• Teachers should be able to create charts in MS Excel to represent data.
• Teachers may read the article at http://www.Howstuffworks.com to understand a practical application of reaction forces in truck weigh stations.

• Gather materials

1. Assemble one complete experimental setup with the ends of a 2x4 beam resting on two blocks that each rest on a scale, as shown below.

Close-up view of how beam is placed on a scale. click for copyright

2. Describe the purpose of the experimental set up (e.g. "this is the beam") and expectations of the students. Involve them in a discussion with questions similar to the following:

• Where would I have to stand on this beam if I wanted both scales to read the same value? (Answer: the middle). Where would I have to stand if I wanted one scale to read zero? (Answer: directly over the other scale). If one scale reads zero, what will the other scale read? (Answer: the weight of the person).
• We are going to investigate how the forces measured by the scales change when the location of the person on the beam changes. What is the independent variable? (Answer: the position of the person) What are the dependent variables or what variables respond to changes in the independent variable? (Answer: the forces measured by the scales.)
• An engineer would call the weight of the person the "applied force" or the "load." An engineer would also call the forces measured by the scales the "reaction forces" since they are caused by the load. What shall we call these things?
• Can you predict what will happen to the reaction forces as the load moves from one end of the beam to the other? (Answer: the further the load is located from a scale, the smaller the size of the reaction force measured by that scale).
• How can a table or graph help us understand the results of our experiments and draw conclusions? (Tables are used to organize data by categories. Each category may represent an independent or dependent variable. For every value of the independent variable, there is a corresponding value for each of the dependent variables. These are the x and y coordinates respectively that can be plotted as a point on the graph. This is how a graph is plotted for each value from the table. Graphs are a useful visual aid in analyzing data as they can clearly demonstrate trends in the data for every dependent variable as well as relationships between these dependent variables.)

3. Tell the students that their objective is to "determine how the position of the load affects the reaction forces."
4. Create groups that consist of 4 students (groups of 3 or 5 will also work). One student reads each scale and reports the readings to the data recorder, another student stands on the beam acting as the load, a third student helps the "load" person remain steady and balanced on the beam, and the final person records the data. Each group needs an experimental setup.
5. Have the students create a data table. An example table is shown below.

• Students are not given a worksheet before the experiment is conducted when the purpose is to make them come up with their own table of variables after they have been introduced to the experiment and involved in the preliminary discussions.
• Make sure students understand that besides recording data in tables and drawing graphs, they should also write down conclusions about the relationship between the variables, trends in the data and predictions about what might happen if the experiment is changed.

Example data sheet for recording experiment results. click for copyright

6. To conduct the experiment, each group should:

• Use a ruler or yardstick to measure the beam and to put a piece of tape on the top of the beam every six inches (these marks will be used for measuring load location).
• Place 1 block on the middle of each scale.
• Place the beam onto the blocks.
• Zero the scales. Most analog scales have a wheel to adjust the initial offset of the reading that is due to the weight of the beam. If your scale cannot be zeroed, then the initial reading needs to be recorded and later subtracted from measured values when the load is applied.

7. Ask one person in each group to volunteer to be the load. Have the load stand at one end of the beam, and have the rest of the group record the reaction forces. Then, have the load move in 6 inch increments towards the other end of the beam. Record the reaction forces R1, R2 at each location.

Sketch of a person standing on the beam, then moving to the right. click for copyright

8. Create a graph with your data showing load position (a) vs reaction forces (R1 & R2). What does the graph tell you? Do you notice any patterns in your data? You may have noticed a relationship between R1, R2 & position. How could you show that on the graph? This step can be done by hand using graph paper or on the computer using MS Excel. It would be beneficial for the students to approximate a trend line and an equation for each line they graph.

The following results were obtained using a load of 176 lb. The experimental data obtained is shown in the table. In theory, the two reactions should add together to give the total weight of the person, regardless of where the person is standing. The table shows that there is some experimental error, because the values vary from 175 to 178 lbs. This error may be attributed to problems in reading the scales because it is difficult for the person loading the beam to hold still, and the scales tend to bounce around some. From the table one can see that as the person moves away from a scale, the value of that reaction force decreases while the other reaction force increases. The same trends will be found for different loads.

The data in the table is also shown in the graph. There are three lines in this graph. The first reaction force line starts at a force of 176 lbs and slopes down toward zero. The second reaction force line starts at zero and increases to 176 lb. The two lines at around a = 2 ft, which is the midpoint of your beam. This tells us that the reaction forces are equal to each other when the load is placed in the middle of the beam. The sum of the two reaction forces is also shown on the graph as a horizontal line, showing that the force of 176 lbs is approximately constant.

The lines on this graph are trend lines that MS Excel can draw through experimental data. The equations for each line that are shown on the graph were obtained from the trend line. For the reaction force R1, the slope of the line is 45 lb/in and the intercept is 0 lb. For the reaction force R2, the slope of the line is -45 lb/in and the intercept is 176 lb. The slope of reaction force two is the negative of the slope of reaction force one. The lines also have opposite slopes, which tell us that the rate of change is the same for both but one is increasing and the other is decreasing.

Table with experiment results. click for copyright

Graph of experiment results. click for copyright

Discussion Questions: Solicit, integrate and summarize student responses:

• All of the questions in step 2 of the procedure can be used to assess the students' preconceptions. Additional pre-activity assessment questions include the following.
• What is the difference between weight and mass of an object? (Answer: the force of gravity acting upon an object is sometimes referred to as the weight of an object. The mass of an object refers to the amount of matter that is contained by the object.)
• Newton's third law of motion comes into play when a flying bird strikes an airplane. The bird hits the airplane and the airplane hits the bird. Which of the two forces is greater: the force on the bird or the force on the airplane? (Answer: Each force is the same size. The fact that the bird gets injured only means that with its smaller mass, it is less able to endure the larger acceleration resulting from the interaction.)

Student Progress: Inspect individual students' tables and charts for completeness.

True/False: Ask a true/false question and have students raise hands if they think the statement is true. Count the votes and subtract their number from the total number of students to obtain the number of students who thought the question contains a wrong statement. Write the totals on the board and give the right answer.

• True or False: When the person stood at different positions along the length of the board, the applied force changed (Answer: False. The applied force is the weight of the person distributed along the beam.)
• True or False: When the person stood at different positions along the length of the board, the reaction forces changed (Answer: True. The further the load is located from the scale the smaller the reaction force measured by the scale.)
• True of False: The sum of the two reaction forces is equal to the applied force (Answer: True. This is a direct application of Newton's Third Law of Motion: "For every action force there is an equal (in size) and opposite (in direction) reaction force". )
• True or False: The trend of the data for the two scale values (reaction forces vs. the position of the load on the beam) from our experiment is linear. (Answer: True. The two reaction forces change proportionately to changes in position.)
• True or False: Weight is a force that is always directed toward the center of the Earth. (Answer: True. Weight is equivalent to the force of gravity, which is directed toward the center of the Earth.)

Open Questions: Solicit, integrate, and summarize student responses to the following open questions:

• Can you explain why the person standing on the beam does not fall despite the force of gravity? (Answer: there are two forces acting upon the person. One force, the Earth's gravitational pull, exerts a downward force. The other force, the push of the beam on the person, exerts an upward force. Since these two forces have the same size but opposite direction, they balance each other and the person is at equilibrium. )
• Knowing the difference between mass & weight and that the center of mass of an object is a point at which the mass of the object is concentrated, answer the following question: What is the center of gravity of an object? (Answer: The center of gravity of an object is the place where the weight of an object is concentrated.)

Evaluation Rubric: In addition to the true/false and open questions, teachers can use the scoring rubric below to determine the effectiveness of student work. The rubric evaluates understanding the purpose of the experiment and the relationship between the variables, organization of data in tables and graphs, and analysis of the results.

Evaluation rubric. click for copyright