Penny Lab

In class you will prepare a chart that compares the number of pennies a bridge holds to how thick it is. Using this table you then make a graph on graph paper of Bridge's Thickness (in layers) verses Bridge's Strength measured in the Breaking Weight (in pennies). In order to make the table and the subsequent graph you must decide which variable in the experiment is the independant variable (x) and which is the dependant variable (y) .

1. What are the independant and dependant variables in this experiment and how do you know?

2. Make a chart of x and y values for bridges of the varous thickness assigned to your group. Make sure to fold your papers correctly and consistantly and avoid changes to the distance between your books. Also be sure to allow time for the bridge to collapse before adding another penny. Once you have done bridges of thicknesses assigned you may go back and repeat the trials if instructed. Do not use the same piece of paper twice. Make an uncompromised brand new layer for every layer of every trial.

3. On graph paper, after labeling your axis, begin plotting your data points from your various trials.

Answer all the following questions in paragraph form, show work for all relevant calculations organized neatly and in order.

4. Does the data on the resulting graph seem pretty-much linear? Does the data indicate an increasing, decreasing, or constant trend. Why does/doesn't this make sense in terms of what adding a layer of paper should do to the strength of the bridge?

5. Draw a straight line on your graph that approximates what the data seems to be doing fairly well and find the equation for it by using two points that lay on the line you drew. (Your line doesn't actually have to hit any of the points you plotted from your experiment. It just needs to be the straight line that you feel does the best job of approximating the results you got in your experiment. This is called the line of best fit.)

6. Tell me what is slope and y-intercept found in your equation specifically mean in terms of the experiment. Do you agree with their validity? Why/ Why not?

7. Use the equation from your eyeballed line of best fit result to predict the number of pennies a bridge of each of the thicknesses assigned to your group should hold. These results are called the predicted value because you are using your equation to predict how the thickness will determine the breaking weight.


8. Comparing the answer that the equation predicts to the average of the answers you actually found, find the percentage of error and tell me "Do you think the your eyeballed equation does a good job modeling the data?" Why/why not?

9. Now use the statistical method discussed in class to find the true line of best fit showing all your calculations.

10. Answer discussion questions 6,7 and 8 again but with respect to the equation you developed in #9 with the added question, which equation do you think does a better job (your eyeballed one or the stats derived one) and why (support you conclusion with comparisions of pertinent results).

11. Find the regression coeffecient for the data and explain what it means in terms of the experiment.

12. Describe some of the factors in the experiment that may have introd uced some error into your results and subsequently the two equations you developed.


13. Use your second equation to estimate how many layers would be needed to hold 100 pennies. Would it be correct to round your answer up or down? Why?

14. Use your equation to predict how many pennies a 5 layer bridge and 12 layer bridge would break at.

15. In reality you can experiment with only integer values for the x and y. You can only use complete layers and complete pennies. Your equation on the other hand allows you do much more. Use one non-integer value for x in your formula which would make sense if the layers weren't paper thin but which would be impossible to try to replicate in an experiment. Explain what your result means.

16.When you answered the previous three questions at what points were you interpolating and at what points were you extrapolating from your experimental model?


17. Finally Engineers and Statisticians, among others, both interpolate and extrapolate regularally by creating models from data to predict tendencies and possible outcomes. In terms of designing and building bridges, why does it make sense to use a scaled-down experimentation and mathematical modeling? Also in this context, why is it important to never throw out strange results from an experiment, until the cause of the deviation has been explained?


Self Check. Go on Rosiework and follow the link to the online linear regression tool. Input your x and y data and compare the resulting mathematically generated line of best fit to the one you created just to double check your results before you turn in the paper.