Partners: Matthew Ibarra, Billy Justin
Date of Lab: 21 November 2016
Centripetal Force
Mission Statement:To release a meter stick, pivoted at or near one end, from a horizontal position. Exactly when the meterstick reaches the bottom of its swing it collides in-elastically with a blob of clay. The meter stick, with clay attached now, continues to rotate to some final position. After measuring the appropriate masses, we are to come up with a prediction for how high the clay-meterstick combination should rise. Then are then to capture the experiment on video and compare the actual results to our prediction.
Procedure and Analysis:
For the theoretical portion of this experiment, we first needed to devise a method of predicting just how high the clay-stick combination would rise under the aforementioned circumstances. To begin with, we first identified that this could be done by segmenting the experiment into three distinct sections.
The first segment would examine the rotational motion of the meterstick from its initial flat horizontal position down until just before the moment when it impacts the clay, the point being to determine the angular velocity (omega 1) of the meterstick just before colliding with the clay.
The second segment would examine the inelastic collision between the meterstick and clay, where we were to employ the principle of conservation of angular momentum in order to determine the initial angular velocity (omega 2) of the combined system.
Finally, the third segment would use the principle of conservation of energy to predict the final height of the clay.
Below are our calculations.
Our calculations first involved finding omega 1 (5.48 rads/second) by establishing an energy
relationship in which the initial gravitational potential energy
transformed into rotational kinetic energy. Next we employed conservation of angular momentum, in conjunction with the parallel axis theorem (since the pivot point is not located at the center of mass of the meterstick). Doing so yielded us omega 2 (2.88 rads/second). Now equipped with omega 2, we set up another energy relationship, this time to calculate the theoretical height which would be reached by the clay-meterstick combo. This is when we were presented with a computational dilemma, the dilemma being that the vertical displacement of the meterstick (if the point of collision is considered the origin) is not equal to the vertical displacement of the clay. In actuality, the clay rises some distance more than the meterstick due to its center of mass being farther from the pivot position. Hence, we needed to devise a ratio between these heights with respect to the pivot point. Using this ratio, we were able to complete our calculation, shown above. We obtained a theoretical value a height of 32 centimeters, or .32 meters.
Next, in order to examine the veracity of our computation and our theoretical value, we conducted the experiment for ourselves, setting it up as shown below.
Capturing video of our experiment, we obtained the following graph.
From the graph above, we see that the maximum height reached by the clay is shown to be 20.71 centimeters, or 0.2071 meters. This value is considerably lower than our predicted height.
Conclusion:
We identified our percent error of 35.4% and then brainstormed reasons for this discrepancy. We first reviewed our calculations thrice, the third time being under the direct supervision of the professor, in order to identify computational errors.When we found no fault in our calculations, we considered experimental factors which we did not consider initially. To begin with, we neglected to consider the friction at the pivot position and at the bottom between the clay and the paperclip stand on which it rested. Furthermore, another potential source of error likely involved unintended oscillations perpendicular to the arc of motion, aka "wabbling."
Procedure and Analysis:
For the theoretical portion of this experiment, we first needed to devise a method of predicting just how high the clay-stick combination would rise under the aforementioned circumstances. To begin with, we first identified that this could be done by segmenting the experiment into three distinct sections.
The first segment would examine the rotational motion of the meterstick from its initial flat horizontal position down until just before the moment when it impacts the clay, the point being to determine the angular velocity (omega 1) of the meterstick just before colliding with the clay.
The second segment would examine the inelastic collision between the meterstick and clay, where we were to employ the principle of conservation of angular momentum in order to determine the initial angular velocity (omega 2) of the combined system.
Finally, the third segment would use the principle of conservation of energy to predict the final height of the clay.
Below are our calculations.
Next, in order to examine the veracity of our computation and our theoretical value, we conducted the experiment for ourselves, setting it up as shown below.
Conclusion:
We identified our percent error of 35.4% and then brainstormed reasons for this discrepancy. We first reviewed our calculations thrice, the third time being under the direct supervision of the professor, in order to identify computational errors.When we found no fault in our calculations, we considered experimental factors which we did not consider initially. To begin with, we neglected to consider the friction at the pivot position and at the bottom between the clay and the paperclip stand on which it rested. Furthermore, another potential source of error likely involved unintended oscillations perpendicular to the arc of motion, aka "wabbling."
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