PHYS 200 Introductory Physics I – LAB 4 2025-2026 COMPLETE SOLUTION ATHABASCA UNIVERSITY COMPLETE UP

Introduction: In this lab, we will explore the relationship between force and displacement in elastic materials, specifically focusing on the stretching behavior of a rubber band or a spring. This study will enable us to understand and verify Hooke's Law, which states that the force exerted by an elastic material is directly proportional to the displacement it experiences, provided the material's elastic limit is not exceeded. The mathematical expression of Hooke's Law is given by: F=−kx where F is the force applied to the material, k is the spring constant (a measure of the stiffness of the material), and x is the displacement from the equilibrium position.

Procedure: In this experiment, a rubber band, plastic bag, and 10 loonies were used to investigate the relationship between displacement and force to verify Hooke’s law. To begin, the plastic bag was taped to the elastic band then taped to the wall, a measuring tape was taped next to it ensuring that 0cm was in line with the top of the elastic. The initial length recorded was 20.6cm or 0.206m. A loonie was added, and the new length was recorded, this step was repeated until all ten loonies were added to the bag, stretching out the elastic.

Pictures:

Data:

Analysis and Discussion: This experiment successfully demonstrated Hooke’s law with the results establishing a linear relationship between the stretching of the elastic band (displacement) and the loonies (weights/ applied force) in the bag. The plotted data on the graph above clearly show the relationship that the force applied is directly proportional to the displacement. The k value is 70/1, or 70 as found from the line of best fit. Using the formula F=kx we were able to find how much weight was needed in order to make the elastic stretch 1.00m, which was 7000g.

Taking 7000 and dividing it by 7 (the weight of each coin in grams) gave us the answer that 1000 loonies were needed to stretch the elastic that far.

Conclusion: The experiment successfully demonstrates Hooke’s Law by establishing a linear relationship between the applied force and the displacement of the rubber band within its elastic limit. The calculated spring constant k (k=70) serves as an essential parameter in understanding the material’s stiffness. Despite some potential sources of error like the measurements accuracy within 0.2cm or the weight within 0.1g, the overall results align well with the theoretical predictions, underscoring the importance of Hooke’s Law in practical applications.

Questions: Answered with data.