did i do something wrong to get high percentages in the error analysis? (instructions and images below)

ge 4 of 8 Data Analysis: Angle 0: o .. _q(035m 8 =tan (n.som) * 0 =tan"1(0.583) = 0 =30.24 Trial 1: Vertical Positions: 1)d=0.144m * h=-0.144m sin (30.24) = h=-0.0725m 2)d=0.075m * h=-0.075m sin (30.24) = h=-0.0377m 3)d=0.319m = h=-0.319m sin (30.24) = h=-0.1606m Trial 2: Vertical Positions: 1) d=0.062m * h=-0.062m sin (30.24) = h=-0.0312m 2) d=0.129m = h=-0.129m sin (30.24) = h=-0.0649m 3) d=0.365m = h=-0.365m sin (30.24) = h=-0.1838m 52 of 520 words [ [3 Focus =5 + 1M1% Trial 1: Total Mechanical Energy KE = = mv2 PE = mgh E = KE + PE Moment 1: KE = = * 0.202kg * (1.150m/s)2 2 KE = 0.1335J PE = 0.202kg * 9.8m/s2 * (-0.0725m) PE = -0.143J E = 0.1335/ + (-0.143J) E = -0.0095J Moment 2: KE = = * 0.202kg * (0.760m/s)2 KE = 0.0583J PE = 0.202kg * 9.8m/s2 * (-0.0377m) PE = -0.074J E = 0.0583/ + (-0.074J) E = -0.0157/ Moment 3: 2 KE = = * 0.202kg * (1.766m/s)2 KE = 0.3149J PE = 0.202kg * 9.8m/s2 * (-0.1606m) PE = -0.317) E = 0.3149/ + (-0.317/) E = -0.0021J\fError Analysis: - Y%diff = X2l 100% o Trial 1: X1+Xx2 = = 9%diff between moment 1 and 2 -0.0095] (0.0157]) %diff = W{m *100% 2 %diff = [ 20| 100% -0.0126] %diff =49.2% = % diff between moment 2 and 3 -0.0157] (0.0021]) w 2 %diff = *100% e _ |-0.0136] %diff = | o] + 100% %diff = 152.8% = %diff between moment 1 and 3 0.0095] (0.0021]) 0 ey | * 100% 2z %diff = %diff = |"1""*j 100% 0.0058] %diff = 127.5% O Trial 2: . %diff between moment 1 and 2 - %diff = -0.0029/ - 0.01/ (0.00297 +.0.01/ * 100% %diff = -0.0129/ [0.00355J * 100% - %diff = 363.3% %diff between moment 2 and 3 %diff = -0.01/ - 0.0365/ 0.017 + 0.0365 * 100% - %diff = -0.0265J (0.02325] * 100% - %diff = 114.0% . %diff between moment 1 and 3 - %diff = -0.0029/ - 0.0365 -0.0029 +.0.0365 * 100% %diff = -0.0394/ 0.01687 * 100% %diff = 234.7%Energy Goals and Introduction In this experiment, we test and apply the principle of conservation of energy and the work- energy theorem. The work-energy theorem states that if there is work, W, performed on an object as it moves from one location to the next, then the kinetic energy, KE, of the object changes. We can symbolize this relationship as KE,+W =KE, (Eq.1) where the kineric energy. or energy of motion, of an object depends on the mass of the object, m, and its speed. v. KE = %mvl . (Eq.2) Work is performed on the object when it is subject to a force, as the object moves from one location to the next. A scenario such as that shown in Figure | is useful for defining the relationship between an applied force, F | the displacement, A7 , the angle between the force and the displacement, @, and the work due to the applied force. In the figure, a person is depicted pulling on a rope that is attached to a box, as the box moves from the point P; to the point Pz. Figure 1 The work performed by the force would be W = FArcos@. (Eq.3) Note that we don't know if the box is initially moving or not, or whether or not it is moving at the end. The act of applying a force either delivers or removes energy from an object or system, as it moves, based on the magnitudes of the force and displacement, and the angle between them. When the angle between the force and the displacement is greater than 90, the cos @ will be negative, meaning that the work performed by that force is negative. Note also, that forces that act perpendicular to the displacement would do (0 work! If we were to consider the work done by friction in the scenario of Figure 1, what would be the angle between the friction force and the displacement? Would the work done by friction be positive or negative? The gravitational force due to the Earth is an example of a force we often experience, and one whose effect must be factored into any laboratory experiment. The gravitational force falls into a class of forces called conservative forces. Conservative forces are forces that would perform the same amount of work on an object as it travels between two points, regardless of the path taken. The work performed by a conservative force depends only on the initial and final locations of the object. For gravity, this depends on the vertical distance between the two points, Ah. We can write the work performed by a conservative force, such as gravity, in terms of a change in potential energy, PE. For gravity the potential energy at a height i above some location where h=0is given by PE =mgh (Eq.4) and the work done by gravity as an object moves from one height to another would be W, =APE =-mgAh. (Eq.5) Because conservative forces allow us to express the potential energy at specific locations, it is possible to consider both the kinetic and potential energies possessed by an object at any moment. Using the mass of the object, m, its speed, v, and its height h above, or below, a location where h =0, we write the rotal mechanical energy of the system, E, as E= KE+PE=%mvl+mg, (Eq 6.) By considering total mechanical energy, we can then restate the work-energy theorem as follows: 1) If there is no work performed by nonconservative forces as an object moves from one position to the next, then the total mechanical energy at position 2 should equal the total mechanical energy at position 1. Or we could write, E =E,. (Eq.T) 2) If there is work performed by nonconservative forces as an object moves from one position to the next, then the total mechanical energy at position 2 should equal the sum of the total mechanical energy at position | and the work. Or we could write, E +W=E,. (Eq.8) Note that we have already accounted for the work done by gravity with our potential energy terms, as part of the total energy, E. It is also possible that the work could be negative, as we discussed earlier, causing the final energy at position 2 to be less than the energy at position 1. Figure 2 is a rough illustration of how you should conduct this experiment. You will want to have some kind of board or surface that can be raised and propped up on one end to act as your rolling surface, or incline. Note that you could just raise a table by placing some books or blocks under one end. Whether you use a raised object on the table or the table itself as your rolling surface, you should be able to measure the raised height, H. This is the difference between the vertical position when the surface is flat and the vertical position of the raised end. You should also find the total length, L, of your rolling surface. Those two measurements will allow you to find the angle, &, of your rolling surface above the horizontal direction. When the 10 device rolls a distance d down the incline, it will have sped up (What causes the 10 device to speed up?). It will also have moved downwards vertically a distance /. These two values, d and h, are also related to the angle , since they would be parts of a triangle similar to that created by L, H, and 6. Figure 2 The \"Wheel\" plots from the 10 device do a great job of telling us about distance traveled along the rolling surface (d), and the speed (v) from the moment we let go of the device. With these kinds of measurements, we can verify aspects of the work-energy theorem with the device rolling down the incline. Goals: (1) Measure and verify aspects of the work-energy theorem. (2) Make appropriate measurements and calculate the kinetic and gravitational potential energies of an object. Procedure Equipment computer with a USB port, the I0 Lab Device, a ruler, a rolling surface (some kind of long board, or a table) that can be propped up on one end 1) Be sure to open the 10 software, plug in the USB wand (Dongle), and then turn on the IO Lab Device. Ensure that the device is connected. 2) Click on the box to select the \"Wheel\" sensor. 3) Prop up the rolling surface for the experiment. Refer to the discussion of Figure 2 and measure the values for L and H. These can be used later to find the angle 6 for this experiment. 4) We are now ready to collect data. You may want to use a pillow or cushion of some kind at the end of your rolling surface to prevent the I0 Lab Device from falling on the floor, or crashing badly. Hold the device at the top of your surface and orient the positive y-axis, as labeled on the device, so that it points down along the surface. Hit \"Record and then release the device so that it rolls down the surface. Verify that the device begins with a position of O and a velocity of 0. Zoom in on your graph as you see fit and include this graph in your Data section of the lab report. Do not clear the graph yet, however! 5) Measure and record the position and velocity of the device at any particular moment while it was rolling down the surface other than the beginning. 6) Repeat step 5 at least two more times before you clear your graph. 7) Repeat steps 4, 5, and 6 so that you have a second, separate, set of data points. Label all the data from this second run, as \"Trial 2,\" in order to distinguish it from what you can call \"Trial 1" (the first set of data). Data Analysis First, work only with the Trial 1 data points. Recall that the accepted value for the mass of the 10 Lab Device is 0.202 kg. Use the values of L and H to find the angle & for this experiment. In the first part of the experiment (steps 5 and 6), you recorded several positons of the device. These were distances, d, from the starting point, where d = 0 (see Figure 2). Use these values and the angle you found to determine the vertical position, &, below the starting point at each moment. Note that if we choose the initial height to be a vertical position of 0 in our coordinate system, we should record these other vertical positions as negative (assuming we use a coordinate system where upwards is the direction of the positive height-axis. Use the velocity and the vertical position in each case to calculate the total mechanical energy at each moment, including the beginning. Question 1: Was there work performed on the device as it moved from one point to another? How can you tell? How do the total mechanical energies at each point compare to each other? Explain your results and justify any similarities or differences you find in the data. Repeat all the Data Analysis steps for the Trial 2 data you collected. Question 2: Compare your Trial 1 and Trial 2 data. What similarities, or differences, do you see? Do those similarities and differences make sense? Explain, Error Analvsis Choose a few of your calculated values of total mechanical energy from Trial 1. Find the percent difference between several of those values. Fodiff W"lem% [ 5+ 4| Separately, repeat this error analysis for the values in Trial 2 Question 3: What accounts for any differences you find in these calculated total energies? Explain your response. Questi i Conclusi Be sure to address Questions 1-3 and describe what has been verified and tested by this experiment. What are the likely sources of error? Where might the physics principles investigated in this lab manifest in everyday life, or in a job setting? Data: Length of Ramp: 23 2 inches = 0.60m Height of Ramp: 14 inches = 0.35m Trial 1: Any Position #1: 0.144m Any Velocity #1: 1.150m/s Any Position #2: 0.075m Any Velocity #2: 0.760m/s Any Position #3: 0.319m Any Velocity #3: 1.766m/s Any Position #1: 0.062m Any Velocity #1: 0.759m/s Any Position #2: 0.129m Any Velocity #2: 1.169m/s Any Position #3: 0.365m Any Velocity #3: 1.989m/s