---
title: "Crash Pulse & Impulse Engineering Interactive Lab | Sandbox Physics"
description: "If the same impulse stops an object, why does it matter when the force acts?"
canonical_url: "https://sandboxphysics.com/labs/crash-pulse/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/crash-pulse/"
last_modified: "2026-10-27"
---

M037 · Stopping dynamics

# Crash Pulse & Impulse Engineering

**If the same impulse stops an object, why does it matter when the force acts?** Because the impulse fixes how much speed is lost, not how far the object travels while losing it. Late force acts while the object is still fast, so it needs more distance. For a given distance, the lowest peak comes from a force that rises at once and then stays flat. If the absorber runs out of room first, the object hits the end still moving, and that kinetic energy is not absorbed.

Shape the force pulse that stops a moving mass, compare the peak force with the stroke it needs, then record force and speed to check the impulse and work. If the absorber runs out of stroke, the mass keeps the kinetic energy that was not absorbed.

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

The dynamics are idealized and the sensors are simulated. The Lab states its stopping conditions and the limits of its approximations explicitly.

Physics tutorial

## Pulse timing and finite stroke

**Background** To stop something, you have to change its momentum and give its kinetic energy somewhere to go.

**Why it matters** The timing of the force, the distance the apparatus travels and the separately integrated sensor data should all tell the same story.

Start with the essentials

- **Focus question**: Can the absorber finish its pulse?
- **One-sentence intuition**: The impulse fixes how much the speed changes, but when the force acts still changes how far the mass travels.

### Core mathematical model

#### Impulse sets the area under the force curve

$$
B(t)=\frac{mv_0}{T}f(t/T),\qquad\int_0^1f(u)\,du=1
$$

A nonnegative pulse shape with unit area delivers exactly the impulse needed to stop. It is a prescribed force history, not a constitutive law for any material.

#### Speed and travel follow the accumulated impulse

$$
\begin{aligned}C(u)&=\int_0^uf(q)\,dq\\v(t)&=v_0[1-C(u)]\\x(t)&=v_0T\int_0^u[1-C(q)]\,dq\end{aligned}
$$

The apparatus drawing, the speed and the stroke all come from the same accumulated pulse.

#### When the force acts changes the travel

$$
x_{\mathrm{stop}}=v_0T\int_0^1u f(u)\,du
$$

The travel depends on the centroid of the force in time. For a triangular pulse that peaks at some fraction of its duration, the centroid lies at one third of one plus that fraction.

#### Absorbed energy and remaining motion

$$
W_B(t)=\int_0^tB(\tau)v(\tau)\,d\tau=\frac{m}{2}[v_0^2-v(t)^2]
$$

When the stroke runs out, the actual pulse is cut short, and the energy left over stays as kinetic energy. No hard stop is added to soak it up.

#### Estimate from sensor data

$$
\begin{aligned}J_{\mathrm{raw}}&\approx-\sum_i\frac{B_i+B_{i+1}}2\Delta t_i\\W_{\mathrm{raw}}&\approx-\sum_i\frac{B_i v_i+B_{i+1}v_{i+1}}2\Delta t_i\end{aligned}
$$

The estimate uses only the raw time, force and speed plus the calibrated mass. Coarse sampling and noise can keep the impulse and work from matching the change in motion.

### Common difficulties

#### An ideal model is not a safety rating

**Typical misconception** If the ideal model stops in time, a real cushion or road distance must be safe.

**Better mental model** This is a teaching model with prescribed force laws and simulated sensors. Real materials, tyres and differences between drivers have to be checked against measurements.

### Run the experiment

1. 01

   #### Compare pulse shapes

   Switch between constant force, half sine and triangular peaks. Keep mass, speed and duration fixed.

   **What to observe:** The same total impulse can come with different peak forces.

2. 02

   #### Move the peak

   Compare the early and late triangular presets. Drag the gold vehicle to replay the motion.

   **What to observe:** Both complete pulses stop the mass, but the one with the later peak needs more travel.

3. 03

   #### Run out of stroke

   Select Stroke exhausted, drag the vehicle to its endpoint, and open Sensors and diagnostics for the remaining kinetic energy.

   **What to observe:** The recorded data end while the mass is still moving. The dashed design curve continues only as a reference.

4. 04

   #### Check the record

   Open Sensors and diagnostics to acquire, clear or export raw sensors; sensor rate and noise are in Vehicle and numerical settings.

   **What to observe:** Whether the raw integrals balance shows the cost of finite sensor resolution.

Physical conclusion

You can only say something stopped if there was enough stroke or braking to do it and the speed actually reached zero.

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)