Hooke’s Law Lab Fahad Al Zaman
DP1 HL Physics
Mr. Richards

Abstract:
The objective of the lab was to find the constant value or spring rate of the specific spring assigned to us. All of our springs are relatively similar, so the constant rate can be comparable amongst each other. The spring was hung from a stand using a clamp. The initial length of this spring was measured. Then, a 100 g hanger was added. The change in length is measured. Following this, more weights are added and the changes in heights are measured. As more weights were added, the changes in length also increased proportionately. By using the law F= –kx, we able to calculate the constant k by graphing Force over Displacement and multiplying the result by negative 1. The constant k determines how much the displacement of a spring is affected by the force. Generally, stronger springs have a lesser value as they are less subject to change. To compare our results, the class average was found which was 28 ± 1. The results from this lab is 27.2 ± 1.2 and only has 3% relative error.

Variables:
Independent
• Mass – grams (g) – 100 g weights – Adding 100 g weights on the springs starting from 100 g weights to 300 g. This will add a downward force (weight)

Dependent • Displacement – meters (m) – Ruler – Measuring the elongation of the spring due to the adding of the weights by measuring the change in spring length from the bottom of the spring before and after the weights are added.
Controlled
• Type of Spring – Different springs may have spring constants or k • Gravity – Keeping the spring the same height from the ground, i.e. same table height • Room Temperature – Heat may change the elasticity of the spring • Same weights – To ensure consistency in uncertainties. Otherwise, a lot of unnecessary calculations need to be made

Apparatus: • Ruler • Retort Stand with clamps • 100 g mass hanger • 100 g weights • Spring

Data Presentation and Evaluation:

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[1]: Standard uncertainty from electric scale device

[2]: Standard uncertainty for measured object is half of smallest graduation or 0.05 cm. However, because the start and end are unidentifiable due to distance and the shape of the spring, the uncertainty, I was able to reasonably measure up to 0.3 cm.

Table 1: Length of Spring at different weights were added
|Mass/ g |Mass/ kg |Length/ ± 0.3 cm[2] |Length/ ± 0.003 m |
|0 |0 |2.1 |0.021 |
| 102 [pic]1 |0.102 [pic]0.001 |5.5 |0.055 |
|201 [pic]2 |0.201 [pic]0.002 |7.8 |0.078 |
|300 [pic]3 |0.300 [pic]0.003 |11.3 |0.113 |
|399 [pic]4 |0.399 [pic]0.004 |15.0 |0.15 |
|498 [pic]5 |0.498 [pic]0.005 |18.8 |0.188 |
|597 [pic]6 |0.597 [pic]0.006 |22.5 |0.225 |
|696 [pic]7 |0.696 [pic]0.007 |26.2 |0.262 |
|795 [pic]8 |0.795 [pic]0.008 |29.8 |0.298 |

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Table 2: Displacement of spring based on applied Force
|[pic]Displacement/ ± 0.006 m