E201: WORK, ENERGY AND POWERFRISNEDI, Nadine T. OBJECTIVE The experiment aims to accomplish its two main objectives. The first one is to determine the power of the fan cart by using the definition of work and the energy conservation principle. Through the experiment, the students will be able to gain more knowledge and appreciation about the concepts of work, energy, and power. The experiment can also help the students understand on how the displacement of an object is important in determining the amount of work done. The experiment will also tell us that work, energy, and power are closely related to each other but not totally the same. The second objective is to be able to learn how to compute for the work, and power not just by the fan cart but also work for a motion along a curved path. The experiment will help the students be able to understand the applications of the given laboratory formulas in real life and will surely be helpful in studying Physics and other concepts about it. This experiment is also significant because it shows the basic situations and examples on how we can define and calculate for work, energy and power. MATERIALS AND METHODS In the first part of the experiment, the dynamics track and fan cart serve as the main materials. Before starting, it is better to make sure that the dynamics track is leveled on the table. Using the angle meter, the track can be checked if it is leveled horizontally when the bubble is at the center below the zero angle. The fan cart’s fan should also be turned around wherein the arrow is pointing to zero. After setting up the track and the fan cart, the pulley with clamp must be placed on the end of the track. The string with the pan connected on the other end it was attached to the fan cart. The fan cart should be placed on the track, while the string should pass over the pulley. Upon turning on the power of the fan cart in a low setting, the direction it goes is based where the fan’s orientation. The cart must move away from the pan to counter the force. Weights was put on the pan and afterwards the fan cart was turned on. If the fan cart goes along the direction of the pan, the force is not yet balanced. Adding more weights to the pan is necessary until the correct amount of weight is reach which is determined when fan cart is on a steady position which means that the force is now balanced. Page | 1 (Figure 1. To check if the dynamics track is leveled horizontally) (Figure 2. To determine the force, a string was attached to the fan cart and the end to the pan.) For the next part of the experiment, the string was removed from the cart. The photogates must be assembled and connected to the smart timer. The two photogates were placed in different positions. We taped the metal fastener to the fan cart since the magnet on the cart is not strong enough to hold it in the position and using tape will secure it in a way that it will not bump the photogates but pass through its sensors when it moves along the track. The fastener served as an indicator of the fan cart so the photogate can detect it. The results in the timer were used to determine the amount of work done. Three trials were performed in every distance to make sure that the experiment was executed properly. Another three trials were also done, this time the second photogate was moved further, in order to have a varying displacement. (Figure 3. To determine the time, the fan cart should pass through the photogates while the smart timers records the time.) (Figure 4. Fan cart in motion) Page | 2 In the second part of the experiment, the mass was attached to the string and the other end was tied to the iron stand. The initial height which is the distance between the mass and floor was measured using the meter stick and the height must be until the middle part of the mass. The mass was pulled slowly by applying a horizontal force using the spring balance. The final height was measures using the meter stick while the force applied can be obtained from the shown measurement on the spring balance. The students performed several trials in this part upon adjusting the height and force applied until the string L becomes horizontally leveled. After obtaining the data, the work done by the force F and gravitational potential energy of the mass was computed. (Figure 5. The mass was pulled by the spring (Figure 6. As the mass is pulled, the height is measured using the meter stick.) balance and the angle was measured.) OBSERVATIONS AND RESULTS In the first part of the experiment, the force, work and power of the fan cart was determined. The force of the fan cart was obtained by adding the mass of the pan and the weight added to it and multiplying it to the gravitational acceleration constant, g = 9.8m/s 2. The force was proven to be correct from the experiment since the fan cart was not moving along the dynamics track when turned on when the added weight was placed on the pan that was connected through the string and to the cart. For the next part of the experiment, the displacement is the component that is changing per trial which is determined using the positions of the two photogates. The displacement was measured by subtracting the distance of the first photogate from the second photogate. The time was determined using the smart timer and the photogates. Work was computed by multiplying the force and the displacement. Power on the other hand was calculated by dividing the computed work by time. Page | 3 Table 1: Determination of Force, Work, and Power Force of the Fan Cart = weight of the pan + weight added = 0.294N Trial Displacement, S Time, t Work Power 1 0.4 m 0.6204 sec 0.1176 Joules 0.1896 Watts 2 0.5 m 0.7593 sec 0.1470 Joules 0.1936 Watts 3 0.6 m 0.8920 sec 0.1764 Joules 0.1978 Watts 4 0.7 m 1.1074 sec 0.2058 Joules 0.1858 Watts Sample Computations: Trial 1 Mass of pan = 5g, Mass added = 25g, g = 9.8m/s2 F = (mass of pan + mass added)(g) (1) F = [(5g + 25g)(1kg/1000g)](9.8m/s2) F = 0.294 Newtons F = 0.294 N, S = 0.4 m W = (Force) (Displacement) (2) W = (0.294 N) (0.4 m) W = 0.1176 Joules W = Joules, t = sec Power= Power= Work Time (3) 0.1176 J 0.6204 s Page | 4 Power=0.1896 Watts In the second part of the experiment, the length of the string, weight of the mass, and the initial height can be easily gathered. The final height, angle, and displacement were determined by measuring using the meter stick and protractor. The force was obtained by pulling the mass using the spring balance. Work and Gravitational Potential Energy was computed by using the given formulas from the laboratory manual that will be shown in the sample computations. Table 2: Work by a Force on a Curved Path Length of String, L = 0.29 m Weight of mass, w = 4.9 N Initial height, ho = 0.1625 m Trial Force Final height, hf Increase in height, h Angle, θ Displacement, X Work Gravitational Potential Energy 1 5N 0.2650m 0.1025m 400 0.181m 0.3325 J 0.5023 J 2 6N 0.2825m 0.1200m 550 0.237m 0.6059 J 0.588 J 3 10N 0.3365m 0.1740m 700 0.285m 0.9349 J 0.8526 J 4 12N 0.4365m 0.2740m 900 0.314m 1.421 J 1.3426 J Sample Computation: L = 0.29 m, w=4.9 N W =wL(1−cosθ) (4) W = ( 4.9 N ) (0.29 m)(1−cos 40 °) W =0.3325 Joules m = w/g = 4.9N/9.8m/s2 = 0.500kg h = hf -ho= 0.2650m - 0.1625m = 0.1025m Page | 5 PEg=mgh PEg=( 0.5 kg )( (5) 9.8 m )(0.1025m) s2 PEg=0.5023 Joules DISCUSSION & CONCLUSION From the performed experiment, I could say that it was a success. By following the procedures stated in the manual properly gave us relevant data. According to the laboratory manual, work is defined as the product of force and its distance. For example, by getting the product of the force applied and its displacement, we can get the value of work. The data we gathered made sense because as shown from Table 1, that as the displacement increases, the value of work done also increases. They have a directly proportional relationship. For example, the second trial has larger displacement compared to the first trial. With this, the value of work done is also larger than the first trial and it continues for the succeeding trials. Upon obtaining the value of work, the power can now be computed by dividing work by time. Our data from Table 1 also tells us that as work and time increase, power also increases. For example, the second trial has larger value for work and for time compared to the first trial. With this, the value of its power is also larger than the first trial and it continues for the succeeding trials. With these conclusions, I could say that we were able to determine the power of the fan cart by using the definition of work and the energy conservation principle which was the first objective of the experiment. In the second part of the experiment, we have computed the work for a motion along a curved path. The data we gathered made sense because as shown from Table 2 tells us that as the height increases, applied force also increases, and so are the other components such as angle, displacement, and work increases. They are all directly proportional. The work was computed using the formula: W= wL(1-cosθ). To have a better understanding, the second trial from Table 2 shows that an increase in height, force, angle, also gives a larger displacement and work done compared to the first trial. The Gravitational Potential energy on the other hand was computed using the formula PEg=mgh. It shows us that mass and height are directly proportional to the Gravitational Potential Energy. For example, since the height, h from the second trial is larger than the first trial, the Gravitational Potential Energy of the second trial is larger than the first trial. With these conclusions, I could say that we have successfully completed the objectives of the experiment. From the experiment, I could honestly say that the errors that might have been committed were very least especially in the first part. The possible sources of error for the first part can be the inaccurate measurement of the displacement of the photogates since it is placed manually and the inconsistency of the smart timer since some trials we did gave us results that were not close to the previous time so we had to run a test again. I believe that the second part of the experiment is much likely to have an occurrence of errors because the data gathered is based from Page | 6 measurements that was done manually. Incorrect measurement can have an effect to the data. We could recommend that obtaining the measurements should be done carefully and accurately. Getting the measurements on eye level can be helpful. ACKNOWLEDGMENT & REFERENCE I would like to thanks my groupmates for being so cooperative upon doing the experiment. I appreciate all of their efforts since without their help, our experiment will have a great chance of failure. I would also like to thank my friends Vivi and Alvin for giving me advice in writing this lab report. They helped me write the appropriate stuff so the report will have a good flow of thoughts. I also thank our professor, Prof. Ricardo F. De Leon, Jr. for guiding all throughout the experiment. I thank him for instructing us on how we should set up the materials and equipment for our experiment and teaching us how to compute easily using MS Excel. Lastly, I would like to thank my family for supporting me in my studies as I pursue my degree in Mapúa. Reference: Calderon, Jose C., (2000) College Physics Laboratory Manual, Mapúa Institute of Technology, Manila: Department of Physics. (Objective, Materials and Methods, Observations and Results, Discussion and Conclusion) Page | 7