# Laboratory Report: Investigating Hooke's Law with Springs and Weights

Categories: Physics

Hooke's Law is a fundamental principle in physics that describes the behavior of springs under the influence of an applied force. This experiment aims to investigate Hooke's Law by stretching springs under the influence of weights, determining the spring constant for two different springs, and identifying the elastic limit from the force vs. spring extension graph. The materials used include labeled weights, springs, a ruler, and a stand.

Hooke's Law states that within the elastic limit of a material, the change in shape is directly proportional to the applied force.

Mathematically, this relationship is expressed as F=kx, where F is the force applied, k is the spring constant, and x is the amount of stretch in the spring. In this experiment, the spring constant will be determined by measuring the force applied and the corresponding spring extension.

If an object is elastic, it can return to its original shape after undergoing force. Hooke's Law applies to springs until the elastic limit is reached, beyond which the relationship between force and deformation becomes nonlinear.

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The elastic limit is the point where the spring does not return to its original shape upon removing the load, indicating permanent deformation.

Procedure:

1. Hang a spring from a stand and measure its initial length without any weights.
2. Attach a mass hanger to the spring and add weights in increments of 100 grams, measuring the corresponding spring position for each mass.
3. Record the data for at least three trials for each spring.
4. Repeat the procedure for the second spring, measuring from 100 grams to a total of 500 grams.

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5. Calculate the change in length, average length, and spring constant for each spring.

Calculations:

1. Calculate the change in length: Change in Length=Final Length−Initial LengthChange in Length=Final Length−Initial Length
2. Calculate the average length: Average Length=Sum of LengthsNumber of TrialsAverage Length=Number of TrialsSum of Lengths​
3. Calculate the force applied: F=m⋅g, where m is the mass in kilograms and g is the acceleration due to gravity (9.8 m/s²).
4. Calculate the spring constant: k=xF​

Sketch a graph with force on the y-axis and spring extension on the x-axis. The slope of the line represents the spring constant.

Compare the spring constants obtained for the two springs. Discuss any differences and possible sources of error. Analyze the force vs. spring extension graph to identify the elastic limit for each spring.

Summarize the findings and restate the importance of Hooke's Law in understanding the behavior of springs under external forces. Discuss any limitations of the experiment and suggest improvements for future investigations.

According to the information provided in the two tables, it is evident that the spring constant (k value) for Spring 1 is higher than that of Spring 2. Upon observation, Spring 1 appeared stiffer, with a smaller equilibrium measurement compared to Spring 2.

As additional weights were added to Spring 2, it exhibited a more elastic behavior, resulting in a consistently higher new equilibrium compared to Spring 1. The graphical representation of the data further confirms that Spring 1 is less elastic in comparison to the highly elastic Spring 2.

However, it's crucial to acknowledge potential sources of error in the experiment, particularly during the measurement of the extended spring length. Human errors and slight movements in the spring during measurements could have introduced inaccuracies in the length readings.

In conclusion, the experiment did not entirely align with its intended purpose. The spring constant is not constant; it varies with the applied force. The two data tables highlight the fluctuations in the spring constant values.

While Hooke's Law is not perfectly accurate based on the experiment, it still holds true to some extent. The spring constant value for Spring 1 did not consistently increase or decrease by a set value, indicating some deviations. Various errors occurred during the experiment, such as excessive stretching of the spring and fluctuations in equilibrium measurements due to the spring's movement. To establish a more accurate understanding of Hooke's Law, conducting the experiment in a controlled environment with minimized disturbances would be beneficial.

Updated: Feb 28, 2024