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Final Velocity of a Rough Block on a Fixed Wedge Calculator

Final Velocity of a Rough Block on a Fixed Wedge Calculator

Final Velocity of a Rough Block on a Fixed Wedge Calculator

Calculate the final velocity of a rough block sliding down a fixed wedge using energy conservation:
\[ v = \sqrt{\frac{2gh\,(1 – \mu_k\,\cot\theta)}{}} \] where \(h\) is the height, \(\theta\) is the wedge angle, \(\mu_k\) is the coefficient of kinetic friction, and \(g\) is the gravitational acceleration.

* Ensure that \(\mu_k < \tan\theta\) so the block can slide.

Step 1: Enter Parameters

Example: 5 m

Example: 30°

Example: 0.2

Example: 9.81 m/s²

Formula: \( v = \sqrt{\frac{2gh\,(1 – \mu_k\,\cot\theta)}{}} \)


Practical Example:
For a height of 5 m, a wedge angle of 30°, a coefficient of kinetic friction of 0.2, and \( g = 9.81 \) m/s²:
First, compute \(\cot 30° = \frac{\cos30°}{\sin30°} \approx \frac{0.866}{0.5} \approx 1.732\).
Then, \(1 – 0.2 \times 1.732 \approx 1 – 0.3464 = 0.6536\).
Finally, \[ v = \sqrt{\frac{2 \times 9.81 \times 5 \times 0.6536}{}} \approx \sqrt{64.16} \approx 8.01\, \text{m/s}. \]

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