Energy Conservation Lab: Investigating Mechanical Energy

Introduction

The principle of conservation of energy stands as one of the most fundamental laws in physics. In this interactive laboratory simulation, students investigate how gravitational potential energy converts to kinetic energy as an object descends along a ramp. By collecting position and velocity data, plotting v² versus height, and analyzing the slope, students can experimentally determine the acceleration due to gravity—connecting abstract theory to measurable results.

Learning Objectives

After completing this lab, students will be able to:

1. Explain the conservation of mechanical energy in a closed system
2. Apply the work-energy theorem to predict final velocities
3. Construct a linearized graph (v² vs h) from experimental data
4. Calculate gravitational acceleration from the slope of the best-fit line
5. Evaluate percent error and identify sources of experimental uncertainty
6. Compare ideal (frictionless) and real (with friction) energy scenarios

Key Equations

Lab Procedure

Part 1: Data Collection

1. Set the release height using the height slider (start with h = 0.5 m)
2. Click "Release Object" to start the simulation
3. Observe the energy bars as PE converts to KE
4. Note the velocity reading from the virtual photogate
5. Click "Record Data Point" to add this measurement to your data table
6. Repeat for at least 5 different heights

Part 2: Graph Construction

1. Switch to the "Graph & Analysis" tab
2. Your data points will appear on the v² vs h graph automatically
3. Enable "Show Best-Fit Line" to see the linear regression
4. Enable "Show Theoretical Line" to compare with the expected relationship

Part 3: Analysis

1. Record the slope of your best-fit line
2. Calculate g using: g = slope / 2
3. Calculate percent error
4. Discuss sources of error and the significance of the y-intercept

Sample Data

Expected slope: 2g ≈ 19.62 m/s²

Real-World Applications

1. Roller coasters - Engineers design drops and hills using energy conservation
2. Hydroelectric dams - Water falling from height converts PE to KE
3. Ski jumping - Athletes convert gravitational PE to kinetic energy
4. Pendulum clocks - Continuous conversion between PE and KE
5. Regenerative braking - Electric vehicles convert KE back to electrical energy

Common Mistakes to Avoid

1. Forgetting to square velocity when plotting the linearized graph
2. Using v vs h instead of v² vs h (results in non-linear curve)
3. Ignoring the y-intercept - it should theoretically be zero
4. Not varying heights enough - need a good spread of data points
5. Comparing with wrong g value - use 9.81 m/s², not 10 m/s²

References

1. Giancoli, D. C. (2014). Physics: Principles with Applications (7th ed.). Pearson.
2. Knight, R. D. (2017). Physics for Scientists and Engineers (4th ed.). Pearson.
3. NIST Reference on Constants, Units, and Uncertainty. Standard g = 9.80665 m/s².