Source: This activity is a revision of the “Stretching a Penny” activity included on the Texas Instruments web site; obtained 1/26/01. <http://www.ti.com/calc/docs/act/hsmotion01.htm>

Hooke's Law is a standard physics formula that mathematically describes a stretching spring. The law states that the force applied to a spring is directly proportional to the distance a spring is stretched. Hooke’s Law is a real-life example of direct variation.

In this activity, you will experiment to discover the relationship between the stretch of a spring and the amount of weight attached to the spring. Here, you will use Skittles to measure “weight”. You shall see that the distance a spring stretches will vary directly with the number of the Skittles hanging from the spring.

Finally, you will use the results to make predictions about how your group's spring behaves in general, and you can compare your spring with the springs of other groups.
 

You'll Need

· 1 CBR unit
· 1 TI-83 Graphing Calculator
· A light spring
· A disposable cup with a length of string attached to it
· Enough Skittles to fill the cup
· A ring stand

 
Setup Instructions

1. Place the ring stand at the edge of a desk or table. Hang the spring from the ring stand and attach the disposable cup to the bottom of the spring.

2. Position the CBR face up under the ring stand.

3. Run the RANGER program on your calculator.

4. Set up the calculator to collect data.

a. From the MAIN MENU select 1:SETUP/SAMPLE. You will see the SETUP MENU (shown below).

b. Press [ENTER] until the REALTIME option reads NO.

c. Move down to the next line TIME and press [ENTER], 4, [ENTER] to set the sample time to 4 seconds.

d. Continue in a similar fashion until the rest of the options are correct, as shown to the right.

e. Move up to the START NOW command and press [ENTER]. The CBR should take a sample. When it is done, you should see a graph of a horizontal line on your calculator display. Now press [ENTER] to return to the PLOT MENU.

Text Box: MAIN MENUSTART NOWREALTIME:NOTIME (S):4DISPLAY:DISTBEGIN ON:[ENTER]SMOOTHING:LIGHTUNITS:METERS

Data Collection Procedure

1. From the PLOT MENU, select 5:REPEAT SAMPLE. After the CBR has collected the distance data, trace along the horizontal line on the graph to determine the approximate distance to the cup. Record this "Distance to Cup" in the Data Collection Table below. (Do not fill out the other columns on the table until you have read Computations section at the bottom of this page.)

2. Count out 30 Skittles and gently add them to the cup. Make sure the cup is level and is not bouncing up and down.

3. Press [ENTER] to return to the PLOT MENU. Repeat these steps until you have filled in the entire “Distance to Cup” column in the table below.
 

Data Collection Table

Number of Skittles
Distance to Cup (from CBR)
Stretch (meters)
Stretch (centimeters)
Stretch per Skittle (centimeters/Skittle)
0
0
0
0
30
60
90
120
150
Computations

1. Compute the total amount of stretch each time 30 Skittles were added to the cup. That is, subtract each distance from the distance when there were NO Skittles on the plate (the double-boxed entry in the upper-left corner). Record the Stretch in the third column of the Data Collection Table.

2. Convert each of the Stretch measurements in the third column from meters to centimeters and record it in the fourth column.

3. Now calculate the amount of Stretch per Skittle by dividing the Stretch (fourth column) by the total number of Skittles in the cup (first column). Record this data in the last column.
 
Data Analysis

1. What do you notice about the Stretch per Skittle for each trial?
 
 

2. If someone gave you a cup of 200 Skittles, could you predict how far the spring would stretch under their weight? Using the information you found for the approximate Stretch per Skittle, make a prediction of the total stretch. Show your work below and place your prediction in the rectangle.
 


 
 
 
Prediction:
3. Fill the cup up with Skittles. Steady the cup and follow the Data Collection Procedure you used to fill out the table. Complete the following table based on your results.
Number of Skittles Distance to Cup from CBR Stretch (meters) Stretch (centimeters)
0   

(from before)

0 0
Full Cup
 
0 0 0
4. From your previous trials, you found the approximate Stretch per Skittle. Use this information to predict the number of Skittles in the cup. Show your work in the space below, and then place your prediction in the rectangle.

 
 
 
 
Prediction:

 
5. Count the total number of Skittles to find out how close your prediction really was. How close were you? Enter this absolute error below.
 
 

6. Dividing the absolute error (above) by the correct answer (the result of your hand-count) and multiplying by 100% gives us relative error. What was the relative error of your prediction? (An error less than 5% is very good.)
 

Examining the Results

Part 1.

a) Since force is directly proportional to the stretch of the spring, we have F = kx. In our experiment, what did we use to provide the force, F?
 
 

b) If x is the amount of stretch in centimeters, then show how to predict how many Skittles, n, there would be in the cup. (You’ll need to use the results of your experiment!)

n = __________________


 
c) What is the constant of proportionality, k, for your spring?
 
 

d) Compare the constant of proportionality for your spring with that obtained by other groups. Does a stiff spring have a higher or lower k-value than a light spring?
 
 

Part 2.

a) If n is the number of Skittles in the plate, then show how to predict the stretch, x (Hint: solve the equation 1b) above for x).

x = ____________
 

b) This is another example of direct variation. In this case, the ____________ is directly proportional to the ____________.
 

c) What is the constant of proportionality for this direct variation?

k = ____________
 
 

Jon Hasenbank, 2000.
 
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