---
title: "Stacked Blocks & Friction Interactive Lab | Sandbox Physics"
description: "When you push one of two stacked blocks, which contact slips first? Test the friction needed at each contact against its static limit."
canonical_url: "https://sandboxphysics.com/labs/stacked-blocks/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/stacked-blocks/"
last_modified: "2026-11-05"
---

M015 · Which of two contacts slips first?

# Stacked Blocks & Friction

**When you push one of two stacked blocks, which contact slips first?** Test the friction needed at each contact against its static limit. Where you push matters: inter-block friction can accelerate the other block.

Push either block and find out which contact slips first. Look at one block alone or at the pair: taken together, the friction between the blocks cancels, and the work you put in equals the kinetic energy gained plus the heat lost to friction.

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

Model assumptions

The blocks start at rest and slide along a guide. The run stops before either block overhangs an edge, so tipping and falling are not modeled.

Physics tutorial

## Test the two contacts separately

**Background** The upper block can slip over the lower, and the lower can slip over the floor. Each contact has its own friction limit.

**Why it matters** The friction that holds the upper block can accelerate it forward. Switching which block receives the push changes how much each contact must supply.

Start with the essentials

- **Focus question**: Which contact first leaves rest when the drive increases?
- **One-sentence intuition**: Assume a contact sticks, calculate the friction that assumption needs, then compare it with the static limit. If it slips, use kinetic friction and check the resulting direction of relative motion.

### Core mathematical model

#### Balance each block

$$
\begin{aligned}m_1a_1&=F_1+f_{21},\\ m_2a_2&=F_2-f_{21}+f_0.\end{aligned}
$$

The inter-block friction has opposite signs on the two bodies. Only one body receives the external drive.

#### Two independent static limits

$$
\begin{aligned}|f_{21}|&\leq\mu_{s,1}m_1g,\\ |f_0|&\leq\mu_{s,0}(m_1+m_2)g.\end{aligned}
$$

These inequalities apply when the corresponding contact sticks. Sliding contacts instead use their kinetic coefficient.

#### The first departure from complete rest

$$
\begin{aligned}C_1&=\mu_{s,1}m_1g,\\ C_0&=\mu_{s,0}(m_1+m_2)g,\\ F_{\mathrm{crit,upper}}&=\min(C_1,C_0),\\ F_{\mathrm{crit,lower}}&=C_0.\end{aligned}
$$

These thresholds compare separate releases from rest as the magnitude of the load increases. The subsequent sliding response must be solved again, using kinetic friction where appropriate.

#### Heat follows relative sliding

$$
\begin{aligned}E_{\mathrm{diss}}={}&|f_{21}|\,|\Delta x_1-\Delta x_2|\\ &+|f_0|\,|\Delta x_2|.\end{aligned}
$$

Within each displayed monotone release, a sticking interface has zero relative travel and produces no frictional heat. The two-body work balance still includes the energy passed from one block to the other.

### Common difficulties

#### Moving together still requires friction

**Typical misconception** If the blocks do not slip against each other, their friction must be zero.

**Better mental model** The block you are not pushing needs a horizontal force to accelerate. Static friction can provide that force while its two contact points move together, transferring energy without interfacial heat.

### Run the experiment

1. 01

   #### Watch friction carry a block

   Start with Carried by friction. Select Upper, Lower and Both blocks.

   **What to observe:** Inter-block friction accelerates the upper block and acts oppositely on the lower. It cancels from the combined system's external forces.

2. 02

   #### Try the other block

   Switch to Upper slips, drag that block to change its drive, and vary the two friction coefficients.

   **What to observe:** The upper can slide while the lower stays still, or both contacts can slide. The two contact strips show actual force and the static limit separately.

3. 03

   #### Inspect each rejected assumption

   Open Contact tests, work and energy, then Test all contact assumptions.

   **What to observe:** All nine signed candidates retain their required forces. A row can fail because a static limit is exceeded or because its predicted slip direction contradicts the assumed one.

Physical conclusion

Check both contacts and the direction of slip. Friction can transfer energy between the blocks while producing no heat at a contact that does not slip.

Physical model, approximation limits and sources

Positions are in metres, time in seconds and forces in newtons. Right and up are positive; on a slope, displacement is positive uphill. Ideal guides allow translation and suppress rotation. Contact pressure and tipping are outside this model.

Every control change defines a new release from rest. Surfaces stay stuck when the required friction lies within the static limit. Force comparisons use a tolerance of one billionth of a newton; equality selects sticking. Kinetic coefficients are the corresponding static coefficients multiplied by the chosen ratio.

There are four contact assumptions and nine signed candidates. A static candidate retains the force it would need; a sliding candidate must also predict its assumed direction. The selected response follows the stated sticking preference. Every plotted force value represents a separate release, not a continuously ramped load.

The blocks are 0.8 and 2.4 metres wide. The finite stacked record ends at 0.8 metres of relative travel, 2.4 metres of lower travel or two seconds. It does not continue into partial support, edge departure or collision. The cable winch holds a nonnegative tension while changing length and stops the record after one metre of travel.

Apparatus lengths share one scale. Force vectors are translated to the selected system centre, with one display gain fixed for the full release and every system boundary and capped at 0.03 metres per newton. The separate force diagram has its own common plot scale. CSV contains 101 model samples; residual roundoff is retained. These are simulated values, not measurements or fitted material properties.

- [OpenStax 5.7 — Free-body diagrams](https://openstax.org/books/university-physics-volume-1/pages/5-7-drawing-free-body-diagrams)
- [OpenStax 5.5 — Newton’s third law](https://openstax.org/books/university-physics-volume-1/pages/5-5-newtons-third-law)
- [OpenStax 6.2 — Static and kinetic friction](https://openstax.org/books/university-physics-volume-1/pages/6-2-friction)
- [OpenStax 15.1 — Spring force and simple harmonic motion](https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion)

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)