Question Description
Templates/Data/Graphs
All lab reports should include the following items.These can be stacked at the beginning of the report or placed inside the main writing section, close to the sentence they are referred to with.Included are examples of good items and examples of mistakes students frequently make.
Experimental Design Template:This should be cut and pasted from the original experiment file and filled in.There should be one of these for each factor your group investigated (you may have up to four of these).Be sure to number and title the tables for easy reference later (ex. “Table 1.Experimental design plan for determining impact of mass on acceleration of car.”)Here are two examples:
Professional Experimental Design Template
This example is of high quality because it has a label, all boxes are filled in and they gave actual values for the CVs.The hypothesis and prediction boxes are filled out correctly.
Newbie Experimental Design Template
Experimental Design Template | |
Research Question: | What factors impact the rotational inertia of a rotating system? |
Dependent variable (DV): | Rotational Inertia |
Independent variable (IV): | mass |
Control Variables (CV): (include actual values once chosen) | Radius, force, pulley radiusL |
Testable Hypothesis: (should contain IV and DV) | The more mass, the more rotational inertia |
Prediction: | Mass will make the rotational inertia larger |
This example is not the best because it has no label above it, gives no actual values for radius, force and pulley radius and also messed up the hypothesis and prediction boxes.
Data Tables:You should have a data table for each factor you investigate.If you investigate one factor twice to improve errors, include both studies.Tables need to have numbers and titles for easy reference (ex. “Table 1.Data for investigating whether car mass impacts acceleration.”)Put column headers with units on each table.
So Close to Professional Data Table
This is professional because it has clearly labeled column headers with units as well as a table number and title.
One error this table has is that the data was not reported in SI units.They should have recorded kg instead of grams.
Newbie Data Table
This table has no column headers, no units and no table number and title.The reader has no idea what these numbers mean.Also the times are very rounded – the group failed to report all sig-figs that were reported by the lab equipment.
Graphs:You should have a graph for each factor you investigate.If you investigate one factor twice to improve errors, include both studies.Label each graph axis with the appropriate variable (spelled out) and units.Include error bars and add an explanatory note on the graph when the error bars are too small to be seen.Include on the graph the equation for the best-fit line and R-squared value.Number and title each graph for easy reference (ex. “Figure 1.Graph of cart mass versus speed.”)
Professional Graph #1
This graph is pro because it includes all of the requested information, has a figure label at the top and very clear error bars (this was from a lab with only y-axis error bars – be sure to include both x-axis and y-axis error bars when that is appropriate).The equation of best fit and R^{2} value is also easy to find.
So Close To Professional Graph #2
This graph is professional because it, too includes are the required information but is also a good example of a graph where the error bars are too small to see.This student chose to label the error bars as too small to see in both the graph label on top as well as the asterisk-note at the bottom (circled in blue).Please be aware that it doesn’t normally occur to professor to look for the error-bar notes in the title – it is much better to have a note about them at the bottom or even in a text-box in the graph itself (as inside the red circle).
The mistake on this graph is that the title is in x vx. y form, “Pendulum Length (m) vs. Time of Period (s)”.Actually, when you use the “vs.” title, it should be y vs. x.So the correct title for this graph would be “Period vs. Length”.
Newbie Graph
Measurement Uncertainties:In a typical lab, you will be taking several measurements.These include lengths, times, masses and accelerations.Each measuring instrument has an uncertainty associated with it.You need to list these uncertainties.Also, a lab may have you measure your measuring technique uncertainty by finding the standard deviation of several identical runs.You need to list all these uncertainties and then write a sentence or two about how your group used those values to determine the error-bar lengths on the graphs.Here is a professional example from a lab where students were figuring out the acceleration due to gravity:
In this lab we used a meter stick (precision of 0.5 mm or 0.0005 m), a digital mass scale (precision of 0.05 g or 0.00005 kg), and the motion detector (precision of 0.0005 m/s^{2}).We tested our measuring technique for getting accelerations and found the standard deviation, σ, to be 0.0766 m/s^{2}.Because the measuring technique for acceleration gave a larger error value than the equipment precision is, we will use the 0.0766 m/s^{2} value for acceleration uncertainty.Therefore, error bars for lengths and mass are 0.0005 m and 0.00005 kg, respectively.Error bars for acceleration are 0.0766 m/s^{2}.
Discussion and Conclusion
- Restate the research question being investigated in the lab.Example: “This lab attempts to answer the question ‘What factors affect the acceleration of a cart on a ramp?’”
- Discuss how each experiment addresses the research question.Include the conclusion of each experiment – the mathematical model that you developed using the experiment and graphs.Be sure to refer directly to the graphs in your discussion.
- Discuss which errors (random and/or systematic) were present and what was done to reduce them (or could be done in the future to reduce them).[I have no advice at this time on this section other than to be sure to include a “way to improve” for every error and to reread pre-lab worksheets for refreshers on what is appropriate to discuss for errors and what random vs. systematic means.]
- Discuss any limitations in this experiment that may impact the generalizability of your results.
- Discuss any assumptions made
Professional Answer to Discussion #2:
Our group investigated what factors may impact the period of a pendulum. The first experiment tested whether varying bob masses affected the period while keeping the string length/type, release angle, ring stand height, number of trials, and device operators consistent (see Table 1). Due to major random error, we could not rely on our recorded data. As such, we analyzed another group’s data, which was collected in a way that minimized error. According to the data collected by Group 3 in PHYS 2001L-007 13FS, we claim that mass has no effect on the pendulum period. This is because as the bob mass steadily increases, the period time first decreased, then increased, and decreased again (see Table 2 & Figure 1). Due to the fluctuations in data, there was no visible pattern or trend signifying a positive or negative correlation. A standard deviation of 0.0142361 was calculated by conducting 10 trials of releasing a 0.02 kg bob from an angle of 110 degrees. The vertical error bars (formed from the computed standard deviation) overlapped amongst all data values. Therefore, we cannot be certain the collected values were valid. Thus, we are confident in our claim that there is no correlation between bob mass and pendulum period.
Our second experiment investigated whether the release angle affected a pendulum’s period. This was done by keeping the bob mass, string type/length, height of ring stand, number of trials, and device operators controlled (see Table 3). We were forced to analyze another group’s data once more because we did not collect a sufficient amount of data for this experiment. According to the data collected by Group 1 in PHYS 2001L-007 19SS, the release angle was found to be positively correlated with the pendulum period (see Table 4 & Figure 2). There was a clear upward trend, which was represented by a polynomial relationship of: T = 0.0002A^{2} - 0.0012A + 1.2474 with an R^{2} value of 0.9619. After testing out all possible trend line relationships, we chose the polynomial curve because it had the R^{2} value closest to 1.000. The graph’s error bars with a range of 0.0142361 overlapped for angles less than 40 degrees, but not for angles larger than 40 degrees. Therefore, we confidently claim that a release angle larger than 40 degrees is positively correlated with the period of a pendulum.
Our third experiment determined whether the pendulum length affected its period. Control variables included: bob mass, release angle, height of ring stand, type of string, number of trials and device operator (see Table 5). This time, however, we incorporated a Photogate device to measure and record our data, thereby providing a range of uncertainty value of 0.001. According to our collected data, a clear upward trend can be seen, so we claim that pendulum length and period are positively correlated (see Table 6 & Figure 3). A power relationship of: T = 2.0066L^{0.5024} with a coefficient of determination of 0.9996 was found to best match the trend line. None of the error bars overlapped for any of the data values. And, considering how close to 1.0000 the R^{2} value is, we are very confident in our claim that the pendulum period increases as its length increases.
Highlights:This student was sure to use a trifecta of information to prove her point for all three studies in the pendulum lab.She used the shape of the graph (highlighted in yellow) as evidence, she used error bars as evidence (highlighted in pink) and she used the R^{2} value of the curve fit – when a curve was fitted - as evidence (in green).
This student also realized that she saw a pattern in the angle study that was true only for angles above 40 degrees.She was careful to point this out to the reader.
Also the discussion included equations for all the experiments, correct references for borrowed data.
Finally, the most important thing – it made frequent references to the data and graphs.
In this section, be sure to emphasize your controls.You only had a certain range of lab equipment to work with.Maybe your masses in a lab were only values from 10 g up to 1 kg so your results might not be valid past a certain mass?Perhaps you only tested small angles of swing so your results aren’t really explored past 60 degrees?Be sure to list any/all limitations like this.Think of it as the “honesty” section.
This section really compliments the errors in #3.Were you assuming that a ramp had zero friction?Were you assuming that springs are infinitely stretchable?Were you assuming something was horizontal when it might have had a curve or tilt to it?Were you assuming materials were or were not stretchy?Did you assume springs don’t die a little bit each time you pull them (sorry that was my depression coming through)?Did you forget to measure the hanging masses and assumed they were actually the value printed on their sides?You could go nuts in this section – make sure you can think of at least three (six is better) assumptions you’ve made.
Final Answer
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SURNAME 1
Students name
Institution affiliation
Professor
Course
Date
Introduction
Periodic motion is the time needed for an object in motion to return to its initial point of start.
Focusing on simple harmonic is a type of special periodic motion whereby the object will oscillate
sinusoidally. When an object returns to its equilibrium position under restorative force which is
directly proportional to the displacement, then that is the simple harmonic motion.
F= -KX…………………………………………………………………………………………………………………………...Equation 1.
This example describes Hooke’s law and the restorative force under motion. For ideal masses spring
elastic spring s will have to obey this equation. The time required to make one oscillation will be
depended on the stiffness of the spring (K) and the mass (M). The key purpose for this lab report is
for us to understand various ways of determining the spring constant. In general, we define spring
constant as the stiffness of the spring being used in the experiment. Springs have elastic property
and you can compress or stretch them and they return their normal state. Spring when compared
with other material have high spring constant and when deformed they follow third newtons law of
motion, which states that action and reaction are equal and opposite. He elastic behavior is analyzed
through Hooke’s experiment in lab. Hooke’s law states that force applied to spring is directly
proportional to the extension. The core objective for this study is t carry investigation on simple
harmonic motion by use of oscillating spring and simple pendulum and determine spring constant.
Materials
Materials used in this experiment include string, mass hanger, table clamp, metal ball, digital
balance, meter stick, springs and stopwatch.
Procedures
Our lab procedures and steps involved using the mentioned apparatus and setting in the lab as
shown in the figure below.
SURNAME 2
Figure 1: experiment setup in the lab.
From the theory introduced in in the first part of this report we have seen that the Hooke’s is obeyed
by springs when ideal is hanged on them. In simple words the force is directly proportional to
extension of the spring. Our prediction or hypothesis is that the graph to be drawn when the data
obtained is set into a graph will have to be a straight line as per the law. This graph will be checked
against the actual graph to be drawn after the results.
Figure 2: Prediction graph
SURNAME 3
In our practical we had various types of springs (long silver, black, blue...
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