31-May-2017: Lab 19: PHYS 4A Lab--Conservation of Energy/Conservation of angular momentum

Eric Chong

Lab 19: PHYS 4A Lab--Conservation of Energy/Conservation of angular momentum

Lab Partners: Nina Song and Joel Cook

Purpose: To predict and measure how high the clay-stick combination should rise after a collision.

Theory/Introduction: The conservation of angular momentum is very similar to the conservation of momentum. The equation is given in the form of Itotal initial * ωinitial = Itotal final * ωfinal, where I is the moment of inertia, and omega is the angular velocity. Using this idea, we can find the total energy of the system and see what form energy it is converted to, such as from gravitational potential energy to rotational kinetic energy, while also combining it with the concept of conservation of angular momentum if a collision occurs. For this experiment, we will be applying the concepts of conservation of angular momentum for the collision of the meter stick and the clay, and the conservation of energy for the transfer of energy between rotational kinetic energy and gravitational potential energy, in order to find how high the clay-stick combination will rise after the collision.

Procedure: To start, we measured the mass of the meter stick and the clay. Both of their masses turned out to be 146.63 g and 34.54 g respectively. Next, we set up an apparatus that looks like this:

(meter stick has nails sticking out in order to help the clay stick)

Before we commence the experiment, we predicted the height at which the clay-stick combination would rise through calculations. We first used conservation of energy of the stick that is angled at 90 degrees horizontally and made it rotate downwards, gaining rotational kinetic energy, until right before it hits the clay. In doing so, we would also have to use the parallel axis theorem to find the moment of inertia, because the pivot has been shifted to the 10 cm mark of the meter stick. We then used the conservation of angular momentum to calculate the final angular velocity. Finally, we used conservation of energy again, but this time with a new moment of inertia, because the clay sticks onto the stick and contributes some moment of inertia, and the new angular velocity, calculated through the conservation of angular momentum. The variable we need to find is theta, the angle. By finding the angle, we can use the value in order to find how high the clay-stick combination rises. Here is what the calculations look like:

The calculations indicate that the clay-stick combination will rise approximately 30 cm.

We next conducted the experiment. We video captured the motion of the stick rotating and colliding with the clay and rising up to a certain height, and plotted the initial position of the clay and the clay's final height. Here is what we found:

The result is strikingly close to what we predicted. The reason that the value is a bit off is most likely that our plotting skills with LoggerPro are not pixel accurate. Since a centimeter is really small, it is possible that even a pixel on LoggerPro could be a centimeter or a half. Nonetheless, we are more concerned with the overall value and how close it is to what we predicted, and looking at this value of 32.45 cm, we are safe to assume that what we predicted was indeed correct.

Conclusion: This experiment showcases the concepts of conservation of energy with rotational kinetic energy and gravitation potential energy, and the conservation of angular momentum. This lab is meant to help us utilize our skills in order to find certain values at certain times while the stick is in motion. And because of this, this lab has high value for our understanding of physics and engineering skills. Some places of uncertainty may lie in the plotting of the graph in LoggerPro, some loss of energy while the meter stick is in motion (most likely due to the fact that there is drag force or friction in between the pivot point and the meter stick), or maybe even the possibility that the meter stick is not exactly 90 degrees when it started (it could have easily been 91 or 89 degrees). Overall, we are safe to say that, due to our predictions being really close to the actual experimental value, the experiment is a success!