---
title: "Accelerating Wedge & Sliding Block Interactive Lab | Sandbox Physics"
description: "Can a frictionless normal force transfer energy? Yes."
canonical_url: "https://sandboxphysics.com/labs/accelerating-wedge/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/accelerating-wedge/"
last_modified: "2026-10-28"
---

M016 · Newtonian contact mechanics

# Accelerating Wedge & Sliding Block

**Can a frictionless normal force transfer energy?** Yes. In the ground frame, a freely recoiling wedge gains the energy that the normal force removes from the block. A horizontal drive can reverse this transfer. In the wedge frame, the normal force does no work on the relative slide; the energy balance includes inertial-force work.

Release or horizontally drive a frictionless wedge. Compare ground and wedge observers at the same instant, with consistent force arrows, inertial forces, kinetic energies and work.

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

Model assumptions

Both bodies are rigid. The floor and the wedge face are frictionless, and the wedge stays level. The wedge starts at rest. The run ends at a face endpoint, six model seconds or two metres of wedge travel, whichever comes first; subsequent motion, impact or detachment is outside the displayed window. The supports and block sizes are schematic.

Physics tutorial

## The same contact transfers energy differently in different frames

**Background** A freely moving wedge recoils as the block slides down. On the ground, the normal force can transfer energy between them; riding with the wedge changes the displacement used to calculate that work.

**Why it matters** Watch one motion from the ground and from the moving base. OpenStax 5.7 and 9.3 provide the force and momentum principles; MIT Engineering Dynamics lecture 8 explains inertial forces in accelerating observers.

Start with the essentials

- **Focus question**: Why does normal-force work change when the observer rides with the wedge?
- **One-sentence intuition**: The normal is perpendicular to the slide relative to the face. Its ground-frame work can be nonzero because the face moves too; the accelerating frame needs inertial-force work in its energy balance.

### Core mathematical model

#### Two coordinates describe the motion

$$
\begin{aligned}x_b&=X+(s-\ell/2)\cos\theta\\y_b&=(\ell-s)\sin\theta\end{aligned}
$$

The wedge moves horizontally; the block coordinate increases downhill along its face. The drawn body has a fixed schematic normal offset, which changes no acceleration or energy difference.

#### Coupled equations of motion

$$
\begin{aligned}(M+m)\ddot X+m\cos\theta\,\ddot s&=H\\\ddot s+\cos\theta\,\ddot X&=g\sin\theta\end{aligned}
$$

The horizontal drive acts on the wedge. The floor and face are frictionless, and the assembly has no rotational degree of freedom.

#### Recoil and contact force

$$
\begin{aligned}\ddot X&=\frac{H-mg\sin\theta\cos\theta}{M+m\sin^2\theta}\\N&=m(g\cos\theta+\ddot X\sin\theta)\end{aligned}
$$

A free wedge accelerates left. A suitable rightward drive can reverse the recoil or make the block slide uphill relative to the wedge. Contact remains compressive over the available ranges.

#### Momentum and energy in the ground frame

$$
\begin{aligned}p_x&=(M+m)\dot X+m\dot s\cos\theta\\\dot p_x&=H\\\Delta(K_b+K_w+U)&=H\Delta X\end{aligned}
$$

With no horizontal drive, total horizontal momentum and mechanical energy stay constant. Each kinetic energy uses the full ground-frame velocity.

#### Contact work on the two bodies

$$
\begin{aligned}W_{N,b}&=N\sin\theta\,\Delta X\\W_{N,w}&=-W_{N,b}\end{aligned}
$$

During free recoil, the block loses energy through contact and the wedge gains it. A drive can reverse the transfer; the two contact-work contributions still cancel.

#### Riding with the accelerating wedge

$$
\begin{aligned}\mathbf a_b^{\prime}&=\mathbf a_b-\ddot X\hat{\mathbf x}\\\mathbf F_{\mathrm{in},b}&=-m\ddot X\hat{\mathbf x}\\\Delta(K_b^{\prime}+U)&=W_{\mathrm{in},b}\end{aligned}
$$

This observer translates without rotating. Normal-force work on the relative slide is zero; the inertial force accounts for the relative energy balance. Switching observers preserves the same physical trial and current time.

### Common difficulties

#### The base motion changes the slide

**Typical misconception** The fixed-incline acceleration applies to every wedge.

**Better mental model** A moving base accelerates the face. Compare Free wedge with Heavy base; the recoil and relative slide both change.

#### Work depends on the observer

**Typical misconception** A normal force can never transfer energy.

**Better mental model** Look at normal work in the ground frame, then switch to the wedge frame. The relative slide is perpendicular to the normal, while the ground displacement includes base motion.

#### Inertial forces belong to an accelerating description

**Typical misconception** The violet arrow is another physical contact.

**Better mental model** Violet dashed arrows appear in the wedge frame. They account for the observer acceleration; the teal contact forces are the same physical interaction in either view.

### Run the experiment

1. 01

   #### Release both bodies

   Watch the Free wedge preset.

   **What to observe:** The base recoils left as the block slides down. Ground-frame normal work on the block is negative.

2. 02

   #### Ride with the wedge

   Pause, then choose Wedge frame.

   **What to observe:** The base stays still and the ground datum moves. Violet inertial forces appear, and normal work on the block becomes zero.

3. 03

   #### Keep the same instant

   Switch between the two observers.

   **What to observe:** The trial and time are preserved. The selected-frame speed, work and kinetic energies change together.

4. 04

   #### Drive the block uphill

   Choose Driven uphill and inspect the relative velocity.

   **What to observe:** The rightward acceleration of the support drives relative uphill motion. External work and impulse account for the ground-frame balance.

5. 05

   #### Keep the block at one place on the face

   Choose Ride with the wedge.

   **What to observe:** Both bodies accelerate horizontally while their relative position stays fixed.

6. 06

   #### Catch a relative turning point

   Choose Uphill release. Open Work, constraints and diagnostics and press Exact zero speed, then Step 1 ms.

   **What to observe:** The relative velocity reaches zero and changes sign. The block starts sliding down the face again.

Physical conclusion

Choose an observer before comparing acceleration, kinetic energy or work. The physical contact is the same in both views.

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)