September 29th - Graphing!

Today’s class was rather 'dense'. Not only did we go over density, but we also went over graphing! We began by quickly reviewing dimensional analysis.  

One interesting point that we examined was the amount of cubed centimetres in a cubed meter. This proved to be quite a number. To find this out, we execute the following steps:

• Examine each side of the large square
• Measure the dimensions (in this case it is 100 cm by 100 cm by 100cm)
• We multiply this, obtain 1.00 x 10⁶ cm³. Therefore, one million cubic centimetres fit in a cubic meter!

Another fact was that 1000L = 1 m³. Therefore, 1L = 10cm³.

Beginning the new lesson, we learned that density is the mass of an object divided by its volume. The equation is:

It's rather simple. Just remember to put those significant digits into action!

Here's an example we went over:

Determine the density of a statue that has a mass of 135kg and a volume of 65L.

d = 135kg / 65L = 2.1 kg / L

An important point to make here is that the limit of significant digits, in this example, is two. This is because 65L has only two significant digits. These digits are not exact. Because of this, in multiplication and division, they will limit the final answer’s certainty. Examples of exact digits include counting (ie. counting 4 washers) or 24 hours in one day. 

We can have fun with density. For example, we can challenge ourselves with experiments and projects:

Well, now that we veered slightly off topic, let’s move to graphing. There are five fundamental parts of a graph:

1.    Labelled axes (with units)

2.    Appropriate scale

3.    Title (ie. y vs. x)

4.    Data points

5.    Line of best fit

Note: To properly label your axis, remember that the independent variable is the factor that is changed or manipulated during the experiment, and goes on the x-axis. The dependent variable is the factor with a value that depends on the independent variable, and is plotted on the y-axis.

Now that we have a graph, with it we should be able to:

1.    Read the graph

2.    Find the slope (rise/run)

3.    Fine the area under the graph

Graphs are very useful. They give us a visual representation of our data. Graphing has many applications.

With a graph, we can multiply and divide the units to find the area or even create a new graph. We can split up the multiple straight line segments and use the formulae we know to find the area. We can split up a graph like so:

Using the formula for the area of a triangle or a rectangle, we can find our answer. With this new information, we can even plot a new graph! The new graph can also be a valuable source of information! Cool!

Posted by Andrew.