Student handout: Box Sliding Down Frictionless Wedge

Theoretical Mechanics 2020
Students solve for the equations of motion of a box sliding down (frictionlessly) a wedge, which itself slides on a horizontal surface, in order to answer the question "how much time does it take for the box to slide a distance \(d\) down the wedge?". This activities highlights finding kinetic energies when the coordinate system is not orthonormal and checking special cases, functional behavior, and dimensions.
What students learn
  • Lagrangian mechanics will work with non-orthonormal coordinate systems
  • To use the dot product to find speed squared for the kinetic energy
  • To make sense of their answer by checking dimensions, functional behavior, and special cases

Block Sliding Down a Frictionless Wedge

(Taylor Example 7.5) Consider a block with mass \(m\) sliding frictionlessly down an wedge with mass \(M\) that makes an angle \(\alpha\). The wedge itself slides frictionlessly across a horizontal floor near the surface of Earth. The block is released from the top of the wedge, with both objects initially at rest.

If length of the sloping face is \(d\), how long does the block take to reach the bottom?


Keywords
Lagrangian Mechanics Generalized Coordinates Special Cases
Learning Outcomes