Sliding Block on a Movable Wedge — Solution Using Lagrangian Mechanics

Rhett Allain
10 min readJan 10, 2021
Photo: Rhett Allain. A block sliding down a movable wedge.

I’m working through some examples of physics problems that use Lagrangian Mechanics. Oh, what’s that? You aren’t sure about this whole Lagrangian thing? Well, here you go — my introduction to this physics method. Also, here is a more basic example finding the motion of a half-Atwood machine.

The Moving Wedge Problem

OK, so here is the problem:

A 100 gram block starts from rest on top of a frictionless wedge. The wedge can also slide. It has a mass of 431 grams (see how I used an unexpected value) with an incline of 34 degrees. The distance from the block down the incline is 14 cm. Find the equation of motion for the two objects once the block is released.

Although this is a pretty nice example to use Lagrangian mechanics — you can actually find the final speed of both objects by using the Momentum Principle and the Work-Energy Principle. But that’s not as much fun as using the Lagrangian.

Let’s start with a diagram, that’s usually a great place to begin.

Degrees of Freedom and Generalized Coordinates



Rhett Allain

Physics faculty, science blogger of all things geek. Technical Consultant for CBS MacGyver and MythBusters. WIRED blogger.