Introduction

Purpose: The purpose of this Physics Lab is to investigate
what factors determine the amount of flexion of the cantilever.
Hence, the objective is to establish a relationship between the
length of a cantilever, which may give some insight into the
physics of cantilevers. Hypothesis: If one increases the length of
a cantilever, one would expect there to be an increase in
deflection/flexion of the cantilever.

Similarly, if one increases the mass of the load, one would
expect there to be an increase in the deflexion/flexion of the
cantilever. In addition, I predict that proportionality will also
occur between the independent and dependent variables. If the
length of the cantilever doubles, it is expected that the
flexion/deflexion would also double. Similarly, if the mass of the
load doubles, the deflexion/flexion would also double. Variables:
In this investigation, I chose two variables: the length of the
cantilever and the mass of the load.

First, I chose to measure the effect of the length of the
cantilever on its deflection when loaded with a constant mass
because I knew from prior experience that there was some
relationship between the two variables. Independent Variable: The
length of the cantilever in metres, which will be varied by
changing the length of the yardstick functioning as a cantilever
that extends over the edge of a table. This will be measured
indirectly by measuring the length of the portion of the yardstick
not in use and subtracting that from the entire length of the
yardstick.

The other independent variable is the mass loaded onto the
cantilever, which will be controlled by initially using the same
mass for each trial, then for the second part, changing the mass of
the load by increasing and decreasing the mass, and subsequently
investigating what the relationship is between load mass and
cantilever length. The initial location of the mass in relation to
the entire yardstick will be controlled by placing the mass at the
same end of the yardstick for each trial and marking the
flexion/deflexion. Dependent Variable: The deflection/flexion of
the cantilever in metres. This will be measured indirectly by
measuring the initial height of the bottom of the cantilever with
no mass added (which is equal to the height of the table) and the
new height of the bottom of the cantilever after each trial, which
will be measured with mass added. Hence, the difference between
these heights is equal to the deflection/flexion of the cantilever.
The material and other physical properties of the cantilever will
be controlled by using the same yardstick as a cantilever for each
trial.

Data Collection and Processing My experiment is divided into
two parts; experiment A (involving the relationship between flexion
and the mass of the load) and experiment B (involving the
relationship between the flexion and the length of the cantilever).
Below are two tables in which I have recorded the data which I
obtained during the experiment. The first table reflects the
Relationship between the deflection/flexion of the cantilever and
the mass of the load and the second table reflects the relationship
between the flexion of the cantilever and the length of the
cantilever. Now I will graph this relation: We can see that there
is an exponential/power relationship (curved) between the flexion
and the cantilever length. Analyzing Evidence Patterns: In
experiment A, the relationship between the flexion and the load is
proportional as predicted. As the load increases, the flexion
increases as well. As the load doubles from 200g to 400g, the
deflection almost doubles too. In experiment B, the deflection
increases as the length of the cantilever increases.

But this time, it reaches a point (20cm, 10cm, 0cm) where the
deflection stays the same even if the cantilever length changes.
Conclusion and Evaluation Conclusion: The experimental results
agree with my prediction/hypothesis because I predicted that in
experiment A, the deflection is proportional to the mass of the
load. In experiment B, I predicted that flexion/deflexion would
increase as the length of the cantilever increases. As the load and
the length of the cantilever increases, then the deflection/flexion
increases.

This happens because of forces acting on the particles in the
cantilever. At the top of the cantilever, particles are pulled
apart proportionately to the load because they are in tension. The
forces between particles increase. However, the attractive force is
bigger than the repelling force in the particles so therefore, the
particles are held together. The particles at the bottom will be
pushed together proportionately to the load because they are in
compression. The forces get larger and the repelling force which is
bigger pushes the particles away from each other.

So they are not disordered. We can also say that they obey
Hooke’s law. Evaluation: From the results that I got after
performing the experiment, I can say that the experiment worked
quite well. In the analyzing evidence section, I can draw the
conclusion that the first table reflects a linear straight line
graph and the second table reflects a curved graph. On this basis,
I can say that the experiment worked out pretty well. I think the
data I obtained was accurate since I did indeed try to graph these
relationships.

A possible improvement to this experiment should be repeating
the experiment twice or more if possible. Then I would get the
average results in a table and in this way, my results would be
even more accurate. General Conclusion: The general conclusion we
can draw from this experiment is that as the mass that we put on
the cantilever increases, the deflection increases too until the
elastic point is reached where the cantilever cannot hold any more
masses so it breaks. Also, we can see from the second graph that
the larger the length of the cantilever, the large the flexion
is.