error in measurement
Difference between the measured value and the targeted true value for the physical quantity.
uncertainty
A number that gauges the doubt of a measured value; it is due to the measurement tool and/or technique.
Ranges of uncertainty
The uncertainty is used to determine the range of uncertainty (see diagram below). Future repeated measurements and the true value are likely to fall in this interval so it is desired to have as small a range of uncertainty as possible.
example of range of uncertainty
The figure illustrates the distinction between error and uncertainty. Assuming that the object's truemass is given to be 130.30 grams, the error in the measurement is 0.03 g which is the difference between the measurement (130.27 g) and the true value (130.30 g).
systematic
These errors result when the actual measurement is not the same as the assumed measurement, such as using a balance that has not been properly calibrated. These are "one-sided" or "biased" errors; repeated measurements favor values either higher or lower than the true value. Error cannot be reducedby repeating measurements and taking an average. These types of errors, ifdetected, can be reduced by "fixing" the problem, such as zeroing the scalewhen nothing is on it.
Random errors
These errors are fluctuations in measurements inherent to the measuring device itself or to the chosen experimental technique. These are "two-sided" errors;repeated measurements have an equal chance of lying above or below the true value. Error can be reduced by repeating the measurements and taking an average or by refining the measurement method or technique. A common source of random error is estimating the least significant figures when reading an instrument, such as the decimal place beyond the closest markings of a graduated cylinder or the drifting numbers of a meter that hasn't settled.
A student measures the mass of a rock three times using the same properly calibrated analog (not digital) balance and gets slightly different values: 22.46g, 22.42g, and 22.44g. What type of error may have occurred here (systematic and/or random)? How would the student minimize the impact of this error during data analysis?
Because the balance was properly calibrated, it is likely that the error here is random error. The fluctuations in measured mass values could be due to a variety of issues including parallax in reading the scale (i.e. not looking head on when taking the measurement readings), scale not being truly balanced when reading was taken, etc. The student could minimize the impact of random error by taking multiple measurements and finding the average.
Q2. After collecting length data a student notices that the tape measure used was stretched out after years of use. What type of error may have occurred here (systematic and/or random)? How would the student minimize the impact of this error during data analysis?
Because the student noticed that the tape measure was stretched after years of use, this implies the presence of systematic error. To reduce this error the student needs to determine how much each measurement may have been off by comparing the original tape measure to one that has not been stretched out over years of use (such as a tape measure made of metal). Once the student knows how much each measurement is off, the student can adjust the original measurements accordingly. NOTE: Use of a tape measure relies on a person reading the scale, which introduces random error. Random error can be minimized by taking multiple measurements and calculating the average.
What measurement and uncertainty should be reported for the length of a pendulum measured from one end of the string at 0.00 mm to the bottom of the bob at the other end, shown here? The smallest division on the ruler shown below is 1 mm.
The length falls between 128.8 and 128.9 cm, with it being closer to 128.9. A common convention is to estimate one digit further than what is known. Therefore, a reading of 128.88 cm or 128.89 cm is reasonable. The uncertainty is estimated as half the smallest division on the measuring device. The smallest division is 0.1 cm so the reported uncertainty is 0.05 cm. This measurement is reported as 128.88 ± 0.05 cm. Note that there are different conventions but this is the one we will use in lab.
Consider an experiment conducted by two students who measure the acceleration due to gravity, g.Student A finds a value for g to be 9.77 ± 0.05 m/s2, and student B finds a value for g to be 9.75 ± 0.02 m/s2. Which student, if any, is consistent with the accepted value of 9.80 m/s2 for the acceleration due to gravity in Cincinnati, where the experiment was conducted? Note that the "true value" of 9.80 m/s2 is a more precisely measured value that has been rounded to three significant figures, so no range of uncertainty is reported here for this value.
To answer this question, each student must first determine the range of uncertainty for their final values to decide if the ranges overlap with the true (accepted) value of 9.80 m/s2. Because statistically 95% of the measurements fall within two standard deviations, the students might choose to use ±2σ in computing their ranges of uncertainty. In this way the students are able to claim at the 95% confidence level that their ranges actually include the true value. Note: In this lab course we will use ±2σ when computing comparison ranges, as this yields a range of values for which there is a high level of confidence that the true value lies within it. However, remember that standard convention is to report measurements with just one standard deviation; that is, mean ±σStudent A: • She calculates the ±2σ range for the measurement to be: (9.77 - 0.1, 9.77 + 0.1) m/s2, where the 0.1 is found from 2σ = 2(0.05).• She calculates the ±2σ range for the accepted value to be the exact value 9.80 m/s2 (σ = 0.00).• The computed range goes from 9.67 to 9.87 m/s2 and includes the accepted value. Student B: • She calculates the ±2σ range for the measurement to be: (9.75 - 0.04, 9.75 + 0.04) m/s2, where the 0.04 is found from 2σ = 2(0.02).• She calculates the ±2σ range for the accepted value to be the exact value 9.80 m/s2 (σ = 0.00).• The computed range goes from 9.69 to 9.79 m/s2 and does not include the accepted value
5. On Monday, a student measures the mass of an open beaker of water to be 150.5 g on an electronic balance with an associated uncertainly of 0.05 g. On Tuesday, the student uses the same balance and measures the mass to be 150.4 g, and on Friday it is measured to be 150.1 g. What conclusion can the student make in regards to whether mass was lost during the week due to evaporation? Ironically, scientists can make completely certain statements or claims once uncertainties are known. This scenario is an example of that!
Taking into account the ranges of uncertainty for each measurement, the ranges for each day arefound using 2σ where σ = 0.05 g in this example:Monday: The measurement of 150.5 ± 0.05 g suggests a range of (150.5 - 0.10 g, 150.5 + 0.10 g)Tuesday: The measurement of 150.4 ± 0.05 g suggests a range of (150.4 - 0.10 g, 150.4 + 0.10 g)Friday: The measurement of 150.1 ± 0.05 g suggests a range of (150.1 - 0.10 g, 150.1 + 0.10 g)The student's claim will therefore be that from Monday to Tuesday, due to the overlap of the two mass ranges, the claim cannot be made that the mass decreased. However, the range of possible masses on Friday does not overlap either of the other ranges indicating that the mass did decrease during the week. The student may use prior knowledge and infer this change in mass is likely due to evaporation (unless other experimental conditions indicate otherwise).
flipMyrtle leaf, orange light, 27°C
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A student measures the temperature of a solution before and after a chemical reaction takes place. In both cases the student finds the temperature to be 25.2 °C, using the same thermometer with an uncertainty of 0.1 °C. Which claim made by the student below is correct?
b.I can't say for sure if the temperature changed or not because there is a range of uncertainty with each measurement. However, I might say it seems reasonable that the temperature did not change given the overlapping ranges of uncertainty.Response Feedback: Correct! Ranges of uncertainty merely indicate that the true value is likely to be in this range. Just because two ranges overlap exactly does not mean the values stayed the same. The true value could still be anywhere in this range.
flip The true value cannot be known.
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FlipElizabeth has more uncertainty associated with her measurements because more of the heights she has recorded are farther away from Tom's measurements than are Janice's.Response Feedback: Correct! When comparing each day's measurements taken by each daughter as compared with their dad, Tom's measurements, most of Elizabeth's measurements are farther away. This means that there is more uncertainty in her overall height measurements.
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.Consider the scenario below in which two students investigate the rate at which mealworms grow by measuring the length of a mealworm each morning for 10 days. Both students measure the length of the same mealworm at the same time each day but use different rulers that have different scale errors. This results in the measurements of Student 1 to have an uncertainty of 0.05 cm (graph on the left) and the measurements of Student 2 to have an uncertainty of 0.1 cm (graph on the right).
Between days 1 and 4, neither student can claim that the mealworm grew because the ranges overlap on both graphs.b. Between days 4 and 7, student 1 can claim that the mealworm grew because the ranges do not overlap on his graph. However, student 2 cannot claim that the mealworm grew because the ±2σ ranges overlap for these two days.c. Between days 4 and 10, both students can claim that the mealworm grew because the ranges do not overlap on either graph for these days
accuracy is
measuring device or overall experiment is a measure of how closely a numerical result agrees with a true value (also called an acceptedvalue or a reference value). Note that in many scientific investigations the true value is not known and claims of accuracy cannot be made
precision
refers to the repeatability of similar measurements under unchanged conditions and does not require knowledge of the true value. Precision is the degree to which future measurements yield the same results; i.e. the reproducibility or repeatability. Measurements may be precise and accurate, precise but not accurate, accurate but not precise, or neither accurate nor precise. See diagram at right
Suppose the goal is to hit the bull's eye (center) with each of five darts. X's on the diagrams indicate the patterns in the darts for four different cases. Below each diagram circle the words precise and/or accurate or neither to indicate how each case exemplifies these concepts.
1. Neither2. Precise (but not accurate)3. Accurate and precise4. Accurate (but not precise)
Which target shown in part (a) best represents the accuracy and precision of each of the following:1. A high-quality digital scale properly adjusted to get the correct mass _________2. A cheaper instrument that is properly adjusted, but has a difficult-to-read scale _________3. A bathroom scale that needs to be adjusted by a few pounds _________4. A broken instrument that still gives a reading _________
1. Target 3. Digital scales will have high precision and "properly adjusted" ensures it will be accurate.2. Target 4. Difficulty in reading the scale will introduce random errors making the measurement less precise. But it will still be accurate since it was calibrated.3. Target 2. The systematic error of a few pounds makes the scale inaccurate. The level of precision might not be as tight as Target 2, but it will still be grouped (unlike Target 1).4. Target 1.
A group of students perform an experiment and obtain a result of 53 ± 3 meters for some given distance. They compare their measurement to the theoretical value of 57 meters (which has no associated uncertainty). What claim can they make using the equivalency criterion that will be used throughout this lab course?
At the 95% confidence level, the range of uncertainty for the measured values is from 47 m to 59 m. This includes the theoretical value so the results are consistent with the theory.Response Feedback: Correct! In this lab course we are using the convention that compares ranges of uncertainty at the 95% confidence level (or 2σ). In this case, σ = 3 m so the range for the measured result should be (53 - 6 m, 53 + 6 m) and span from 47 m to 59 m. Because the theoretical value falls within this range, the best claim the student can make is "At the 95% confidence level, the range of uncertainty for the measured values is from 47 m to 59 m. This includes the theoretical value so the results are consistent with the theory.
5 out of 5 pointsA student measures the mass of a solution before and after a chemical reaction takes place. In both cases the students measures the mass to be 50.25 g on an electronic balance with an uncertainty of 0.05 g. The student realizes that the ranges of uncertainty for each measurement overlap exactly. Which claim can the student make?
We can't know for sure whether or not the mass changed, but it seems reasonable to claim that the mass did not change, given that the ranges of uncertainty overlap.Response Feedback: Correct! As long as there is uncertainty in a measurement, we cannot say for sure that two measurements are the same even if the ranges of uncertainty overlap exactly. We can say, however, that the masses are the same within the uncertainty of the balance.
In the pre-lab notes you learned that a measurement system can be accurate but not precise, precise but not accurate, neither, or both. If an experiment contains a systematic error, then increasing the sample size will in general... increase (precision/accuracy) and and not improve (precision/accuracy)
Selected Answer: increase precision but will not improve accuracyResponse Feedback: Correct! Precision is the degree to which future measurements yield the same results. By increasing the sample size the standard error is decreased meaning that future measurements will likely fall closer to the average. Accuracy, on the other hand, is a measure of how closely the results agree with a true value. If systematic error is present, then taking more measurements will not address this error and improve accuracy as each measurement will be "off" by the same amount from the true value. Instead the systematic error needs to be removed, if possible, and this will improve accuracy.
The cloth tape measure that you use to measure the length of an object had been stretched out from years of use. As a result, all of your length measurements were too small. How would you compensate for the incorrect results of using the stretched out tape measure?
Selected Answer: This is due to systematic error. Assuming that a new tape is more accurate, compare the stretched tape to a new tape to see how much the measurements are off. This difference will tell you how much to correct each original length measurement, causing the systematic error to be minimized.Response Feedback: Correct! This is a systematic error. The way to minimize this error is to understand by how much the faulty equipment is off and account for that difference.
You measure the mass of a ring to be used in your experiment three times using the same balance and get slightly different values: 17.46 g, 17.42 g, 17.44 g. How can you minimize experimental error?
Selected Answer: This variation is due to random error. Take more data. Random errors can be reduced by averaging over a large number of observations.Response Feedback: Correct! This is a random error. By taking more data, more and more of your measurements will be closer to the true value. Random errors will be minimized. Averaging this data will reduce experimental error.
Two students collect data from grocery stores located in twelve different cities for the price per pound of apples, plums, and oranges. They compute the average price for each as well as the standard deviation for the data set they collected. What conclusion may be drawn about the price of apples, plums, and oranges using the graph below and employing the equivalency criterion? (see picture)
The cost of oranges and apples may be similar in some grocery stores due to the overlapping error bars shown, but plums cost less per pound.Response Feedback: Correct! Often it suffices to visually inspect differences between means and their uncertainties in order to draw a conclusion. The graph compares prices among the three fruits and by employing the equivalency criterion, there is a clear difference in cost between plums and oranges, but the uncertainty ranges for the cost of apples and oranges overlap so one can only claim that these prices may be similar.
student measures the diameter of a can to be 12.55 cm. The uncertainty in the measurement due to the spacing of the lines on the ruler is 0.05 cm. Compute the circumference of the can using the equation C = πd and include the uncertainty with the reported value.
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The supplier of trapezoidal piece of metal states that the area is 668 ± 7 cm2. Just to double check, you measure the following: a= 13.43 ± 0.03 cm, b = 31.75 ± 0.03 cm, and ℎ = 29.3 ± 0.1cm (see diagram below). Do you agree with the supplier?To calculate the area:Area = ½(h)(a + b)Area = ½(29.3 cm)(13.43 cm + 31.75 cm)Area = 661.9 cm
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Consider measuring the period of a pendulum with a stopwatch. Suppose that the stopwatch is running slow. Which one of the following statements is correct?
Selected Answer: This will lead to underestimation of all of our time results. Systematic errors, unlike random errors, shift the results in one direction.Response Feedback: Correct! Systematic errors shift the results in one direction, but this is not necessarily the positive direction. In this case, a slow stopwatch will underestimate the elapsed time, so the best answer is "This will lead to underestimation of all our time results. Systematic errors, unlike random errors, shift the results in one direction.
A student discovers that a photogate consistently reads 5% higher than expected, after all the data is collected. How should this error be handled?
Selected Answer: Each measurement can be reduced by the same amount (5%) in the first step of the data analysis.Response Feedback: Correct! Systematic errors shift the results in one direction, so once this error is identified, all values can be shifted by this same amount. In this case, the best answer is "Each measurement can be reduced by the same amount (5%) in the first step of the data analysis.
The length and width of a living room is 5.5 m and 4.8 m with an uncertainty of 0.1 m in each measurement. The perimeter of the room with associated uncertainty using either the "general method" or the "high/low method" presented in the pre-lab notes is:
b. 20.6 ± 0.4 m
A cylindrical gas bottle has a radius of 4.5 cm and a height of 30.0 cm. The uncertainty in both measurements is 0.1 cm. The directly calculated volume (V = π r2 h) of the bottle is 1908.5 cm3. Using one of the methods presented in the pre-lab notes, either the general or high/low method, which of the following is the best approximation to the uncertainty in this calculation?
90 cm3
This is a review question. The pre-lab notes from Week 1 covered this topic. Consider the graph at below which shows data obtained when carbon dioxide levels were measured each January at the Mauna Loa observatory in Hawaii. The independent and dependent variables in this experiment are _________________ and __________________ respectively. (picture)
ear (IV); Atmospheric carbon dioxide (DV)
A group of students in a geology class plot historical data as shown below to model how sea level has changed in New York City since the year 1900. They found the slope of the best fit line to be 0.29 cm/year and the y-intercept to be 1.30 cm. Write out the equation for this situation by including appropriate variables and units.
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2. Two students in another lab wish to determine the mathematical relationship between thermal resistance (R) and air velocity (Vair) using the graph below. After doing a curve fit, they estimate it to be: �!"# = !""!!.!" . Are they correct?
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Based on this plot, choose the best mathematical model from the following equations to describe the relationship of the temperature of a steel beam and its length. Note that the lowest left point of the graph is not (0,0). Assume that T is the temperature of the steel, L is the length of the beam, and all other variables are constants that will be determined another way (i.e. fitting the data).
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Consider a group of students who conducted the same projectile lab you completed for Lab 04. They found the uncertainty of their calculated trajectory range and, following standard laboratory practices, assumed that this was one standard deviation σ. They used this value to draw the bands on their target. After their initial launch, they recorded a number of additional launches to verify their estimate of σ. Of the following choices, what is the best interpretation if after 40 launches the group's carbon paper looked like the following? (The middle blue line is the prediction, the outer lines indicate the range of uncertainty.)
Selected Answer: The uncertainty was overestimated.Response Feedback: Correct! The rectangle defined by the two outer blue lines should enclose approximately 68% of the data, which means we should observe approximately 32% of 40 (12 or 13) hits outside the lines. Only 4 events fall outside the estimate, so the uncertainty was overestimated.
As in the previous question: what is the best interpretation if your carbon paper had looked like the following?
Selected Answer: There is a systematic error.Response Feedback: Correct! The rectangle and the data should be centered on the same position.
If we want to determine how much fertilizer makes a particular type of plant grow bigger, what might be identified as the independent (IV), dependent (DV) and controlled variables (CV)?
Answer: IV - amount of fertilizer, DV - how tall the plant grows, CV - same type plant and planted in same size pot
assumption:
is something that is taken for granted; something that is believed to be true without proof. All scientific investigations involve assumptions made by the researchers. These are justified claims that if they are not true, may impact results.
Consider the following scenario: According to Sustainable Enterprises, coffee grounds can greatly benefit plants. They allow for a slow release of nitrogen and they can also increase nitrogen balance. Nitrogen helps plants use carbohydrates to gain energy. Nitrogen controls how plants take their form and how they function inside, and nitrogen helps plants make proteins that help them grow strong and healthy. Coffee grounds have been shown to increase the growth of plants because they have been said to release important nutrients used by the plants. According to Grow Joe, coffee grounds also release magnesium and zinc, micronutrients and amino acids. Without enough magnesium, plants may have brown/yellow older leaves. The coffee grounds can also feed earthworms; they loosen the soil; they retain water; and they release caffeine which repels slugs. Based on this information, students hypothesized that adding coffee grounds to the soil would affect the growth of Brassica rapa plants as measured by their leaf mass (size of leaves grown). They tested this by adding different amounts of coffee grounds to pots of soil before transplanting Brassica rapa seedlings into the pots. These amounts included 0, ¼, ½, ¾, and 1 cup of coffee grounds in each pot.Consider the following assumption made by the students:"The Brassica rapa seedlings transplanted into each pot were similar in health
a. This is an appropriate assumption because the health of the plant might impact leaf growth.Response Feedback: Correct! If the seedlings were not of similar health then the leaf growth might be affected by this factor. This is a reasonable inference based on past experiences even though the students may not be able to check the health of each plant used in the experiment.
Consider the following assumption made by the students:"The amount of coffee grounds was measured accurately before adding them to the soil."is it appropriate?
Answer: c.Although inaccurate measurements might impact the results of the experiment, this is not considered an appropriate assumption to report.Response Feedback: Correct! Although inaccurate measurements might impact the results of the experiment, there are too many assumptions such as this one to report. The convention we use in this lab course is not to report those assumptions that refer to a student's ability to take and record data accurately.
A group of students conducted an experiment to determine what impacts the rate mold grows on bread. They decided to test whether or not preservatives in the bread made a difference in addition to the temperature in which the bread was stored. They purchased 2 loaves of bread that contain preservatives and 2 loaves that did not. They placed 5 pieces of each type of bread in 6 different environments of various temperatures ranging from 40°F to 85°F. The students were careful that each environment was basically identical except for temperature. After collecting data over 3 weeks the students made the claim that bread containing preservatives has a slower rate of mold growth when compared to bread without preservatives. They also made the claim that storing bread at lower temperatures reduces the rate of mold growth. Consider the following statements made by each student as they discuss what assumptions need to be discussed in their lab reports:Sam: In our report we need to write that we assumed that the two loaves of preservative-free bread were from the same batch and therefore identical to one another in terms of ingredients and age. We also need to write that we assumed the two loaves of bread with preservatives were identical in terms of ingredients and age. Alex: I agree with Sam but we should take it one step further and include a statement that we assumed that all four loaves of bread were actually of the same age and freshness as well. Troy: I agree with both of you, but we also need to include a statement that we assumed that our method of measuring the area of mold growth on each piece of bread was the most accurate.
I agree most with Alex's statement.Response Feedback: Correct! Although inaccurate measurements might impact the results of the experiment, there are too many assumptions such as this one to report. The convention we use in this lab course is not to report those assumptions that refer to a student's ability to take and record data accurately.
When discussing assumptions in lab reports for this course, which of the following is the best course of action that you should take?
Correct! Listing assumptions and their possible effects on the experiment, as well as suggestions to mitigate these effects, is good scientific practice.
poaitive, negative, no
no. no , positive
A physics student claims that Newton's second law(f = ma) can be used to predict the net force necessary to obtain a desired acceleration. What type of relationship exists between net force and acceleration if mass is constant?
If mass is constant then the relationship betweennet force and acceleration is causal (i.e. a change in net force causes a change in acceleration). However, if instead mass is NOT constant, then all that can be said is either (1) that net force is positively correlated to acceleration (an increase in net force causes an increase in acceleration) or (2) that F/m and acceleration are causal and that a change in the ratio F/m causes a change in acceleration.
Two educational researchers find that higher student SAT scores result in higher student success in an introductory biology course. What type of relationship exists between SAT scores and student success?
The relationship between SAT score and student success can only be claimed to be correlated. No variables were manipulated here to establish a causal relationship. This also means that one should not interpret the results of this study to mean that if you have a high SAT score that you will be successful in biology. It could be that students with high SAT scores are also those who in general study more or attend class more.
Women who take hormone replacement therapy (HRT) are less likely to have coronary heart disease (CHD).
At first glance this article title implies a causal relationship and that taking HRT a woman will be less likely to develop CHD. But, one must consider the many other factors that have been linked to CHD such as access to healthcare, socio-economic status, social and behavioral risk factors. In the end another study controlled for some of these factors and determined that women who take HRT wereactually more likely to develop heart disease.
As ice cream sales increase, the rate of drowning deaths increase.
At first glance this article title implies a causal relationship between buying ice cream and the number of drowning deaths. But, one must consider when people eat ice cream and when they actually swim more often. Both happen in the summer! So both are expected to increase due to the season of the year rather than one causing the other
Consider the student, who after determining the experimental mathematical model for the period of a pendulum and comparing it to the theoretical model of � = 2� �/�, makes the claim that because the length impacts the period of the pendulum but mass and angle of release (for small angles) do not, that length (l) and period (T) demonstrate a causal relationship. That is, a change in length causes a change in the period. Do you agree with this statement? _______________
Be careful! The claim is incorrect. The theoretical model � = 2� �/� indicates that the period is actually determined by two variables, length (l) and acceleration due to gravity (g). This implies that thecausal relationship is between T and two variables taken together (l and g). Therefore, the student would have been correct if he had said that the length and period have a causal relationship when g is held constant. When g is not held constant, the best the student can claim is that period and length are positively correlated (as shown in the graphs above).
A fitness store conducted a study and randomly chose 10 people to complete a survey regarding the number of months they owned a treadmill and the number of hours they spent exercising in the past week. The data is presented below. Table 1. Exercise Data for Ten PeopleMonths Owned 5 10 4 8 2 7 9 6 1 1 2Hours Exercised 5 2 8 3 8 5 5 7 10 3The relationship between the "number of months the treadmill was owned" and the "number of hours it was used by the buyer in the past week" is an example of:
Negative correlationResponse Feedback: Correct! If the data is plotted, a negative trend is observed. That is, as the months from purchase date increased, the number of hours exercised in the past week decreased.
A group of students conduct an experiment to determine what factors impact the period of an oscillating spring-mass system. They choose 4 different springs of various stiffnesses which are listed in the data table from the most stiff (largest k) to the least stiff (smallest k). Based on this data, what claim can the students make?Selected Answer: No relationship can be determined as the students did not properly control all variables.Response Feedback: Correct! The students did not make proper use of control variables. For each trial a different spring was used (each with a different stiffness) while the mass was changed each time as well.
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Much has been written about the relationship between SAT scores and a test-takers' family income. Consider the graph below concerning SAT Math Scores and family income as reported in The New York Times on August 27, 2009.What type of relationship between SAT test score and family income is demonstrated here?
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A group of students conduct an experiment to determine how a change in mass hung on a spring impacts the amount it stretches. They select one spring and collect the data as shown below. They are excited to see that their collected data supports Hooke's Law (F=-kx) as presented in their textbook. What claim can the students make about the relationship between the mass hung and the amount of spring stretch assuming the spring constant (k) is held constant?
A causal relationship exists between the mass hung and the amount of spring stretch because a change in mass caused a change in the amount of spring stretch.Response Feedback: Correct! According to Hooke's Law, if k is constant then an increase in the mass causes an increase in the spring stretch. If k is not considered a constant, then the most that the students can claim is that there is a positive correlation between mass hung and spring stretch.
In the pre-lab notes for Lab 09, the differences between causal relationships and correlations were explored. In terms of the lab topic this week, the moment of inertia I, choose the best statement below for a single object of mass M.
Selected Answer: A causal relationship exists between the distribution of mass of an object and its moment of inertia (I).Response Feedback: Correct! According to Table 1 in the pre-lab notes, if we consider a single object of mass, M, then a change in the distance of the mass from the axis of rotation causes a change in the moment of inertia. If mass is not considered a constant (such as if we compare two different objects of different masses), then the best statement that can be made is that a positive correlation exists between the distance the mass is from axis of rotation and the object's moment of inertia.