I need a little help with these kind of math kind of physics problems . . .?

Question

The Earth has a mass of 5.98 1024 kg. The average mass of the atoms that make up the Earth is about 38 u. How many atoms are in the Earth?

Suppose that it takes 12 h to drain a container of 5700 m3 of water. What is the "mass flow rate," in kilograms per second, of water from the container?

A typical sugar cube has an edge length of 1 cm. If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole = 6.02 1023 units.)

For about 10 years after the French revolution, the French government attempted to base measures of time on multiples of ten: One week consisted of 10 days, one day consisted of 10 hours, one hour consisted of 100 minutes, and one minute consisted of 100 seconds. What is the ratio of the French decimal week to the standard week? What is the ratio of the French decimal second to the standard second?


Please and thank you!

Answer 1

Convert mass to grams
Divide result by 38
Multiply result by Avagadro's #

Note that 1000 liter = 1 m^3
and 1 L = 1 kg appx. Then you can convert your volume to kg. 12 hr = 43200 sec.

First, you need to find mol wt of sugar (C6H12O6)
Then you need to find density of sugar (about 2 g/cc). Then you can find volume of mol wt, and if you take cube root, you get side of cube.

A "regular" day is 86400 sec, while a "French" day is 10^5 French seconds. A French week is then 10^6 French seconds, while 10 days consists of 864,000 seconds. This gives you the French to standard second comparison. The standard week is 86,400 sec * 7 days. So the French week to standard week can be worked out.

Answer 2

This is assuming that you meant 5,981,024 kg and that 38u stands for 38 amu (atomic mass units).
1.) There are 9.478349086 * 10^31 atoms in the earth

2.)131.94 kg/s

3.)8.445 cm

Enjoy =)