# The Conservation of Energy (Elastic Potential Energy) Practical Report

Categories: Physics

The Conservation of Energy is a fundamental principle in physics that states energy cannot be created or destroyed, only transformed from one form to another. In this experiment, we will focus on the conservation of elastic potential energy. Elastic potential energy is the energy stored in an object when it is stretched or compressed. The aim of this laboratory is to investigate the relationship between the amount of elastic potential energy stored in a spring and the displacement of the spring from its equilibrium position.

Materials and Apparatus:

1. Spring
2. Meterstick
3. Masses (weights)
4. Stopwatch
5. Balance
6. Data logger
7. Vernier calipers

Procedure:

1. Set up the experimental apparatus by attaching one end of the spring to a fixed point and the other end to a mass hanger.
2. Measure the equilibrium position of the spring using a meterstick and record this value as the initial position (xo).
3. Add masses to the mass hanger and measure the displacement (x) of the spring from its equilibrium position for each mass added.
4. Record the mass added to the hanger and the corresponding displacement for each trial.
5. Repeat the experiment for different masses to gather a range of data points.
6. Use the data logger to measure the force applied to the spring at each displacement.
7. Calculate the elastic potential energy (PE) stored in the spring using the formula: PE = 0.5 * k * x^2, where k is the spring constant.
8. Determine the spring constant by plotting a graph of elastic potential energy versus displacement and fitting a linear trendline.

Calculations and Formulas:

1. Displacement (x): The displacement of the spring from its equilibrium position is measured using the formula x = xf - xo, where xf is the final position and xo is the initial position.
2. Force (F): The force applied to the spring can be calculated using Hooke's Law, F = k * x, where k is the spring constant.
3. Elastic Potential Energy (PE): The elastic potential energy stored in the spring is given by PE = 0.5 * k * x^2.
4. Spring Constant (k): The spring constant can be determined by rearranging Hooke's Law: k = F / x.

Data Table:

Mass (kg) Displacement (m) Force (N) Elastic Potential Energy (J)
0.1 0.05 (calculated) (calculated)
0.2 0.10 (calculated) (calculated)
0.3 0.15 (calculated) (calculated)

Plot a graph of Elastic Potential Energy (PE) versus Displacement (x).

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Fit a linear trendline to the data, and the slope of the trendline will represent the spring constant (k).

In conclusion, this experiment demonstrates the conservation of elastic potential energy in a spring.

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By systematically varying the mass applied to the spring and measuring the resulting displacement, we can observe the relationship between elastic potential energy and displacement. The calculated spring constant provides a quantitative measure of the stiffness of the spring. This laboratory serves as a practical application of fundamental physics principles and reinforces the concept of energy conservation in mechanical systems.

Hooke's Law asserts that the force required to stretch or compress a spring is directly proportional to the distance of deformation. The deformation, which refers to the stretching and compression of a spring, is directly related to the force causing it. The energy stored in a stretched or compressed spring can be determined using the equation EPE = ½kx^2, where k represents the spring constant, indicating the spring's stiffness. This experiment aims to find the k value of a coil spring by applying forces, measuring extensions, and calculating energy. The stored energy can also be calculated using Gravitational Potential Energy (mgh). The objective is to derive the k value and compare the loss of Gravitational Potential Energy with the gain in Elastic Potential Energy.

Materials:

• Coil spring
• Retort stand
• Clamp
• Metre ruler
• Hooked mass set (increments of 100g)

Procedure:

1. Clamp the retort stand to the bench and hang the coil spring.
2. Measure the height from the floor to the bottom of the spring at its natural equilibrium position.
3. Add a 1kg weight to the spring, measure the maximum extension, and record the results ten times.
4. Add weights from 100g to 1.00kg in 100g increments, measuring the extension caused by each weight.

Discussion and Analysis of Results: The experiment used millimeters and grams, converted to kilograms and meters for precision. Gravitational Potential Energy (GPE) and Elastic Potential Energy (EPE) were considered, neglecting negligible energies like heat loss and friction. The spring constant (K) was determined as 28.9J, and EPE was calculated as 3.71J. Discrepancies between GPE and EPE were attributed to the miscalculation of EPE using the equation ½kx^2.

The expression EPE = ½kx^2 assumed ideal elastic properties, but the experiment showed non-proportional Force vs Extension initially. The actual relationship was found as F = 28.9x + 2.58. The EPE was then calculated as 5.02J, showing a 1.03% difference from GPE. Measurement uncertainties and human errors were considered.

Conclusion: The experiment partially verified the Conservation of Energy, acknowledging the limitations in measuring spring extension. The spring's non-ideal properties and the brief period of maximum extension affected accuracy. Losses to energies other than EPE were assumed negligible. Further improvements in measurement precision are recommended.

Task 2: Graphs and calculations were provided, including the average extension (0.507m), uncertainty (∆x = ± 3.6mm, 0.71%), spring constant (28.9N/m), loss of GPE (4.97J), gain in EPE (3.71J), difference between GPE and EPE (1.26J, 25.4% of GPE). Questions 6 and 7 were addressed in the discussion section.

Updated: Feb 26, 2024