The purpose of this lab is to use linear regression and data analysis to calculate the elasticity constant for a single spring, and for springs arranged in series and in parallel.

 

 

 

 

 

 

Part I: Single springs. Complete ten trials for each spring. Initially record the equilibrium length of the spring without any suspended masses.

 

 

Then increase the hanging mass by increments of 100 grams and record each stretched length.

 

 

Continue until you have suspended a total of 1000 grams from each spring. Complete the following data table for each individual spring.
 

single spring #1		Equilibrium length	_____________
Trial	Total Hanging Mass	Total force (mg)	Stretched length	Displacement
1	100 g
2	200 g
3	300 g
4	400 g
5	500 g
6	600 g
7	700 g
8	800 g
9	900 g
10	1000 g

 

 

single spring #2		Equilibrium length	_____________
Trial	Total Hanging Mass	Total force (mg)	Stretched length	Displacement
1	100 g
2	200 g
3	300 g
4	400 g
5	500 g
6	600 g
7	700 g
8	800 g
9	900 g
10	1000 g

 

 

Part II: Springs in Series. Complete five trials using both springs arranged in series by linking them together one below the other. Initially record the equilibrium length of the springs without any suspended masses. Complete five trials ranging from 100 grams to 500 grams.

 

springs in series		Equilibrium length	_____________
Trial	Total Hanging Mass	Total force (mg)	Stretched length	Displacement
1	100 g
2	200 g
3	300 g
4	400 g
5	500 g

 

Part III: Springs in Parallel. Complete five trials using both springs arranged side-by-side, or in parallel. Initially record the equilibrium length of the springs without any suspended masses. Complete five trials ranging from 200 grams to 1000 grams. Be careful to make sure that the suspended masses are centered so that they are supported equally by both springs.

 

springs in parallel		Equilibrium length	_____________
Trial	Total Hanging Mass	Total force (mg)	Stretched length	Displacement
1	200 g
2	400 g
3	600 g
4	800 g
5	1000 g

 

 

 

EXCEL will now graph your data. Minimize your browser, double click My Computer, double click the shared drive called colwell/bay on Lederman, double click your period's folder and then finally double click 1-HookesLawAPC.xls. You will most likely be asked to open the file as "read only" - that is fine. As soon as the file is open, use File Save As to rename the file as 

LastnameLastnameHookesLawAPC.xls

 

in your period's folder. This copy of the file now belongs uniquely to your group. Remember that there are to be no spaces in the file name.

 

Once you save your file with all of the information for each of the individual springs as well as the two special arrangements, print out a copy of your file for your lab reports. Don't forget to rescale any axes to insure that you maximize the display of your data.

 

On your printout, use the form y = mx + b to rewrite the equation of each graph next to the graph's title. Remember to use the variables s and F.

 

 

When working with springs, Hooke's Law states that F_external = ks where F_external is the applied force, k is the spring's elasticity constant measured in N/m, and s is the displacement, or how far the spring is stretched from its equilibrium position.

 

 

Note that our graphs have the applied force (the suspended weights) displayed on the x-axis and the spring displacements along the y-axis. This is because we manipulated the values of the suspended masses, resulting in force or weight being our independent variable while we merely recorded the stretched lengths as our experimental outcomes, or dependent values.

 

Since our graphs are s vs F, the elasticity constant for each of our spring systems will be calculated as the reciprocal of each graph's slope.

 

 

We will now investigate the elasticity constant for springs arranged in series. The theoretical constant for such a system of springs is given by the formula:

 

 

We will now investigate the elasticity constant for springs arranged in parallel. The theoretical constant for a system of springs in parallel is given by the formula:

 

 

As shown above, the area bounded by the displacement axis and the curve represents the energy stored in the spring system.

 

 

At this time, examine each of your four data sets and choose two displacement values that are represented "as closely as possible" in all four sets. Using these values, calculate the area of the trapezoid bounded by the displacement (y-axis) and each experiment's graph.

 

Lightly shade in your trapezoids and show your calculations on each graph. Place your answers in the chart provided below.