---
title: "Spring Launcher Interactive Lab | Sandbox Physics"
description: "Will the ball actually leave the spring? Only if the spring is squeezed far enough."
canonical_url: "https://sandboxphysics.com/labs/spring-launcher/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/spring-launcher/"
last_modified: "2026-10-27"
---

M048 · Stored energy takes flight

# Spring Launcher

**Will the ball actually leave the spring?** Only if the spring is squeezed far enough. While the spring pushes, the ball is already rising, so gravity takes part of the stored energy before flight begins. The ball flies off only if the compression is more than twice the sag the ball's weight alone would cause; below that, it just rides up and down with the spring.

Compress a spring, release a ball and follow its energy into flight. Find the smallest compression that launches the ball, compare different gravity and work out the spring stiffness from recorded apex heights.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

The spring can only push, and both the spring stroke and the flight are solved exactly. Air resistance and the mass of the spring are ignored.

Physics tutorial

## Spring Launcher

**Background** A unilateral spring can push a ball but cannot pull it.

**Why it matters** Predict from the compression whether the ball will fly and how high, then test where launching begins.

Start with the essentials

- **Focus question**: Will the ball actually leave the spring?
- **One-sentence intuition**: Gravity takes energy during the spring stroke before flight even begins.

### Core mathematical model

#### Contact and flight

$$
m\ddot q=-k\min(q,0)-mg
$$

The coordinate is measured from the tip of the relaxed spring, and the spring never pulls.

#### Flight threshold

$$
c>\frac{2mg}{k}
$$

The ball leaves with a positive speed only if the compression exceeds twice the sag of the spring holding the ball at rest.

#### Apex above the floor

$$
H_{\max}=L-c+\frac{kc^2}{2mg}
$$

This holds only if the ball leaves the spring. Height is measured from the floor to the bottom of the ball.

#### Stiffness from recorded heights

$$
\widehat k=\frac{2mg}{c^2}(\overline H_{\rm peak}-L+c)
$$

This ideal estimate uses only recorded peaks above the relaxed spring tip.

### Common difficulties

#### Not every compression launches

**Typical misconception** Any compression guarantees flight.

**Better mental model** Compare the weak-spring preset with the launch threshold. Below the threshold the ball never leaves the spring.

### Run the experiment

1. 01

   #### Set the height

   Drag the gold handle or use its keyboard slider.

   **What to observe:** The scene and predicted motion update together.

2. 02

   #### Follow the event

   Play, pause and jump to the next event.

   **What to observe:** Height changes smoothly, but an impact can change the velocity instantly.

3. 03

   #### Track the energy

   Drag the time between turning points.

   **What to observe:** Stored, kinetic, gravitational and transferred energy always add up to the same total.

4. 04

   #### Measure a run

   Record apex heights, export the CSV and compare the inferred parameter.

   **What to observe:** Replaying preserves the same measurements; changing physical parameters clears them.

Physical conclusion

Not every spring release becomes a launch.

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)