Question

Collars $A$ and $B$ slide along the fixed right angled rods and are connected by a cord of length $L$. Determine the acceleration $a_{\times }$ of collar $B$ as a function of $y$ if collage $A$ is given a constant upward velocity $V_A$

Answer 1

$x^2+y^2=l^2$

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$ $v_x\times x=-v_y\times y$

$x{v}_x+y{v}_y=0$

$x^{{}^{\prime }}{v}_x+x{a}_x+y^{{}^{\prime }}{v}_y+y{a}_y=0$

$v{x}^2+a_{x}x+v_y^2+a_{y}y=0$

$a_x=\frac{-(v_x^2+v_y^2)-a_y.y}{x}$

because $A$ is given constant upward velocity $v_y=const$

$\therefore a_y=0$

$a_x=\frac{-v_A^2{L}^2}{x^3}$