Answer:
D
Explanation:
Part 1: Graphing Techniques
In Physics we use a variety of tools – including words, equations, and graphs – to make models of the motion of
objects and the interactions between objects in a system. Graphs are one of the best ways to directly visualize
the quantitative relationship between two variables – in other words, whether the variables are directly
proportional, inversely proportional, not related at all, or something else entirely.
When we construct a graph, we plot the independent variable – the variable that the experimenter controls – on
the x-axis, and the dependent variable – the variable that responds when the independent variable is changed –
on the y-axis. There are also control variables – variables that are kept constant throughout the experiment so
that they do not influence the data. So, for example, if you were trying to determine how the period of a
pendulum changes when the length of the pendulum is varied, the dependent variable would be the pendulum’s
period, and the independent variable would be the pendulum’s length. Controlled variables would include the
pendulum’s mass and the angle at which the pendulum was launched.
An appropriate graph for this experiment is shown below.
Notice that the title lists the dependent variable, which is plotted on the y-axis, first, and the independent
variable, which is plotted on the x-axis, second. The axes are correctly labeled with the appropriate units. The
graph begins at (0, 0) with no “jumps”, and increments are equally spaced.
In this experiment, we can clearly see that as the length of the pendulum increases, the period also increases, but
are the variables directly proportional? In other words, can we write an equation for the relationship in the form
y = mx + b? Excel will draw a trend line for a graph that can help us to determine this.
0
1
2
3
4
5
6
0 1 2 3 4 5 6 7
P
e
r
i
o
d
( s)
Length (m)
Period vs. Length of a Pendulum
While the graph appears to be somewhat linear, we can see a few problems – first, the majority of the points do
not fall on the line; second, the line does not cross the y-axis at zero, and we would expect it to – after all, a
pendulum with a length very close to zero meters should have a period very close to zero seconds. To
determine the correct relationship between the variables, we will have to linearize the graph.
