Lab #4 - Electrical Energy

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City College of San Francisco *

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Mechanical Engineering

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Dec 6, 2023

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Lab #4 : Electrical Energy Willem Botha Deobrah Harris 9/14/23 Abstract : In this lab we were tasked with measuring the power and electrical energy used by an electric motor. The equipment we used was similar to the previous labs but also included an electric motor, 100g weight set, weight holder, and string. We used this equipment to determine the gain in potential energy of mass lifted by the motor, calculate the motor’s efficiency, study the efficiency under different conditions, and see if a falling mass could cause our motor to act as a generator. Experimental Setup : First, we set up all of our equipment and plugged in our wires via the diagram on page 2 of the lab instructions. We began the experiment by doing a test run of the motor by adding a 10g weight to the string and turning on the power supply. We increased the voltage of the power supply being sure to not exceed 6V and observed the motor slowly raising the weight off the ground. Simultaneously, recording the current and voltage over a distance of 1 meter. We noticed once the power supply got to 3.1V it started to pull the weight up and as the weight got closer to the motor the current decreased to 1.5-1.7 Amps. One of the things we noticed was the energy change in the motor, it required more power in order to lift the weight due to inertia. Before proceeding with our experiment we made a hypothesis about what we thought the efficiency of the electric motor would be. Taking into account our first trial, we thought it would be around 50% due to the wasted heat and the power that the motor would have to omit. Proceeding with our experiment, we placed a 10g weight at the end of the string, started the Logger Pro data collection and increased the voltage until the weight reached the top of the motor. After collecting the voltage and current data we repeated the process by adding 10g each time until we reached 100g. To see if our motor could act as a generator, we attached a 100g mass to the motor and let it drop one meter while collecting data on the current and voltage. Because our falling mass would not fall due to the friction of the motor, we used another group’s data instead of producing our own. Experimental Data: Distance mass was lifted: 1m Load Lifted (g) ± 0.03 Electrical Energy Input (J) ± 0.001 Mechanical Energy Output (J) Efficiency % 12.80 1.054 0.1256 ± 0.0006 11.92

22.75 2.291 0.2232 ± 0.0009 9.742 32.75 2.234 0.321 ± 0.001 14.38 42.88 3.053 0.421 ± 0.001 13.78 52.91 2.248 0.519 ± 0.002 22.82 62.89 2.904 0.617 ± 0.002 21.25 72.92 2.328 0.716 ± 0.002 30.73 82.91 3.781 0.814 ± 0.002 21.52 92.90 3.705 0.912 ± 0.003 24.60 103.4 2.888 1.015 ± 0.003 36.39 Efficiency as a function of load: Energy generated through the falling mass: 0.2883 ± 0.001J Data Analysis:

To find the total mass between the hanger and the weights placed on it, we added the mass of the hanger (2.80 ± 0.02 g) to all of our measured masses. The first mass was calculated through this equation: 10.00g + 2.80g = 12.80g ± 0.03. Since the Logger Pro data collector measured the current and the voltage over the time the masses were lifted, we were able to calculate the electrical energy that was sent to the motor through the power supply. Since current multiplied by voltage gives us power, we created a graph that calculated power over time using the previous two variables. The area under this graph gives us the total energy sent to the electric motor, which can be seen in the second column of our table. Because the electric motor and the cables used to connect it are not 100% efficient in carrying electricity, the actual input of electrical energy is not equal to the amount of energy the motor actually uses in carrying the mass. This energy, known as the mechanical energy output in the table above, can be found through the equation PE = MGH. PE is the potential energy of gravity that the masses gain when they are being lifted, which is also equal to the amount of energy the motor uses in lifting the masses. M is for the total mass being lifted in KG, G is the gravitational constant of 9.8120 m/s^2, and H is the height that the masses travel. The first mechanical energy output data point was calculated through this equation: PE = 0.01280 kg x 9.8120 m / s 2 x 1.000 m . Since the mechanical energy output varies from mass to mass, its uncertainty also varies between each mass. To calculate this uncertainty we used the error propagation for multiplying different data points: δPE = PE x (δM/M + δG/G + δH/H). The first uncertainty was calculated through this equation: 0.0006J = 0.1256J x (0.00003KG / 0.01280KG + 0.02m/s^2 / 9.8120m/s^2 + 0.0005M / 1.000M). Finally, we were able to calculate the efficiency of our system by dividing the mechanical energy used by the electrical energy sent out. Our first efficiency was calculated through this equation: (0.1256J / 1.054J) x 100% = 11.92%. Using our efficiencies and our load values we were able to create the scatter plot above. We can see that our motor was most efficient at our highest load, and overall the efficiency was greater when the load had more mass. The remainder of the electrical energy that was sent out was lost due to heat loss. The efficiencies in the table and scatter plot above are much smaller than our previous guess of 50%. Another group found the voltage and current as a function of time for a falling mass that spun a motor. They then integrated the power found by the voltage multiplied by the current, and came out with a total energy of 0.2883J. This means that the falling mass created 0.2883J when it spun the motor. Conclusion : We were able to successfully calculate the efficiency of an electric motor moving a mass. The efficiencies varied across the different masses, however the efficiencies became greater when the mass was heavier as a whole. This means that the electric motor is more efficient at carrying higher mass loads when compared to carrying lower mass loads. We were also able to generate energy through a falling mass of 100g, which came out to be 0.2883J. A possible source of error could have been the exact distance the masses traveled. It was extremely

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difficult to stop the motor when the masses traveled exactly one meter. However, since we integrated the power over time to get a final energy, this variance in height did not actually play a significant role in our results. We can then conclude that our results and calculations are accurate.