Physics Lab Conservation of Mechanical Energy PDF

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professor Olugbenga Adeyemi Olunloyo ...

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Physics 221 Section 009 Olugbenga Adeyemi Olunloyo Experiment Performed: 26 September 2017 Report Handed In: 10 October 2017

Conservation of Mechanical Energy Introduction This experiment was designed to study the law of conservation of mechanical energy in a system where gravitational potential energy is converted into kinetic energy, to teach how to apply the equations for kinetic and potential energy and to teach how to measure the parameters for determining kinetic and potential energy. The experiment conducted demonstrates the connection between kinetic and potential energy and to see that with a frictionless system, energy is to be conserved. Potential energy is found by multiplying the mass of an object by acceleration due to g’ravity and the height of the object from the ground ( ΔP E = mhangingg(xf-xi), where xf and xi indicate final and initial position). Kinetic energy is the product of 0.5, the mass of the object, and velocity squared. In this instance, kinetic energy at a specific point was calculated by subtracting the initial kinetic energy from the final kinetic energy ( ΔKE glider= ½mglider  vf 2 - ½mglidervi2). The total kinetic energy is found by adding the kinetic energy of the glider and the kinetic energy of the hanging mass (ΔKE system = ΔKE glider + ΔKE hanging mass). The total energy of an object is the summation of kinetic energy and potential energy. Procedure The equipment used for this lab consisted of: a two meter horizontal air track, a glider, a pulley, two photogates, masses, an air blower, a Pasco 850 Universal Interface system, and a computer with Microsoft Excel and Pasco Capstone. All of the above mentioned equipment, excluding the computer is seen in Figure 1 in the lab manual. The weights were applied to the end of the pulley (hanging mass) with the values that were stated in the lab manual. The glider was then pushed and let the air track and hanging mass take the glider past the two photogates. The computer program connected to the photogates gave values for time. With these values, the kinetic energy of the glider, the kinetic energy of the hanging mass, the kinetic energy of the entire system, the potential energy of the hanging mass, and the percent error of the experimental values could be calculated. Data See attached. Analysis For this experiment, all calculations were done in an Excel spreadsheet. To demonstrate the calculations, values from trial 1 will be used as an example. The initial and final velocities in each trial were calculated using the measured time values as follows: vi= Δx/Δt i = 0.025m/0.04s = 0.63 m/s vf= Δx/Δt f = 0.025m/0.07s = 0.36 m/s

These values were then used to calculate the change in kinetic energy of the glider and the hanging mass, as follows: 2 2 2 2 ΔKE glider=  ½mgliderv  f - ½mglidervi = (½)(0.1909kg)(0.36m/s) - (½)(0.1909kg)(0.63m/s) = -0.026J ΔKE hanging mass= ½mhangingvf 2 - ½mhangingvi 2 = (½)(0.007kg)(0.36m/s)2 - (½)(0.007kg)(0.63m/s)2 = -0.00094J These changes in kinetic energy of the components of the system were then added together to get the total change in kinetic energy of the system. ΔKE system = ΔKE glider + ΔKE hanging mass = -0.026J - 0.00094J = -0.027J The change in potential energy of the system was calculated as follows: ΔP E = mhangingg(xf-xi) = (0.007kg)(9.8m/s2 )(1m-0.4m) = 0.041 J The percent difference values between the kinetic energy and the potential energy for each trial are shown below. The expectation is that the change in potential energy will equal the change in kinetic energy, thus supporting the law of conservation of mechanical energy. Trial Number

Percent Difference

1

51.85%

2

136.67%

3

58.73%

4

78.42%

5

49.29%

6

50.00%

Average

70.83%

Table I: Percent Error Sample Calculation: percent differencetrial 1 = |(change in KE - change in PE)|/change in KE] x 100% = |(0.027J-0.041J)|/0.027J| x 100% = 51.85% This experiment demonstrates how potential and kinetic energy can be interconverted, with the overall amount of energy remaining the same. In this experiment, potential energy was supposed to decrease as the mass attached to the pulley fell, while the kinetic energy was supposed to increase. In an ideal situation, the percent difference between these two values would be 0%, as all potential energy would be converted to kinetic energy. However, an average percent difference value of 70.83% demonstrates that this was not the case. This is due to experimental error in the form of random error, since it is not consistent between trials. Though the apparatus was meant to mimic a frictionless surface with the use of an air blower, some friction was still present, as the air blower on the apparatus was not as strong as it should have been. This caused friction and therefore lower velocity values to be measured, resulting in

lower calculated kinetic energy values. Thus, the results shown in the data section partially support the law of conservation of mechanical energy, though the presence of friction and human measurement error prevented the results from aligning perfectly with the conservation of energy equations. Conclusions The prediction that all of the potential energy would be converted to kinetic energy was partially supported by this experiment. The values for the change in the potential energy of the system were larger than the values for change in kinetic energy of the system. The kinetic energy values were smaller than expected due to the presence of friction. Friction caused lower velocity values to be measured, resulting in lower kinetic energy values. Therefore, the experiment can be considered successful in demonstrating the conversion of potential energy into kinetic energy, but not successful in demonstrating the conservation of mechanical energy. This lab taught the physics concepts of the conservation of mechanical energy, the conversion of gravitational potential energy into kinetic energy, and the energy equations. The results show that, in this setting with the given equipment, it is almost impossible to completely eliminate the presence of friction. To improve the experiment in the future, it would thus be useful to have a more powerful air blower or another means of decreasing the friction on the surface. This would result in more accurately measured kinetic energy values, and thus lower percent difference values....