Conservation of Mechanical Energy

Experiment: Conservation of Mechanical Energy Purpose The purpose of this experiment was to observe that energy is conserved in the gravitational field near the surface of the earth. To do this, we ran a series of trials of a cart moving along an inclined plane and determined the initial height from measuring the speed as it traveled. Theory The total amount of energy in the universe remains constant, meaning that energy can not be created nor destroyed. However, it can change from one form to another. This is the law of the conservation of energy. Different types of energy for interconversion include: mechanical, heat, chemical, potential, electrical, radiative, and nuclear. Energy is a scalar. In this experiment, we modeled an isolated system with no friction, assuring that the mechanical energy would be conserved. Mechanical energy is either kinetic or potential in nature. Kinetic energy is the energy an object possesses due to its motion. It is the work needed to accelerate a body of a given mass from rest to its current velocity. Kinetic Energy: Potential energy is the energy an object has due to its position in a physical system. Gravitational potential energy is the potential energy an object has due to its mass and the gravitational force acting upon it. Gravitational Potential Energy: In our experiment, because total mechanical energy is conserved, the total energy in the system can be defined by the following equation (the initial energy will be equal to the final energy): To determine potential energy, a measured value for height is needed. After assembling the system and measuring various lengths, the height for the potential energy can be found with the following equation: Another value of height can be found using an equation derived from the law of conservation of energy equation: The speed at which the cart of this system will pass through the light beams is another value needed in order to determine kinetic energy. Velocity: The percent error formula can be used to compare measured values to generally accepted values. The formula below helps us determine the accuracy of our measurements. Percent error: Procedure The experiment consisted of three main types of trials: downhill runs, uphill runs, and steep slope downhill runs. We first set up the Capstone computer software, photogates, cart, and air track as described by the manual. We made sure to level the track and measure the length of the card on the top of the cart using a ruler. We also measured the thickness of two blocks (H) with a caliper, the distance between the two legs of the air track (D) using the meterstick on the air track, and the distance between the photogates (d) also by using the meterstick on the air track. I was responsible for measuring the lengths D and d. Before running the trials, we also measured the mass of the cart using a triple beam balance, and I was also responsible for this part. Part one of the experiment was conducted with downhill runs. To make an inclined plane, we placed two blocks under the leg of the air track which was to be the upper level/photogate. When we changed the height, we made sure the photogates would properly detect the card on the cart during its motion down the track. One person controlled the computer by pressing Record and Stop buttons. Another was responsible for releasing the cart from the top of the track after turning on the air blower, and another person stopped the cart and told the computer person to click Stop. The computer program recorded the time in seconds that the 10 cm card of the cart spent moving through the photogates. We were able to calculate the values requested by our lab manual, and this process was repeated for a total of 5 trials. For part two, we recreated the inclined plane, but instead we put the blocks under the other (more distal) leg in order to obtain an uphill slope. Similar processes were followed, except the cart had to be pushed up the inclined plane by a group member. We repeated this for a total of 5 trials as before. For part three of the experiment, we reverted to a downhill slope, but we added an extra block (three blocks total) in order to achieve a steeper slope. We repeated the process from the first part of the lab, repeating it for 5 trials. Here are pictures of some of the equipment we used in order to obtain our measurements. Data (attached) Analysis (attached) Conclusion Our first part of the experiment yielded rather accurate and precise results, with a very low percent error (3.39%) when we compared our average height of 0.0222 m to the GAV of 0.02298 m (accuracy) and a standard deviation of 7.7E-5 m (precision). For the average of ratios of final energy to initial energy, we obtained 0.9996. We expected 1 (GAV) to be the ratio for each trial, as energy is conserved. Our results gave us a 0.04% error, which is very accurate. The uphill trials gave us an average height of 0.0238 m. The calculated GAV was 0.02298 m again, and the percent error was found to be 3.57%, showing accuracy in this part of the experiment, as well. The third aspect of the experiment also was accurate, with a percent error of 1.11%. This was found by comparing the average height here (0.034 m) to the calculated GAV due to three blocks (0.03438 m). Some sources of error for these experiments may have been that the mass of the air cart was measured improperly, the blocks may not have been measured properly, and there could have been scratches on the air track leading to friction and slower movement of the cart (loss of energy there). Also, it is possible that the computer person pressed the Start button after the cart actually passed the first photogate, or likewise, the Stop button before the cart passed the second photogate.