- Please enter spring constant.
- Please enter compression/extension.
- Please enter mass.
Example data
| # | k (N/m) | x (m) | m (kg) | η (%) | Elastic energy (J) | Speed (m/s) |
|---|---|---|---|---|---|---|
| 1 | 250 | 0.08 | 1.60 | 90 | 0.80 | 0.95 |
| 2 | 1200 | 0.05 | 0.50 | 85 | 1.50 | 2.26 |
| 3 | 800 | 0.12 | 2.00 | 70 | 5.76 | 2.01 |
| 4 | 3000 | 0.03 | 0.20 | 95 | 1.35 | 3.58 |
| 5 | 100 | 0.20 | 5.00 | 60 | 2.00 | 0.69 |
| 6 | 1500 | 0.10 | 1.00 | 80 | 7.50 | 3.46 |
| 7 | 500 | 0.15 | 0.75 | 90 | 5.63 | 3.67 |
| 8 | 2000 | 0.04 | 0.30 | 65 | 1.60 | 2.63 |
Examples assume translational motion and a linear spring.
Formula used
Elastic potential energy:
E = ½ · k · x²
Loss-adjusted kinetic energy:
KE = η · E
Kinetic energy and speed:
KE = ½ · m · v² → v = √(2·KE / m)
k is spring constant, x is displacement, m is mass, v is speed, and η is efficiency (0–1). Set η = 100% for an ideal conversion.
How to use this calculator
- Pick what you want to solve for.
- Enter k, x, and m with correct units.
- Set η to match expected losses.
- Enter speed if you are solving for k, x, m, or η.
- Click Calculate to see results.
- Use the CSV or PDF buttons to export.
Elastic potential energy to kinetic energy
Springs store energy when stretched or compressed, and that energy can drive motion when released. This calculator models that transfer with a linear spring assumption and an efficiency factor for losses. Use it to compare setups, plan experiments, and sanity-check speeds. It also helps students connect measurements with the underlying energy equations clearly.
1) What you can solve
Choose a solve mode to find speed, kinetic energy, spring constant, displacement, mass, or efficiency. For speed, the tool converts stored spring energy into kinetic energy and then into velocity. For reverse solving, it rearranges the same equations to match your target output.
2) Inputs and units
Enter stiffness k, displacement x, and mass m with units. Stiffness supports N/m, N/cm, N/mm, and lbf/in. Length supports m, cm, mm, inches, and feet. Mass supports kg, g, lb, and oz. Energy outputs can be shown in J, kJ, Wh, or ft·lbf.
3) Formula used
Stored energy is E = ½kx². Loss-adjusted kinetic energy is KE = ηE. Speed comes from KE = ½mv², so v = √(2KE/m). Efficiency η ranges from 0 to 1.
4) Working with the example table
Use “Load example inputs” to copy a row into the form. For example 6, k=1500 N/m and x=0.10 m store about 7.50 J. With η=80%, kinetic energy is about 6.00 J, giving roughly 3.46 m/s for 1.0 kg.
5) Understanding efficiency
If measured speed is lower than the ideal prediction, lower η. Friction, damping, impacts, and flexing structures reduce usable energy. To estimate η from a test, select “Efficiency (η)” and enter measured speed with k, x, and m.
6) Sensitivity and safety
Displacement is squared, so small changes in x have a large effect. Doubling x increases energy four times and can raise speed sharply. Higher energy also means higher peak spring forces, so verify hardware limits.
7) Export workflow
After calculating, export CSV for logs or export PDF for sharing and records. Keep unit settings consistent when comparing runs, and write down the efficiency used. For better accuracy, calibrate η once using real speed measurements.
FAQs
1) What is elastic potential energy?
It is energy stored in a stretched or compressed spring. For a linear spring, it is E = ½kx², where k is stiffness and x is displacement.
2) Why include efficiency?
Efficiency models losses to friction, damping, vibration, and sound. Set 100% for an ideal estimate, or lower it to match real behavior.
3) Can this handle nonlinear springs?
This tool assumes linear behavior. If stiffness changes with displacement, results can differ. Use a measured “effective k” near your operating range or validate with tests.
4) Does it include gravity or height change?
No. It converts spring energy into motion only. If the mass rises or falls, account for gravitational potential energy separately or adjust efficiency using measured data.
5) What if my object also spins?
Some energy becomes rotational kinetic energy, reducing translational speed. Treat that as a loss by lowering efficiency, or compute rotation separately if inertia is known.
6) How do I validate my setup?
Measure speed with a sensor or video timing, then use “Solve for efficiency” to estimate η. Reuse that η for similar runs with the same mechanism and contact conditions.