---
title: "Inclined Plane & Friction Interactive Lab | Sandbox Physics"
description: "At zero speed, will the block stick or reverse? It sticks if static friction can hold it."
canonical_url: "https://sandboxphysics.com/labs/inclined-plane/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/inclined-plane/"
last_modified: "2026-10-28"
---

M012 · Newtonian contact mechanics

# Inclined Plane & Friction

**At zero speed, will the block stick or reverse?** It sticks if static friction can hold it. At the moment it stops, work out the friction needed to balance gravity along the slope and any applied force. If that is within the static limit, the block stays put; if not, it slides off in the direction of the net force.

Drag a block on a rough incline, change the two friction coefficients and apply an uphill or downhill force. Compare stopping, sticking and reversal with the release-from-rest map and the energy dissipated along the path.

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

Model assumptions

Friction follows the ideal Coulomb law with constant coefficients, and the incline is rigid and fixed. The kinetic coefficient is constrained not to exceed the static coefficient. The track is finite, and the record ends before the block hits anything. Temperature, deformation and speed-dependent friction are left out.

Physics tutorial

## Friction changes its rule when the block stops

**Background** The block slides downhill while friction points uphill. Launch it uphill, and friction turns downhill; when it stops, the next motion depends on how much static friction is available.

**Why it matters** Compare a block that stops and stays with one that turns back. OpenStax University Physics 6.2 explains the static-friction inequality and the sliding-friction law behind this difference.

Start with the essentials

- **Focus question**: At zero speed, will the block stay or reverse?
- **One-sentence intuition**: Stopping gives static friction a chance to hold. The block stays only when the force it needs is within the static limit.

### Core mathematical model

#### Gravity and the applied force

$$
N=mg\cos\theta,\qquad D=mg\sin\theta+F
$$

Distance and force are positive downhill. The applied force acts along the face, so it adds no normal loading.

#### The force needed to remain at rest

$$
f_s=-D,\qquad |D|\le\mu_sN
$$

Static friction adjusts to hold the block at rest, up to its maximum. The margin subtracts the required holding force from the largest static friction; equality is included in the ideal sticking condition.

#### Sliding friction

$$
\begin{aligned}m\ddot s&=D-\mu_kN\operatorname{sgn}(\dot s)\\0&\le\mu_k\le\mu_s\end{aligned}
$$

The first coefficient slider sets static friction, and the second sets kinetic friction. Lowering the static coefficient below the kinetic value lowers the kinetic value to match; this keeps the stated coefficient ordering valid. At zero speed, the static condition is checked again.

#### Motion between stops and endpoints

$$
\begin{aligned}s&=s_a+v_a(t-t_a)+\tfrac12a(t-t_a)^2\\v&=v_a+a(t-t_a)\end{aligned}
$$

Forces are constant within each segment. The first track-end or future zero-velocity event changes what happens next. The track endpoint is shown before a collision, detachment or tipping is modeled.

#### Energy loss follows the full path

$$
\Delta K+\Delta U=F(s-s_0)-\mu_kN\int_0^t|\dot s|\,\mathrm dt
$$

Friction dissipates energy on both sides of a reversal. The energy-loss plot therefore uses travelled distance, not the net displacement. Temperature, deformation and velocity-dependent coefficients are outside this Coulomb model.

### Common difficulties

#### Static friction can be below its maximum

**Typical misconception** Static friction always equals its maximum value.

**Better mental model** Choose Static hold. The actual friction balances gravity and the applied force along the face. Its maximum is larger.

#### A stop can be a turning point

**Typical misconception** Zero speed means the block will stay there.

**Better mental model** Compare Stop and stick with Stop and reverse at their zero-speed event. Only the first can be held by static friction.

#### The green region predicts release from rest

**Typical misconception** A moving block must stop as soon as its settings lie in the rest region.

**Better mental model** The map asks what happens when released with zero relative velocity. An already sliding block can keep moving inside that region.

### Run the experiment

1. 01

   #### Watch the default slide

   Watch the block, its amber friction arrow and the growing energy-loss curve.

   **What to observe:** Friction points uphill while the block moves downhill.

2. 02

   #### Let static friction hold it

   Choose Static hold.

   **What to observe:** The friction arrow balances the force pulling downhill, and the block remains still.

3. 03

   #### Compare two stops

   Choose Stop and stick, then Stop and reverse. Open Work, constraints and diagnostics and press Exact zero speed.

   **What to observe:** Both reach zero velocity. One stays, and the other begins sliding downhill.

4. 04

   #### Pull uphill

   Choose Pull uphill.

   **What to observe:** A sufficiently strong uphill force changes the direction of motion and the friction arrow.

5. 05

   #### Read the release map

   Change the slope or applied force and follow the marker in the release-from-rest map.

   **What to observe:** The marker crosses between uphill, possible-rest and downhill regions. A nonzero initial velocity is a separate condition.

6. 06

   #### Reset and place the block

   Press Reset, then drag the block along the face or use the Release slider in the folded group.

   **What to observe:** A new trial begins from the chosen release coordinate. Replay repeats the current trial.

Physical conclusion

At rest, compare the required holding force with the largest static friction. During sliding, use the direction of relative motion and count the full distance travelled when calculating energy loss.

Starter path · Step 3 of 6

## From a falling ball to an orbit

[Next step → **One-Dimensional Collision Bench** Move the restitution from elastic to sticking and check which quantity survives the collision: momentum or kinetic energy. Model · 20 min](https://sandboxphysics.com/labs/collision-bench/)

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)