Physics Experiment: Measuring Potential Energy of a Spring

Experiment: Potential Energy of a Spring

Understanding the relationship between work, potential energy, and kinetic energy is fundamental in physics and engineering. This experiment demonstrates the Law of Conservation of Energy using a simple spring-mass system. By measuring the extension of a spring and the fall of a mass, we can calculate the spring’s potential energy and compare it to the work done.

Theoretical Background

Hooke’s Law: The force required to extend or compress a spring is directly proportional to the distance it is stretched. This is expressed as F = -kx, where k is the spring constant (a measure of stiffness) and x is the displacement.

Elastic Potential Energy (PE): When a spring is stretched or compressed, it stores energy. This energy is calculated as PE = 1/2 kx².

Work-Energy Theorem: The work done on an object equals the change in its kinetic energy. In this system, the potential energy stored in the spring is converted into kinetic energy as the mass falls (and gravitational potential energy changes).

Experiment Setup

Materials:

• A spring (helical coil)
• A meter stick or tape measure
• A known mass (e.g., a 100g, 200g, or 500g weight)
• A ruler
• Stopwatch or timer
• Clamp stand (to hold the spring vertically)

Procedure:

1. Setup: Securely clamp the spring so that it hangs vertically. Ensure it is stable.
2. Initial Measurement: Use the meter stick to measure the height from the bottom of the un-stretched spring to the floor. Record this as h1.
3. Load the Spring: Attach the mass to the bottom of the spring. Lower it slowly until it hangs at equilibrium (not bouncing).
4. Measure Displacement: Use the ruler to measure how much the spring stretched from its original length. Record this extension as x.
5. The Drop: Lift the mass slightly to relieve tension (or release from a specific height if testing impact) and release it. *For this specific calculation, we often measure the time of free fall if we detach the mass, or the period of oscillation if we let it bounce.*
6. Final Measurement: If dropping the mass to the floor, measure the height from the floor to the release point. Record the time t it takes to hit the floor.

Calculations and Analysis

Perform the following calculations to analyze the energy transformation:

1. Change in Height (Δh): Subtract the final height from the initial height: Δh = h2 – h1.
2. Spring Potential Energy (PE): Calculate the energy stored in the stretched spring: PE = 0.5 * k * x^2. (Note: You may need to calculate k first by using F = mg = kx, so k = mg/x).
3. Kinetic Energy (KE): Calculate the kinetic energy of the mass just before impact: KE = 0.5 * m * v^2. You can approximate velocity v using kinematic equations for falling bodies (v = gt).
4. Work Done (W): Verify if the Work Done by the spring (and gravity) equals the change in Kinetic Energy. W = PE_spring + PE_gravity.
5. Power (P): Calculate the power generated during the fall: P = W / t.

Discussion

Observations: You should observe that a stiffer spring (higher k) stores more energy for the same displacement. However, it is harder to stretch.

Sources of Error:

• Air Resistance: slows down the falling mass, reducing the measured kinetic energy.
• Spring Mass: Ideally, the spring is massless, but in reality, the spring’s own mass contributes to the system’s energy.
• Measurement Error: Reaction time when using a stopwatch can introduce significant variance.

Simulation

Use the interactive simulation below to visualize the vectors of Force, Velocity, and Acceleration as the spring oscillates. Try changing the “Spring Constant” and “Mass” to see how they affect the energy.