Final Velocity of a Block on a Movable Wedge Calculator

Final Velocity of a Block on a Movable Wedge Calculator

Calculate the final velocity of a smooth block sliding down a movable frictionless wedge.
The derived formula is:
\[ v = \sqrt{\frac{2gh\,(m+M)}{(m+M)\sin^2\theta+M\cos^2\theta}}\,\sqrt{\sin^2\theta+\left(\frac{M}{m+M}\cos\theta\right)^2} \]

* Enter mass of the block \(m\) (kg), mass of the wedge \(M\) (kg), drop height \(h\) (m), wedge angle \( \theta \) (°), and gravitational acceleration \(g\) (m/s²).

Step 1: Enter Parameters

Example: 2 kg

Example: 10 kg

Example: 1 m

Example: 30°

Example: 9.81 m/s²

Derived Formula: \[ v = \sqrt{\frac{2gh\,(m+M)}{(m+M)\sin^2\theta+M\cos^2\theta}} \sqrt{\sin^2\theta+\left(\frac{M}{m+M}\cos\theta\right)^2} \]


Practical Example:
For a block of mass 2 kg, a wedge of mass 10 kg, dropped from a height of 1 m on a wedge of 30° and \( g=9.81 \) m/s², the final speed of the block (relative to the ground) is computed by the calculator.