Working through Unfamiliar, Complex and/or multi-step problemsWatch
- Study Helper
How do you do it?
For example, questions like these:
I would really like to be able to do these
To solve questions like these, you need to start by looking at all of the information provided. There is no set method that works everytime. It's a bit like a cryptic crossword and you will need to pull in unstated knowledge of more than one topic area (and therefore your ability to make associations with both what is stated and unstated) before you can solve them.
The clues are to look at the quantitative values and also any starting equations given as these are the big hint for the direction in which to look.
I like to look at the problem from both ends (working both backwards and forwards) and simultaneously looking at the quantitative values given since these are normally the linking association joining in the middle.
e.g. you should see that some of the base units and/or equations are common so its a case of equating and rearranging one formula in terms of another by substitution. Finally, with the link established, crunch the numbers.
For instance question b(i) the atmospheric pressure is quoted at 1x105 Pascals.
We are also given the mass of the 'average' air molecule as 5x10-26 Kg.
The question also states acceleration due to gravity is 10ms-2.
So from this we can safely deduce that the solution SHOULD involve all of these values.
Look closer at pressure. Ask yourself what is pressure and why Pascals?
Pressure = Force per unit area and Pascals is stated in N/m2
Newtons is the measure of force and force = mass x acceleration.
Subject knowledge 1. recognises that force = mass x acceleration means the mass of the earths atmosphere and the acceleration is that due to gravity and also force is measured in Newtons.
Subject knowledge 2. recognises that Pascals pressure describes the force of a column of air covering 1 m2 at the earths surface is 1x105 Newtons).
Light bulb moment no. 1 associates the above two pieces of subject knowledge and that the solution requires estimating the mass of the earths atmosphere from the stated quantitave information.
Light bulb moment no. 2 associates that if you know the mass of the atmosphere and the average mass of an air molecule, the total number of air molecules in the atosphere will be a simple division.
With the link established, write down the associated formula, rearranging and substitute:
pressure = force / area
force = mass x acceleration
pressure = (mass x acceleration) / area
mass = pressure x area / acceleration
in terms of this question:
Atmosphere mass = atmosphere pressure x surface area / gravity.
Plugging in the values:
= pressure x (4 x pi x r2) / gravity
= 1x105 x (4 x 3.14159 x (6x106)2)/ 10
Atmospheric mass = 4.52x1018 Kg
You are also told that the average mass of a molecule is 5x10-26 Kg
It's then just a case of dividing the total mass by the molecular mass to get the number of molecules:
Total number of molecules = Total mass / molecule mass
= 4.52x1018 / 5x10-26
= 9x1044 molecules.