​​Derived Quantities and Density (Page23--26)

Purpose: We need to identify what derived quantities are.
The reason why density is considered as derived quantities.
Getting to know some other examples of derived quantities.


Key words: derived quantity, derived unit, mass, density
To begin with, a derived quantity means the combination of other quantities. For instance, density is a derived quantity because is determined by using the mass and the volume of an object.
Density = mass per unit volume or Density = mass / volume
If mass is in g and volume is in mL,
for example, then the unit for density will be in g/mL.
Here is an example problem: If a 5.0 mL (or 5.0 cm3) piece of copper has a mass of 44.6 g, calculate the density of copper. d = mass / volume d = 44.6 g / 5.0 mL = 8.9 g/mL
Explain: both mass and volume can be directly measured, but density is calculated using two known quantities ( d = m / V), so density is a derived quantity.
Another derived quantity could be speed, as it is calculated using distance and time. v = d / t, where v is the speed, d is the distance (or displacement), and t is the time. Quantities like mass, length, temperature, etc. can be measured directly and are not determined using other quantities, so they are not "derived" quantities.

Why?

Quantities like mass, length, temperature, etc. can be measured directly and are not determined using other quantities. Like mass can be measured by balance, while length and temperature can be calculated by ruler and thermometer. Thus, they are not consider as "derived" quantities.
table1.jpg
In table1,they are not consider as derived quantities because they can be measured by some tools.

table2.jpg
In table2, all of them are consider as derived quantities because these quantities cannot be directly by some tools. While, they need to combine some quantities in order to get the results.


Some practice problem:

1.An iron bar has a mass of 125g. If iron's density is 7.86 x 10 3g/L, What volume does the bar occupy?

2.If the density of copper is 8.92 x 103 g/L and the densiy of magnesium is 1.74 x 10 3 g/L, what mass of magnesium occupies the same volume as 100.0 g of copper?

Do these two practice problems by yourself to test whether you understand the material or not~



Here is the answer key for practice problems above:
1.V=m/d =125g/7.86 x 10 3g/L=0.0159 L
2.Vcopper=m/d=100.0/8.92 x10 3g/L=0.01121 L=volume of magnesium
mass of magnesium=d x V=1.74 x10 3g/L x0.01121=19.5g of magnesium



Resources: table1&table2
http://physics.nist.gov/cuu/Units/units.html