AS90774 (Physics 3.1) Carry out a practical physics investigation with guidance, that leads to a mathematical relationship (version 2)

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1 Physics Exemplars AS90774 (Physics 3.1) Carry out a practical physics investigation with guidance, that leads to a mathematical relationship (version 2) Level 3, 5 credits. The following extracts from student work are intended to exemplify the boundaries between Achievement, Merit and Excellence for this achievement standard. While a particular grade would not be awarded on the basis of a single aspect of a student s work, these exemplars are designed to show features typical of work that level. See also: 2008 National Moderator s Report [ National Moderator s Report [ The explanatory notes (EN) of the standard give guidance about typical evidence that contributes to a particular grade. For Achievement, evidence will typically include (EN4): data relevant to the aim based on the manipulation of the independent variable and the consideration of other variable(s) that could affect the results uncertainties in raw data appropriate to the measurement a linear graph, including an error line, based on the data and relevant to the aim a conclusion that links to the aim and is drawn from information calculated from the linear graph. For Merit, evidence will typically include (EN5): accurate data relevant to the aim based on the manipulation of the independent variable over a reasonable range and number of values a description of the control of other variable(s) that could significantly affect the results the use of techniques to improve the accuracy of measurements appropriate uncertainties in raw and plotted data a linear graph with error bars and appropriate error line, based on sufficient data, relevant to the aim a conclusion that is relevant to the aim, based on the data, and is drawn from information calculated from the linear graph, including a processed uncertainty a discussion that evaluates the quality of the results. For Excellence, evidence will typically include, in addition (EN6):

2 uncertainties appropriately calculated in all processed data information from the linear graph is correctly rounded a discussion that shows critical thinking, evaluates and explains the validity of the results, and considers relevant physics theory. Conclusion Achievement: a conclusion that links to the aim and is drawn from information calculated from the linear graph. Merit: a conclusion that is relevant to the aim, based on the data, and is drawn from information calculated from the linear graph, including a processed uncertainty Excellence: information from the linear graph is correctly rounded Student Grade Student Response Moderator Commentary 1 Not Achieved My results clearly show that the greater the mass the longer the period of oscillation The aim is to give a mathematical relationship. This is too general as it does not refer to the nonlinear nature of the relationship. 2 Not Achieved / Achieved The relationship is y = m x 2 If the student shows no indication that they know what y, m and x refer to, this is not adequate. However if elsewhere they have identified y, x, and have calculated a value for m, this would be acceptable. 3 Achieved m = 24 L The relationship given is correct, but without uncertainties. 4 Merit m = 24 (± 3.95) L (± 5.8) The relationship given by the equation is correct but uncertainties are not rounded appropriately, which is required for Excellence. 5 Excellence m = 24 (± 4) L (± 6) Uncertainties are rounded appropriately.

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4 Linear graph and error line Achievement: a linear graph, including an error line, based on the data and relevant to the aim Merit/Excellence: a linear graph with error bars and appropriate error line, based on sufficient data, relevant to the aim Student Grade Moderator Commentary 6 Not Achieved Students must have applied the appropriate transformation to their raw data, to give a linear graph. This graph of the raw data has a straight line drawn (i.e. a linear relationship implied), but it does not show the expected transformation (T 2 ) so cannot be accepted.

5 7 Achieved For Achieved, an attempted error line is needed, but error bars are not. 8 Merit / Excellence Error bars and error line show the effect data uncertainty has on the gradient. There is no distinction between Merit and Excellence in the graph, so the final grade would depend on other aspects of the report.

6 Discussion Merit: a discussion that evaluates the quality of the results. Excellence: a discussion that shows critical thinking, evaluates and explains the validity of the results, and considers relevant physics theory. Student Grade Student Response Moderator Commentary 9 Achieved The period of oscillation is a T α L B relationship, as the graph drawn with the transformation is a straight line. The range over which the lengths were measured was relatively small which provided only a small range of results. A large range could be used in further experiments. The angle from which the pendulum was released was also inexact, as this had to be estimated. In future experiments a protractor could be used to measure this more accurately. The lengths were hard to measure as the metre ruler was accurate to 1 mm but the string could bend. Also the centre of mass had to be estimated. This could be found accurately, and then used. Air resistance would have an effect on the system, causing it to have a different period. The original equipment changed L, but this would also affect the period, so the method was modified to only change L B. There was human error in the timing, as the distances had to be judged by sight. For Merit, students should have a discussion that evaluates the quality of the results. This discussion does not evaluate the quality of the results beyond general comment on experimental limitations.

7 10 Merit I improved my accuracy in many ways. I timed the period for each mass three times and took the average, and the range helped me make a reasonable uncertainty. By repeating and taking averages I reduced the human timing error. I also times 10 oscillations and divided it by 10 as it would have been hard to time one oscillation, especially with the smaller masses where the period is quite small. If I had timed a single oscillation my uncertainty would be unreasonably high. I controlled variables by making sure they were all the same for each test. I made sure that I pulled the end of the cantilever down 2 cm for each one, so the distance of the oscillations is the same. I also kept the length of the cantilever the same for each test and made sure that when I added masses, they were stacked on top of each other so the weight force acted on the same part of the cantilever for all tests. 11 Merit The relationship between the distance apart of the ropes (D) and the period of oscillation (T) is: T = (0.74 ± 0.04)/D + (0.0 ± 0.3) Discussion evaluates the quality of the results, giving reasons why they are reliable. This comparison of theory and experiment assesses the validity of the results (shows how they fit with expected values), and also considers relevant physics theory. However this is not enough for Excellence. When I substitute values of g = 9.81, r = 1.01, L = 0.4 into the theory equation I get:

8 T = (0.75)/D This fits with my experimental relationship as the value 0.75 is near the middle of my gradient range 0.74 ± 0.04, and the intercept (0) is also in the middle of my intercept range (0 ± 0.3). 12 Excellence This experiment was designed to model a person jumping on a trampoline, but there are some flaws: The ruler is not the same shape as a trampoline, and it is not known whether the ruler will deflect in the same way as a trampoline as it is loaded. However, without a real trampoline, this cannot be tested. On a trampoline the mass (person) bounces on top of the mat, inputting their own energy to the motion. Also the force they exert will change, increasing as they land, and maybe disappearing if they leave the surface. In my experiment the mass was hung passively below the ruler, a so it applied a constant force to the ruler. This would cause the ruler to oscillate with damped SHM, unlike the trampoline, which would not do SHM on account of the irregular force being applied by the person jumping. Critical thinking shown in the comparison of model and reallife situation (ruler c.f. trampoline). A factor is identified, and its effect is described (changing force applied as person bounces, causing non-shm motion).

9 Below are further examples of individual discussion statements. In most which exemplify Excellence level critical thinking, the student identifies some factor which could affect the results and explains the effect which that factor might have had. The overall grade attained would, of course, depend on many other aspects of the report. Student Student Response Moderator Commentary 13 It was extremely hard to get all of the string lengths exactly the same. A possible factor, but no explanation of its effect on the results: Not Excellence. 14 To determine the accuracy of my results and their validity I decided to use my mathematical relationship to interpolate a temperature value for an arbitrary current, and then compare this to a theoretical value 15 The experimental gradient is steeper than the theory predicted. This could be because the theory doesn t take into account friction in the real-life scenario. 16 The bridge wouldn t be uniform along its length like a ruler. That would obscure the results. 17 In the real life situation there were people standing on the swing-bridge. This would affect the position of the centre of mass, moving it towards the end where the people were. 18 I noticed that the wood was made up of several layers. This means its stiffness factor may have varied depending on the degree to which the wood was bent. As it bent, the upper layers would be stretched more, so could become stiffer. Similarly the lower layers would be compressed, changing their stiffness. Evaluating the quality of the results: Merit level, so far. Explanation too vague to be of use: Not Excellence. A possible factor, but no specific effect suggested: Not Excellence. Identifies the factor of people standing on the bridge, and describes it in terms of relevant physics (COM), but does not specify its effect on the results: Not Excellence Possible factors described in some detail, though their actual effect on the results obtained is not stated: A weak Excellence.

10 19 With my graph there is an intercept at T = -0.2 s, implying that the period is negative, which cannot happen. A possible reason for this is the way I timed the pendulum. I judged the end of the 10 oscillations by eye, but if I anticipated the end point too early, my times would be too short, and the periods would be shorter than they should be, causing the negative intercept. 20 The formula would not apply in real life as the suspensions would be steel cables, not cotton thread. Because the steel cable has more mass, it would have greater rotational inertia about the axis. This would make the bridge more reluctant to move, making its period longer. 21 The horizontal length of the ruler varied when it sagged. This sagging meant that the mass was significantly closer to the bench than if the ruler remained horizontal. At larger masses (greater sags), the effective length would therefore be smaller, so the period would be smaller than expected. 22 The mass of the rod itself was not taken into account. This resulted in the intercept being far from zero. When the square root of the mass was found the effect of the non-zero mass of the rod would be more significant for smaller masses. 23 According to the formula the period for no mass should be zero. If my line passed through Attempts to give a reason for the negative intercept. A weak Excellence at best. (It is unlikely, where the time for ten swings has been measured, that the period would be out by 0.2 s.) Identifies an aspect of physics, that heavier cables mean greater inertia, and how this might affect the period: Excellence. Explains why the applied mass will affect the period differently from expectation: Excellence. Explains why the rod s mass will affect the gradient of the graph: Excellence. Uses physics theory to evaluate student s results, and account for differences between actual and expected results:

11 that point (0, 0), the gradient would be steeper, so the stiffness factor would be lower and closer to the theoretical value. 24 For one of the masses (0.075 kg) the times were all the same so there was no range of data to estimate uncertainty from. There must be some uncertainty, given human reaction time, so a nominal uncertainty of 0.05 s was assigned to it. 25 The range of masses used is nowhere near the mass of the object it is designed to model. Even though my data fits the graph well, I cannot be sure that the trend would continue like this for the much larger real-life mass, so the conclusion might not apply in reality. 26 As the mass swung back and forth it also spun. The spinning caused the string to untwist, increasing the length of L. The increased length would cause the time period to be greater, increasing the value of the intercept. Excellence. Evaluates and explains the validity of the results: Excellence. Evaluates and explains the validity of the results: Excellence. A factor identified, and its effect described: Excellence.