All Problems The Fundamental Equation of Dynamics
Problem 1.102
A small bar starts sliding down an inclined plane forming an angle \(\alpha\) with the horizontal. The friction coefficient depends on the distance \(x\) covered as \(k=a x,\) where \(a\) is a constant. Find the distance covered by the bar till it stops, and its maximum velocity over this distance.
\[ \text { 1.102. } s=\frac{2}{a} \tan \alpha, \quad v_{\max }=\sqrt{\frac{g}{a} \sin \alpha \tan \alpha} \text { . } \] Instruction. To reduce the equation to the form which is convenient to integrate, the acceleration must be represented as \(d v / d t\) and then a change of variables made according to the formula \(d t=d x / v\).