Hooke’s law refers to a physics principle which states that “the extension of a spring is in direct proportion with the load (force) applied to it.” The law is used to approximate the elasticity of a string or response of elastic bodies. Hooke’s experiment also illustrates the relationship between the force of an object and the distance of the ring. The law is mostly applicable to numerous materials while noting that the elastic limit of the material is not exceeded. The elastic limit is the point at which the spring will not stand the force anymore but to break. The law is described as stress is directly proportional to the strain (hemantmore.org). The originates from a British physicist Robert Hooke in the 17th century where he was experimenting aiming at establishing the relationship between elasticity and the forces applied to a spring. Hooke’s laws were then mathematically expressed as F= -kX (where F stands for the force applied, k stands for the spring constant, X stands for spring displacement, and the negative sign shows the direction of displacement). This lab experiment aims to investigate the spring constants of springs in parallel and series arrangements. The data will be collected from the spring extension measurement and comparing association of the extending the spring with the masses added to the springs. This steps will help in determining the spring constant which will prove Hooke’s law on the relationship of force and distance.
Methodology
The series arrangement follows the hypothesis that if the first string is loading with a weight W, the spring extends by x, and if a second spring is attached in series, the same force will act in each spring thus making the total stretch be 2x. The parallel experiment has the hypothesis that if two springs are arranged in parallel with a weight W attached, the springs extend by 0.5x because the stretching weight is shared among the two springs hence the new spring constant is twice an individual spring.
Apparatus required: two springs, mass hanger, support stand, rulers and slotted masses
Procedure
• Set up the support stand I a balanced position
• Suspend the spring from the clamp while carefully measuring the un-stretched length of the spring
• Attach the mass hanger at the end of the spring and measure the new length, calculate and record the results.
• Repeat the above steps while adding the masses in the spring up to 1000g (independent variable).
• Measure the final length after removing the masses then determine the spring constant k
• Add another spring in series to evaluate the spring constant for the two springs and repeat the above steps for all the masses. (For a parallel experiment, attach the second spring parallel to the first one).
• The controlled variables will be kept constant by adding masses while are sustainable on the spring while ensuring that the elastic limit is not exceeded.
Potential health and safety issues in the experiment
Sharp objects and tools and rusted metals can bring in bacteria to the affected areas of the experimenter’s cut body part. This might affect the individual with unexpected diseases upon the completion of the experiment or lab accidents during the process of investigating the practical variables thus I will ensure the tools and objects are not used in the experiment, or the sharp objects are kept away from cuts.
2D Diagram
Data collection and processing
Data and graph for series arrangement
Mass
Force
Ext1
Ext2
Ext3
average
0.1
1.0
6.5
6.7
7.0
6.7
0.2
2.0
14.4
14.6
14.5
14.5
0.3
3.0
21.0
21.3
21.6
21.3
0.4
4.0
29.5
28.7
28.5
28.9
0.5
5.0
36.5
36.8
36.9
36.7
0.6
6.0
43.2
43.5
43.5
43.4
0.7
7.0
50.8
51.0
50.5
50.8
0.8
8.0
57.5
57.5
57.9
57.6
0.9
9.0
64.5
64.5
67.3
65.4
1.0
10.0
72.2
72.0
72.5
72.2
Graph
Data and graph for series arrangement
mass
force
ext1
ext2
ext3
average
0.1
1.0
1.0
1.3
1.2
1.2
0.2
2.0
3.4
3.6
3.7
3.6
0.3
3.0
5.0
5.2
5.1
5.1
0.4
4.0
6.5
6.2
6.6
6.4
0.5
5.0
8.5
8.4
8.7
8.5
0.6
6.0
10.1
10.0
10.3
10.1
0.7
7.0
12.3
12.5
17.7
14.2
0.8
8.0
14.5
14.7
14.8
14.7
0.9
9.0
15.8
15.9
15.6
15.8
1.0
10.0
17.3
17.1
17.4
17.3
Graph
Actual length vs force table and graph
Mass
Force
Extension
Ext2
Ext3
Average
0.1
1.0
3.7
3.6
3.5
3.6
0.2
2.0
7.5
7.4
7.5
7.5
0.3
3.0
11.5
11.4
11.6
11.5
0.4
4.0
15.3
15.4
15.1
15.3
0.5
5.0
19.1
19.2
19.3
19.2
0.6
6.0
22.8
22.9
22.6
22.8
0.7
7.0
23.7
23.9
23.8
23.8
0.8
8.0
30.4
30.2
30.5
30.4
0.9
9.0
34.1
34.5
34.3
34.3
1.0
10.0
38.5
38.1
38.2
38.3
Graph
Example calculations
The formula => f = kX
Using the results of the series arrangement, we can evaluate the validity of the argument where the gradient serves as the spring constant and extension values chosen from any level.
The equation => y = 0.1381x => f = kX
F = 0.1381 * 6.7 = > 0.925
Conclusion and Evaluation
According to the assessment of both the series and parallel experiment, Hooke’s law is confirmed by the line of best fit since the trend line indicate a linear trend with a straight line through the origin (Colorado.edu n.d.). The spring constants for series and parallel arrangement differs as shown by the gradients of the graph. There were outliers in the data collected for the parallel arrangement. However, the data was ignored since the line of best fit passes through both the upper and lower outlier values to confirm the experiment hypothesis. Some of the faults made in the experiment especially in the second experiment where the technique required a repeat of the experiment while using the same methodology but same different arrangements which resulted in the variance of some values in the parallel experiment. Moreover, the possible sources of errors in the experiments include parallax errors due to reading from wrong angles and not straight at the point of measurement, ruler limitations as the minimum value is 1mm where the readings might have gone beyond this point. The confidence levels of the data are increased by the ten repetitive measurements which helped approximate future behaviour of the data and the equipment used were appropriate since there were minimal errors and besides having few outliers. Additionally, the ways of improving the experiment entail utilization of a meter ruler or labelling the clamp with measurement values which will increase the accuracy of the data instead of a spring or simple ruler. Control variables are kept constant by using the same ruler and measuring at a specific length.
In conclusion, the experiments indicate that spring constants for series arrangement halves upon using two springs while they double when the same two springs are ordered in parallel. Future experiments to be done to verify the conclusions will involve testing the behaviour of Hooke’s law using different combinations of dashpots and combinations of springs (Peng 2014).
References
Colorado.edu. [Online] < https://www.colorado.edu/physics/phys1140/phys1140_fa00/Experiments/M5/M5.html>[ Accessed on 5/17/18]
Hemantmore.org [Online] < https://hemantmore.org.in/foundation/science/physics/elasticity- stress-strain/2561/>[Accessed on 5/17/18]
Peng, B. 2014. Discrete Element Method (DEM) Contact Models Applied to Pavement Simulation. < https://vtechworks.lib.vt.edu/bitstream/handle/10919/50399/Peng_B_T_2014.pdf;sequen ce=1>[Accessed on 5/17/18]
