# UTA The Relationship Between the Mass & Volume of The Samples Question

QUESTION #1: Several samples of pure iron were weighted and placed into a graduated cylinder filled with water to measure their volume by water displacement.  Show the relationship between the mass and volume of the samples using a line graph.  The volume should be the independent variable.

Volume of sample (cm3)

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Mass of sample (g)

0.50

3.25

0.75

5.62

1.15

8.57

1.30

9.63

1.42

11.3

1.65

12.6

2.00

15.2

2.20

17.3

Plot an HAND DRAWN appropriate graph of the data (no excel or graphing software accepted).  Draw the Line of Best Fit.

GRAPHING PAPER:

– SCREENSHOT #138

QUESTION #2:

Calculate the slope of the line with the correct units, show work.  What does the slope represent… hint consistency (synonyms)?

QUESTION #3What mass_____ g would you expect for a 1.50 cm3 of the pure iron?  (interpolate or extrapolate)QUESTION #4What mass_____ g would you expect for a 0.50 cm3 of the pure iron?  (interpolate or extrapolate)

QUESTION #5:

What volume_____ cm3  would you expect for a 18.0 g of the pure iron?  (interpolate or extrapolate)

video 1: (1:16-10:39)

video 2:

Data Tables and GraphingDATA TABLES
Whenever you make a data table of any kind, the data table should:
1. Have a title (usually manipulated variable first and responding variable second)
2. Have column headings (include units)
3. The manipulated variable should appear in the first column
4. All values should be recorded to the correct significant digits
GRAPHING
The following steps should be followed to achieve an acceptable graph
1. Title at the top of the graph (responding variable first)
[Responding variable] vs. [Manipulated variable] OR y vs. x
2. Label each axis Manipulate variable on the x-axis and Responding variable on the y
axis.
3. Calculate scale of each axis
If the maximum value to be plotted is less than the number of squares on the axis, divide
the number of squares on the axis by the max. Value to be plotted on the axis. e.g. y-axis
has 50 squares and a max. Value of 25 metres. 50/25= 2, so every 2 squares have a value
of 1 metre.
Or If the maximum value is greater than the number of squares, like 200 metres on a 50
square axis, take the number and divide by the number of squares. 200/50 = 4 each
square has a value of 4 metres.
Remember the following:
a) Data should cover most of the graph paper (80%)
b) The scale must be even; each square on the axis must have the same value c)
Each square must have a simple value i.e. 2 metres not 2.3 metres, round values 4. Plot
the points on the graph and circle the points
5. Draw the best-fit line OR curve (Do NOT connect the dots)VARIABLES AND TERMS
1. Manipulated variable (independent variable)
-On x-axis (horizontal) on graph, first column in data table
-Usually the variable changed by the experimenter (the thing you decided to
change) 2. Responding Variable (dependant variable)
– On the y-axis (vertical) on the graph, second column in a data table.
-Usually the variable that changes based on the other variable (the one that changes after
you do something)
3. Controlled variables
– The variables that might affect the results and so are held constant.
– There is usually more that one controlled variable
4. Interpolation with a best-fit line this is the process of estimating data points within the
data set.
5. Extrapolation is the process of predicting data points on the line outside the data set.
Extrapolation assumes that the trend of the best fit line continues beyond what was
measured.Slope
variable.
Slope is a measure of the average change of one variable on a line graph with respect to a second
e.g. if water was heated and the temperature was measured every minute, a graph of the change in
temperature with respect to time could be drawn.
If a best-fit line is drawn through the points it shows how the temperature of the water rose, on
average. If the slope of the line is calculated, it gives a number to that average change.
By definition, the slope is the rise of the line on the graph (how much it moves up and down)
divided by the run of the line (how much it moves side to side).
Slope = rise
run
When the two numbers for rise and run are put into the formula, the slope is the result.
Another way to look at the points is as coordinates. Each point has an x-value and a y-value
which were used to plot the points on the graph. Each coordinate is written as (x, y). Of the two points
chosen for the slope, the one closest to the origin is called (x, y) and the second point is called (x, y₂).
Slope is then calculated using the formula:
Slope =V₂-V
Xạ – XI
Remember: Both the rise and the run have units. e.g. if the x-axis is in minutes, the units of run are in
minutes. If the y-axis is in degrees Celsius, the units of rise are in degrees Celsius. When the slope is
calculated, the value of slope will be in degrees Celsius/minute (C/min).print-graph-paper.com

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