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Dimensional Analysis, Vectors, etc.

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Please solve each and give a complete detailed step by step solution to solving each problem no matter how easy. I am trying to learn and not an expert. Give answer and way to solve. Adult student trying to make my way through all this and need your help!

1) A flat circular plate of copper has a radius of 0.265m and a mass of 42.4kg. What is the thickness of the plate? Answer in meters.

2) The mass of the planet Saturn is 5.64*10^26 kg and its radius is 6*10^7m. Calculate density. Answer in units of kg/m^3.

3) One cubic meter (1.0m^3) of aluminum has a mass of 2700kg, and a cubic meter of iron has a mass of 7860kg. Find the radius of a solid aluminum sphere that has the same mass as a solid iron sphere of radius 4.32cm. Answer in units of cm.

4) This problem demonstrates dimensional analysis. A rope has a cross section A=9.1 m^2 and density p=2140kg/m^3. The "linear" density of the rope "mu" is defined to be the mass per unit length, in the form mu = p^xA^y. Based on dimensional analysis find the powers x and y.

a) x=-1, y=-1
b) x=1, y=2
c) x=-2, y=1
d) x=-1, y=1
e) x=-2, y=2
f) x=1, y=1
g) x=-2, y=-1
h) x=-1, y=2
i) x=1, y=-1

6) How many seconds are their in a year? Answer in units of s/year.

7) If 2 micrometerorite(s) (a sphere with a diameter of 1*10^-6 m) strikes each square meter of the moon each second, how many years would it take to cover the moon to a depth of 0.684m?
Hint: Consider a cubic box on the moon 1m on a side, and find how long it willl take to fill the box. Answer in units of years.

8) Needing help, george asked, "If a chicken and a half can lay an egg and a half in a day and a half, how many days will it take one chicken to lay a dozen eggs? Assume 1 month has 30 days and select the best answer.

a) a dozen eggs in 24 days
b) a dozen eggs in 8 days
c) a dozen eggs in 2/3 of a month
d) a dozen eggs in 12 days
e) a dozen eggs in 18 days
f) a dozen eggs in 1/3 of a month
g) a dozen eggs in 6 days
h) a dozen eggs in 9 days
i) a dozen eggs in 16 days

9) Assume the sun is mostly composed of hydrogen atoms. Assume the mass of the sun is 1.89*10^30kg, and the mass of a hydrogen atom is 1.672*10^-27kg. How many atoms are their in the sun? Answer in units of atoms.

10) Assume that an oil slick consists of a single layer of molecules and that each molecule occupies a cube 1.09nm on a side. Find the area of an oil slick formed by 0.684m^3 of oil. Answer in units of m^2.

11) Assuming that 68.6% of the earth's surface is covered with water at an average depth of 1.01 mile(s), estimate the mass of the water on earth in kg.

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