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The report covers hookes law experiment, there is objectives, procedure, calculations, discussion on how the report was conducted
Typology: Lab Reports
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k โ the spring constant or stiffness (N/m) x โ deformation or extension (m)
Initial tension of the spring is the tension that is already present between the coils in extension (Superior, 2018). It keeps the extension springs compressed and holds their coils tightly. Following is the formula on how to calculate initial tension of the spring: ๐ผ๐ = ๐น โ ๐๐ฅ Equation 2 : Initial tension formula where IT = Initial tension F = Force in Newton k = the spring constant or stiffness (N/m) x = deformation or extension (m) The formulas discussed above will help in accomplishing the objective of this experiment.
i. The spring properties were measured (outside diameter, wire diameter, initial tension, maximum tension, spring rate). ii. One end of the spring was fitted into the hook on top of the spring testing apparatus. iii. The hook and the transparent pointer were fitted on the bottom of the spring. iv. The reading of the extension scale was recorded. v. A weight hanger was fitted in the bottom of the transparent pointer. vi. The weights were added gradually and as each weight was being added the reading on the extension scale was taken. vii. The weights were removed and the until the spring was back to its original length.
Following are the spring properties that were used for this experiment. Spring Properties: 1 st^ Spring: Outside diameter: 12.7 mm Theoretical Spring Constant: 0.07 N/mm Pull to Pull Length: 76.2 mm 2 nd^ spring: Outside diameter: 12.7mm Theoretical spring Constant: 0.1 N/mm Pull to Pull Length: 63.5 mm
Table 1 : Results obtained during the experiment Mass (kg) Scale Reading (mm) 0,016 ( Transparent Pointer and Hook) 151 0,116 151 0,216 151 0,316 154 0,416 161 0,516 169 0,616 176 0,716 184 0,816 191 0,916 199 1,016 207 The above values in Table 1are the values which were read from the lab these are the values of the mass of the weights in kg and the extension of the spring in mm.
Table 2 : Calculated experimental results Reading Mass (kg) Force(N) Scale Reading (mm) Extension (mm) Spring Constant (N/mm) 0,016 ( Transparent Pointer and Hook) 0,16 151 0 1 0,116 1,13796 151 0 0 2 0,216 2,11896 151 0 0 3 0,316 3,09996 154 0 0 , 4 0,416 4,08096 161 3 0, 5 0,516 5,06196 169 10 0, 6 0,616 6,04296 176 17 0, 7 0,716 7,02396 184 25 0, 8 0,816 8,00496 191 33 0, 9 0,916 8,98596 199 40 0, 10 1,016 9,96696 207 47 0, AVERAGE 0 , 12379
Experimental Error 1 st^ Spring : % ๐๐๐๐๐ =
Experimental Error 2 nd^ Spring : % ๐๐๐๐๐ =
Graph 1 : Relationship of force and extension
The experiment was conducted, and the experimental data was measured and recorded. Equation 1 and 2 were used to determine the initial tension and the spring constant as it was required. Graph 1 was plotted using the calculated results to show the relationship between the force and the extension. It is observed that there is a linearity between these two parameter, as it can be seen that when the force increases also the extension increases. This agrees with Hookeโs law stated earlier on in which from this relationship a spring constant can be determined. The initial tension was found to be 2,97743 N which is an acceptable force springs might manage by assumptions. The spring constant was found to be 0, 12 377 N/mm by using both the formulas ( average and gradient formula). This spring constant was compared to the theoretical spring constant of the 1st^ and the 2 nd^ spring. The percentage error between the theoretical spring constant of the 1st^ spring and the experimental one was found to be 76,81% as shown on Table 3 and 23,77% for the 2nd^ spring. Based on this it can be seen that the spring used for this experiment is the 2 nd^ spring as the error its value and the one from the experiment is small as compared to the 1st^ spring, as human error might have caused this small difference when measuring the results. Therefore, it is recommended that the experiment must be repeated 3 times in the future to avoid discrepancy.
The experiment was successfully conducted as the objective was accomplished. The initial tension was found to be 2,97743 N which was assumed to be an acceptable force that the springs can withstand. The spring stiffness was found to be 0,12377 N/mm which was compared with the 1 st^ and 2nd^ spring constants given to determine which spring might have been used during the experiment. It was found out that the 2nd^ spring is the one being used as the percentage difference between its coefficient and the experimental coefficient is small ( 23,77% difference) as compared to the 1st^ spring (78,86%). It was recommended that the experiment must be repeated in future experiment to avoid discrepancy in the results. In conclusion, Hookeโs law was proven as the linear relationship was observed between the Force and the extension.
Bernhardt, G., 2014. Physics Forum. [Online] Available at: https://www.physicsforums.com/threads/what-is-a-spring.763175/ [Accessed 02 October 2020]. EngStaff, 2019. ENGGSTAFF. [Online] Available at: https://www.enggstudy.com/eulers-bernoullis- derivation/#Assumptions_of_Bernoulli%E2%80%99s_Equation [Accessed 21 MAY 2020]. J, D., 2011. Strength of Materials. 4 ed. s1: Pears.
Figure 1 :Hook and weights used for the experiment Figure 2 : The TQ SM110 spring testing apparatus
