RESPONSE --> To find the volume or m^3 we multiply the 1,700,000 by the 0.015m to yield 25500 m^3. Density=mass/volume so we can multiply the volume by the density to yield 21,930,000 kg.
.................................................
......!!!!!!!!...................................
21:39:46 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.
......!!!!!!!!...................................
RESPONSE --> I have four zeros calculated at the end of 2193.
.................................................
......!!!!!!!!...................................
21:40:26 `q011. Summary Question 1: How do we find the surface area of a cylinder?
......!!!!!!!!...................................
RESPONSE --> The surface area of a cylinder is 2 pi r^2 + 2 pi r*h.
.................................................
......!!!!!!!!...................................
21:40:37 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.
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
21:40:55 `q012. Summary Question 2: What is the formula for the surface area of a sphere?
......!!!!!!!!...................................
RESPONSE --> The surface area of a sphere is 4 pi (r^2).
.................................................
......!!!!!!!!...................................
21:40:58 The surface area of a sphere is A = 4 pi r^2, where r is the radius of the sphere.
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
21:41:11 `q013. Summary Question 3: What is the meaning of the term 'density'.
......!!!!!!!!...................................
RESPONSE --> Density is the amount of mass per unit volume.
.................................................
......!!!!!!!!...................................
21:41:25 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'
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
21:42:16 `q014. Summary Question 4: If we know average density and mass, how can we find volume?
......!!!!!!!!...................................
RESPONSE --> Divide the mass by the average density.
.................................................
......!!!!!!!!...................................
21:42:22 Since mass = ave density * volume, it follows by simple algebra that volume = mass / ave density.
......!!!!!!!!...................................
RESPONSE -->
.................................................
......!!!!!!!!...................................
21:43:57 `q015. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.
......!!!!!!!!...................................
RESPONSE --> I wrote each equation down and visualized the area and the three dimensionality of the object.
.................................................
"