PhysicsLAB Lab
Static Springs: Hooke's Law

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Purpose
 
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.
 
 
Equipment
 
  • one spring
  • slotted masses
  • mass hanger
  • meter stick
  • support stand
 
 
Procedure and Data Tables
 
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
   
 
Now hang the unknown mass from your spring and record the spring's total length. 

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
 
 
Data Analysis
 
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.

What is the name of your file? 


In Part I, what is the numerical value of the slope? 

What are the units on the slope? 

What is the numerical value of the y-axis intercept? 

What are the units on the y-axis intercept? 

What property of the spring does the y-axis intercept represent? 

Write the equation of your group's graph using the correct experimental variables instead of EXCEL's generic x and y? 


In Part II, what is the numerical value of the slope? 

What are the units on the slope? 

What is the numerical value of the y-axis intercept? 

What are the units on the y-axis intercept? 

Write the equation of your group's graph using the correct experimental variables instead of EXCEL's generic x and y? 

 
 
Hooke's Law and Elastic Potential Energy
 
When working with springs, Hooke's Law states that
where Fdistorting is the applied force, k is the spring's elasticity constant measured in N/m, x is the final length, and xo is the original length. The slope of the graph of Force vs Displacement is the spring's force constant. Displacement, s = (x - xo) , represents how far the spring is stretched from its equilibrium position by the applied force. Note that Fdistorting = 0 when the spring is in its equilbrium position, xo.
 
 
When calculating the amount of potential energy PEelastic 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.
If you need to determine how much work an object does in stretching or compressing a spring, we use the following formula.
 
Conclusions
 
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.
 
What is the elasticity constant for your group's original spring? 

Based on your equation for EXCEL’s trend line, what would be the total length of the spring when it is supporting a 1.8-kg mass? 

How far would a 1.8-kg mass stretch your spring? 

How much elastic potential energy would be stored in the spring? 

Using the equation for EXCEL’s trend line, what is the weight of your unknown mass in newtons? 

Calculate the unknown's mass in kilograms. 

Now measure the unkown mass on a triple beam balance and record its value in grams. 

What was your group’s percent error? 


In Part II your EXCEL graph has the total length of the spring in the video displayed on the x-axis and the applied force the y-axis. Consequently the elasticity constant for this spring will be graph's slope.

What is the elasticity constant for the spring in the video? 

What was the percent error for the y-axis intercept? 

Was this spring "weaker" or "stronger" that the spring you used in Part I? 

Based on your equation for EXCEL’s trend line, what would be the total length of the spring if it were to support a hanging mass of 1.8-kg? 

How far would the 1.8-kg mass stretch the video's spring? 

How much elastic potential energy would be stored in the video's spring? 



After submitting your results online, turn in your written lab report to the one-way box. Each group should have a paper to support any and all numerical values that were submitted online as well as a printout of your graphs.

 
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