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Open Inquiry: The Pendulum

Concept Day

 

 

 

 

 

 

 

Open Inquiry: The Pendulum

Concept Day

SLIDE PENDULUM-1-1

This is a special, but short CELL. If one searches the Internet, they will find that there are many different ways to outline the scientific method. Here is one:

  • Make an Observation
  • Ask a Question
  • Form a Hypothesis
  • Make a Prediction
  • Conduct an experiment to test prediction
  • Analyze Data
  • Draw Conclusions

In real-life science, the first two steps may be done over long periods of time. Often, observations don’t seem significant or important until they have been observed repeatedly, perhaps in different contexts. Or when an unexpected contradiction to a common observation is encountered. Until meaningful observations are made, specific questions about it, of course, can’t be asked.

For this reason, while you should be aware of the first steps in the scientific method, we will stress hypothesis and prediction and prediction testing in this CELL. In essence, this may be referred to as “experimental design”.

Not all of the many different renditions of the steps of the scientific method found on the Internet and in textbooks include the prediction step that we have included above. However, during this CELL, it will become quite clear that the ability to systematically make testable predictions from hypotheses statements is a wonderful way for you to learn to make the connection between a hypothesis and a good experiment.

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SLIDE PENDULUM-1-2

  • The three elements of designing a good experiment (hypothesis, prediction, and variables) are outlined on this overview slide. Each of these elements will be expanded upon in subsequent slides. We will come to understand this approach to “experimental design” by using a specific example:

Note: You may have already performed this exact experiment earlier in LabLearner Investigation 2 of the Chemical Reactions.

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SLIDE PENDULUM-1-3

  • This slide introduces the concept of a hypothesis. A hypothesis is a statement about the relationship between observed variables. It is NOT a question. This is a common mistake students make. For example, a terrible hypothesis related to our example reaction might be:
    • “Why do magnesium and hydrochloric acid form magnesium chloride and hydrogen gas?”
  • Such a question does not immediately suggest an experiment. In fact, it is unclear what the next step would be in answering such a broad question. There would likely be many different potential directions to go.
  • On the other hand, a specific statement relating only two variables in our example might be:
    • “H2  formation is dependent on HCl concentration in this chemical reaction.”
  • Here, two variables, H2 formation, and HCl concentration are clearly and simply related. This is a positive statement. However, the statement of the hypothesis need not be positive to be just as useful. For example, the following hypothesis is just as good as the first:
    • “H2  formation is NOT dependent on HCl concentration in this chemical reaction.”
  • We can easily make a testable prediction from either of these hypotheses. However, we will continue forward using the positive statement.

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SLIDE PENDULUM-1-4

  • A prediction is a statement that presents the relationship between the variables in a hypothesis in a testable way. An easy “trick” for you to use is to consider predictions as “If-Then” statements that include the hypothesis. For example:
    • If H2  formation is dependent on HCl concentration in this chemical reaction, then increasing HCl concentration will increase the amount of H2 gas formed.”
  • Notice the hypothesis is placed between the “If” and the “Then” elements of the prediction statement. Also, notice the remainder of the sentence following the “Then” element directly suggests an experiment to do. Importantly, performing this experiment will tell us if our prediction is correct and if our original hypothesis was true! Thus, a prediction, based on a simply stated hypothesis, is a very powerful statement indeed.
  • Prior to designing the actual experiment to test our prediction, we will consider which variable we wish to be independent and which we wish to make dependent.

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SLIDE PENDULUM-1-5

  • The independent variable is the variable that we will control in the experiment we are designing. The dependent variable is the remaining variable and our experiment will be designed to see how it responds when we make changes to the independent variable.
  • The independent variable in our original prediction is the HCl added, while the dependent variable is the H2 gas formed. Thus, we will want to change the amount of HCl we add to the reaction and measure the effect these changes have on the amount of H2 gas formed.
  • By following this hypothesis/prediction procedure, the experiment we want to conduct has almost designed itself. All that remains is to determine how we want to vary the independent variable and how we want to measure the dependent variable.

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SLIDE PENDULUM-1-6

  • In the lab, we will indirectly measure H2 formation by measuring the diameter of a balloon affixed over the mouth of a flask to which different amounts of HCl are added to the same amount of magnesium metal. For each different reaction (Trial) we will wait the same period of time before measuring the balloon (if not, we would be introducing another variable and our experiment would be ruined).

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SLIDE PENDULUM-1-7

  • This slide presents the hypothetical results of the experiment that we designed and conducted in the previous slides. On the left is the data table from which the graph on the right was constructed. Notice the volumes of HCl (independent variable) that were chosen and that the other component of the reaction, the magnesium metal, was kept constant at 0.5g.

Note: Obviously, in another hypothesis/prediction/experiment scenario, we could hold the amount of HCl constant and make the amount (mass) of Mg metal our independent variable. We could then test the effect of this variable on the dependent variable, which would remain H2 gas formation.

  • When we plot the data for analysis, notice that we typically place the independent variable on the x-axis and the dependent variable on the y-axis
  • Now that the results are collected and plotted, we can analyze the results and come to some conclusions.

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SLIDE PENDULUM-1-8

  • This slide simply states that, based on the experimental results presented on the previous slide, our prediction was correct. Therefore, we can now remove the “If/Then” elements of the prediction and state:
    • “H2 formation is dependent on HCl concentration in this chemical reaction.”
  • Notice that this is our original hypothesis! And we have conducted an experiment that proved it.
  • Next, let’s consider a different result for the experiment we conducted.

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SLIDE PENDULUM-1-9

  • This slide presents different hypothetical results of the exact same experiment that we designed and conducted on previous slides. On the left is the data table from which the graph on the right was constructed. Again, notice the other component of the reaction, the magnesium metal, was kept constant at 0.5g.
  • Notice that the volume of the balloon and therefore indirectly the amount of H2 gas formed did not change regardless of the amount of HCl we added.
  • Now that the results are collected and plotted, we can analyze the results and come to some conclusions.

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SLIDE PENDULUM-1-10

  • This slide suggests that the analysis of the experimental results from the last slide leads us to conclude that our prediction was not correct. That is:
    • “H2 formation is NOT dependent on HCl concentration in this chemical reaction.”
  • Notice that not only was our prediction incorrect, but our original hypothesis was untrue. However, we learned a lot and, in fact, actually proved the negative form of our hypothesis statement that we mentioned before making a prediction and designing the experiment. Remember, we had stated:
    • “H2 formation is NOT dependent on HCl concentration in this chemical reaction.”
  • Had we gone with this negative statement of the hypothesis, the exact same experiment would have proved our hypothesis correct (second hypothetical results).
  • The most important thing when stating a hypothesis, making a prediction based on it, and designing/conducting an experiment to test your prediction is that, when the experiment is over, we find out if our prediction was correct or incorrect.
  • Let’s consider our original prediction again:
    • “If H2 formation is dependent on HCl concentration in this chemical reaction, then increasing HCl concentration will increase the amount of H2 gas formed.”
  • Note, however, that based on this terrible experiment as it relates to the prediction we made, it nonetheless may well serve as the basis of an observation that can lead to a separate hypothesis. What might that hypothesis be? How about:
    • “Temperature is dependent on HCl concentration in this chemical reaction.”
  • But in this case, instead of measuring the volume of a balloon affixed to the flask, we measured the temperature of the reaction. No matter what results we get from such an experiment, we will not prove or disprove our prediction or hypothesis. We designed a very poor experiment for testing or prediction.
  • What might the prediction be? How about:
    • “If temperature is dependent on HCl concentration in this chemical reaction, then increasing HCl concentration will increase the temperature of the reaction.”
  • This prediction is easily testable with a simple experiment. 

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SLIDE PENDULUM-1-11

  • This slide lists six example hypotheses. It also indicates that “hypotheses” is the plural of “hypothesis”.

Note: The teacher may wish to have students, as a class, make predictions and indicate which variables are independent in their predictions and which are dependent.

Student Practice

Note: Alternatively, the teacher may wish to download the student document PDF above as homework or group work for students:

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SLIDE PENDULUM-1-12

Note: You may have previously seen this slide in the CELL Kinetic and Potential Energy. It is included here as a simple review of pendulum energy transitions.

  • When the pendulum is pulled up to its highest amplitude (to the left), it is not moving and thus consists of 100% potential energy due to its position and the force of gravity. As the pendulum is released, its kinetic energy of movement is increased as its potential energy of position decreases.
  • At a position perpendicular to the table/ground, 100% of the pendulum’s energy is kinetic energy. As it continues moving past this point, its potential energy increases while it’s kinetic energy decreases until it stops its upward movement and pauses at the far right. At this point, the pendulum is once again at 100% potential energy. The cycle then proceeds to the left in an identical fashion.

 

  • Note that in this illustration, the color of the pendulum switches from yellow to red as it moves from full potential energy to full kinetic energy. At the intermediate positions, the pendulum is a mix of yellow and red indicating the mix of potential and kinetic energy.
  • Without the force of friction slowing down the pendulum, this transition from potential to kinetic energy and back again would continue to cycle infinitely.

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SLIDE PENDULUM-1-13

  • This slide identifies four important variables of pendulum motion that you will address in the lab. The mass (M) of the weight attached (the bob) to the string is one variable that you might change in the experiment you design and conduct.
  • The amplitude (A) is a measurement of the angle between the position of the mass just prior to release and the perpendicular. This is a second variable that you might wish to alter in designing your experiment.
  • The length (L) of the string is a third variable that you could decide to alter in designing your experiment. The length may be measured from the attachment point on the ring stand to the mass.
  • Finally, the period (T) is the time it takes for the mass to complete one entire “cycle”, from far-left to far-right and back to its starting point. It is measured with a stopwatch. Thus, the period will be the dependent variable in the experiment you design.

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SLIDE PENDULUM-1-14

Note: This slide briefly outlines the activities and experiment you will design and conduct in lab.

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