### Physics Cantilever Lab

Independent Assessment Physics Lab (SL): Cantilever Flexion Cherno Okafor Mr. Ebrahimi SPH4U7 October 21st, 2012 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. i) Relationship between the deflection/flexion of the cantilever and the load mass (5 trials) Table #1-Experiment A Factor/Variable| Trial 1| Trial 2| Trial 3| Trial 4| Trial 5| Trial 6| Trial 7| Trial 8| Trial 9| Trial 10| Trial 11| Load (g)| 0| 100| 200| 300| 400| 500| 600| 700| 800| 900| 1000| Without Load (cm)| 96| 96| 96| 96| 96| 96| 96| 96| 96| 96| 96| With Load (cm)| 96| 92. 7| 90| 87. 6| 85| 82. 2| 79. 5| 77| 74. 6| 71. 5| 69. 5| Flexion (cm)| 0| 3. 3| 6| 8. 4| 11| 13. 8| 16. 5| 19| 21. 4| 24. 5| 26. 5| Now, I will graph this relation:

We can see that there is a linear relationship between flexion and the load mass. (ii) Relationship between the deflection/flexion and the length of the cantilever (5 trials) Table #2- Experiment B Factor/Variable| Trial 1| Trial 2| Trial 3| Trial 4| Trial 5| Trial 6| Trial 7| Trial 8| Trial 9| Trial 10| Length of cantilever (cm)| 90| 80| 70| 60| 50| 40| 30| 20| 10| 0| Height without Load (cm)| 95. 5| 95. 5| 95. 5| 95. 5| 95. 5| 95. 5| 95. 5| 95. 5| 95. 5| 95. 5| Height with Load (cm)| 69. 5| 76. 5| 82. 5| 87. 4| 90. 9| 93. 2| 94. 5| 95. 5| 95. | 95. 5| Flexion (cm)| 26| 19| 13| 8. 1| 4. 6| 2. 3| 1| 0| 0| 0| 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: 1) 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. 2) 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.