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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.


Solution Summary

This Solution contains calculations to aid you in understanding the Solution to these questions.