Question

The rod of the fixed hydraulic cylinder is moving to the left with a constant speed vA = 25 mm/s. Determine the corresponding velocity of slider B when sA = 425 mm. The length of the cord is 1050 mm, and the effects of the radius of the small pulley A may be neglected.

Answer 1

Explanation:

let vertical distance from A to C be  $h=250mm$ the constraint equation is:

$l_{ac} +l_{ab} =L$

we want to find $l_{bc}$ distance can be written as $l_{bc} =h_{1}+h_{2}$ which we will find by using Pythagorean theorem h 1 is a constant and can be written as h:

$h_{2} =\sqrt{l_{ab}^2- s_{A} ^2}$

$l_{ac} =\sqrt{s_{A}^2+ h^2 }$

$l_{ab} =L-\sqrt{s_{A} ^2+h^2 }$

taking derivative w.r.t time we get

$h^._{2} =-v_{B =(l_{ab} l_{ab} ^.-s_{A} v_{A} )/h_{2}$

$l_{ab} ^.=(s_{A} v_{A} )/l_{ab} -L$

given $s_{A} =425mm$ which gives us

$l_{ab} =1050-\sqrt{450^2+250^2} =556.923mm\\\\h_{2} =\sqrt{556.923^2-425^2}=359.914mm$

$l_{ab} ^.=(425.25)/(556.923-1050)=-21.548mm\\\\-v_{B} =(-556.923*21.548-425.25)/(359.914)\\\\v_{B} =62.864mm/s$