The purpose of this lab is to use linear regression and data analysis to calculate the elasticity constant for a single spring and to distinquish between dependent and independent variables in an experiment.

 

 

 

 

 

 

Part I: Increasing Mass. Complete ten trials using your spring. Initially record the equilibrium length of the spring without any suspended masses.

 

 

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

 

 

Continue until you have suspended a total of 1000 grams from the spring. Remember that the pan contributes 50 grams to each combination. Complete the following data table for your spring.
 

single spring		Equilibrium length	________
Trial	Total Hanging Mass	Total Force (mg)	Final Length (cm)
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

 

You are to watch this video, Part II: Increasing Length. Physics Lab Demo: Exploring Hooke’s Law Springs, and fill in the following data chart. In the lab these students are performing you need to record the total length of the spring and the force required to maintain that length. So the spring's length will be your independent variable and required force will be your dependent variable.

 

video spring		Equilibrium = ________
Trial	Total Length	Total force (N)
1	31 cm
2	33 cm
3	35 cm
4	37 cm
5	39 cm
6	41 cm
7	43 cm
8	45 cm
9	47 cm
10	49 cm
11	51 cm
12	53 cm
13	55 cm
14	57 cm
15	59 cm
16	61 cm
17	63 cm
18	65 cm
19	67 cm

 

 

You will now use EXCEL to graph both data tables. Start by opening a new EXCEL file and save it in the thaw space as LastnameLastnameHookesLaw.xls

 

In Part I you should plot weight on the x-axis (independent variable) since we arbitrarily decided on the amount of mass to suspend from the spring, and plot total length on the y-axis (dependent variable) since the spring's final length (original length + stretch) depended on the amount of suspended mass. Please use the following cell designations. Be CAREFUL of the switch in units!

• A1 Mass
• B1 Weight
• C1 Total Length

• A2 (kg)
• B2 (N)
• C2 (meters)

After entering your data, highlight the numerical data in columns 2 and 3 and graph as a scatter plot. Right click on a data point and add a trend line. Display the line's equation and correlation coefficient (R²). Title this graph as Length vs Force.

In Part II you should plot total length on the x-axis (independent variable) since the students in the video arbitarily decided to increase the length of the spring in 2-cm increments, and plot applied force on the y-axis (dependent variable) since the amount of force to stretch the spring dependent of the amount of displacement. Once again, be CAREFUL of the switch in units!

• A20 Total Length
• B20 Applied Force

• A21 (meters)
• B21 (N)

After entering your data from the video, highlight your numerical data in columns 1 and 2 and graph as a new scatter plot. Right click on a data point and add a trend line. Display the line's equation and correlation coefficient (R²). Title this graph as Force vs Length.

After you resave your file with all of the information from your data tables and graphs, go back and rescale any axes to insure that you maximize the display of that graph's data. Before closing EXCEL, print your data tables and graphs. Please use print-preview to make sure that all of information (data tables and graphs) fit on only one page.

 

 

 

When working with springs, Hooke's Law states that

where F_distorting is the applied force, k is the spring's elasticity constant measured in N/m, x is the final length, and x_o is the original length. The slope of the graph of Force vs Displacement is the spring's force constant. Displacement, s = (x - x_o) , represents how far the spring is stretched from its equilibrium position by the applied force. Note that F_distorting = 0 when the spring is in its equilbrium position, x_o. When calculating the amount of potential energy PE_elastic that is stored in the spring when the spring has been either stretched or compressed from its equilbrium position, we use the following equation. This energy is measured in Joules, just like KE = ½mv² and gravitational PE = mgh.

 

 

In Part I your graph has the applied force (the suspended weights) displayed on the x-axis and the spring's length along the y-axis. Consequently the elasticity constant for your spring will be calculated as the reciprocal of each graph's slope.