Partners: Chong and Aiqi
Theory/Introduction:
The purpose of this lab is to test how the conservation of energy and angular momentum apply to a ruler on a pivot that is released into a swing where it picks up a clay block from the ground and travels up.
In order to do this experiment we will be making equations based on four points during the swing. Right after it is let go, right before it makes impact with the clay, right after it makes impact with the clay, and when the new meter-clay system reaches its maximum height.
We went into this lab knowing that before the ruler is released all of its energy is stored as GPE, before/after impact with the clay all of its energy is rotational kinetic energy, and when the final height of the meter-clay system is reached all the energy is stored as GPE once again.
Apparatus/Procedure:
To set things up we attached a motion detector to a pole and attached the pole to the ruler’s hole at the 20 cm mark which will act as our pivot. On the bottom of the ruler will be taped down paper clips pointed to puncture the clay block that will be right underneath the pivot point on the floor. We made sure to measure the mass of the meter stick and clay block and also measure the height off the ground of the center of mass. Here is what the set up looks like:
Once everything is set up we took the video and started the experiment. We had the ruler let go from horizontal and proceeded to watch it puncture the clay and take it to a max height. After we uploaded the video onto LoggerPro and got the height of the object by going frame by frame until it reached peak height. Slow motion videos are recommended since it gives you a more exact maximum height. Make sure to scale the video to something, we used a ruler in the background.
Our experimental maximum height turned out to be 0.3299 meters.
Analysis:
After getting the experimental height we compared it to our theoretical height. In order to get theoretical height we made a conservation of energy equation involving the initial energy of the GPE when the ruler is at horizontal and the final energy of the rotational kinetic energy in order to find the angular speed of the ruler before impact with the clay. However, we have to solve for the inertia of the meter stick since its needed for the rotational KE equation. This is done by using the parallel axis theorem and solving for the Inertia around the axis of rotation. Once we have the final angular velocity before it hits we have to solve for the angular velocity after it hits the clay. This is done by setting up a conservation of angular momentum equation from right before impact equal to right after impact. However we had to get the inertia of the new system which is just the added on inertia of the clay around the pivot (clay is considered a point mass).
After getting the angular velocity we made a conservation of energy equation again, but this time the initial energy will be the rotational energy of the ruler after impact and the final energy will be the GPE at the ruler-clay system’s maximum height:
Conclusion:
Overall, this lab was a success. We had a ridiculously small percent error of .06%. However, there are always random and systematic errors that occur in our labs. Some of the errors in the lab include the resistance from outside forces such as the friction at the pivot and air drag. Also when marking the maximum height of the ruler-clay system on LoggerPro we don’t get the true maximum height since our video only will give us the frame before and the frame after max height. Treating the clay as a point mass also skewed our data since it was really more of a spherical blob. One interesting thing to point out is that, theoretically, the experimental calculation should have had a smaller height due to the resistance of outside forces decreasing its overall energy however that was not the case.
phys4AF18avnguyen 