Answer every question you are able to answer in this lab:
Hooke’s Law 
Purpose 
To verify the linear proportionality of a spring within the elastic region and to determine the relationship between similar springs connected in parallel and series connections.
Equipment
Base stand with clamp holders
2 identical springs
Mass hanger with slotted masses
Ruler
Rubber band
Theory
Springs have a force that opposes their stretch or compression. In the video you will add mass to compress a spring. The spring force is governed by its spring constant, a measure of the stiffness of the spring. This is known as Hooke’s Law developed after Robert Hooke, an industrious English scientist who was a contemporary of Isaac Newton.
F=-kx	(1)
Where Δx is the stretch or compression length. If we hang masses from a vertical spring, the mass-spring system will be at rest. If we let the hanging mass be the object of interest then it is in static equilibrium. Using Newton’s First Law in conjunction with Hooke’s Law we have
ky-mg=0		(2)
Using this model what happens to the spring constant if you add two springs together in parallel or series? Compare the spring constant, k, for a single spring and for two springs in parallel and series.
Procedure
Hang the spring vertically as similar to figure 1. Record the initial position of the mass hanger by measuring the bottom of the mass hanger. Record this position in Table 1 for all the rows.

Add mass to the mass hanger in the range of 5 to 20 grams. Enough to make a noticeable difference. Measure this new position of the mass hanger and record the value in Table 1. Record the amount of mass added. We are not going to take into account the mass hanger. Calculate the load force (weight of the added masses) and record the value in Table 1.
Repeat these steps until you have recorded 10 data points.
Graph your Load Force versus stretch and use a line of best fit. Include a sketch of your graph with the line of best fit.
Table 1
Initial position (m)
Final position (m)
Added mass (kg)
Load Force (F=mg) (N)
Stretch distance (Final position minus Initial position) (m)






































































































Question 1: Using equation 2 from the theory section. What would you expect the slope of your Load Force versus Stretch graph to be?

Question 2: Using your line of best fit, what is the spring constant for your single spring?

Question 3: Ask your instructor for the known spring constant of your spring. Calculate your percent error between your experimental value and your known value. % Error=xmeasured-xexpectedxexpected×100%

Attach the second spring of the same spring constant such that they are in parallel. Use the figure for reference. You might need a rod to attach the mass hanger to both springs.

Repeat the procedure like before now for the springs in parallel. Record all your values in Table 2. Make a scatter plot of your Load Force versus Stretch. Include a sketch of your graph along with the line of best fit.
Table 2
Initial position (m)
Final position (m)
Added mass (kg)
Load Force (F=mg) (N)
Stretch distance (Final position minus Initial position) (m)







































































































Question 4: What is the spring constant for the two springs in parallel? How does this compare to the single spring?


Question 5: Which model best describes the total spring constant for two springs connected in parallel?
Model 1	 k=k1+k2k1k2
Model 2	 k=k1+k2
Model 3	1k=1k1+1k2 

Attach the second spring of the same spring constant such that they are in series. Use the figure  for reference. 

Repeat the procedure like before now for the springs in Series. Record all your values in Table 3. Make a scatter plot of your Load Force versus Stretch. Include a sketch of your graph along with the line of best fit.
Table 3
Initial position (m)
Final position (m)
Added mass (kg)
Load Force (F=mg) (N)
Stretch distance (Final position minus Initial position) (m)






































































































Question 6: What is the spring constant for the two springs in series? How does this compare to the single spring?


Question 7: Which model best describes the total spring constant for two springs connected in parallel?
Model 1	 k=k1+k2k1k2
Model 2	 k=k1+k2
Model 3	1k=1k1+1k2 

Question 10: Using the model for parallel and series springs, calculate the theoretical value for the combined spring constant using the known spring constant for the similar springs. Calculate your percent error between your experimental value and theoretical value. 



Question 9: There might be some error in connecting to two springs is series. We didn’t take into account the masses of the springs themselves. Do you think this had a large affect on your results? What could have been other sources of error?



Now take a rubber band are replace the springs. Repeat the procedure like before by adding masses and record all your values in Table 4. Make a scatter plot of your Load Force versus Stretch. Include a sketch of your graph along with the line of best fit.
Table 4
Initial position (m)
Final position (m)
Added mass (kg)
Load Force (F=mg) (N)
Stretch distance (Final position minus Initial position) (m)







































































































Question 10: Does a rubber band obey Hooke’s Law? Site your evidence.


Question 11: How is a stiffer (higher spring constant) shown on a graph of force vs stretch?


Question 12: What is the spring constant of a spring that is 10 cm in length stretches to 12 cm when a 250 N mass is suspended from it? 


Question 13: Using the same spring in question 12, an unknown object is added to the spring and the spring stretches to 13.8 cm. What is the mass of this unknown object?