fbpx

If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed at which block B rises.

Step-by-step

Position-Coordinate Equation: Datum is established at fixed pulley D. The
position of point A, block B and pulley C with respect to datum are {s}_{A} , {s}_{B} , and {s}_{C} respectively. Since the system consists of two cords, two position-coordinate
equations can be derived.

({s}_{A}{s}_{C}) + ({s}_{B}{s}_{C}) + {s}_{B} ={l}_{1}

{s}_{B}{s}_{C} = {l}_{2}

{s}_{A} + 4{s}_{B}  = {l}_{1} = 2{l}_{2}

Time Derivative: Taking the time derivative of the above equation yields

{v}_{A} + 4{v}_{B} = 0

since  {v}_{A} = 2 m/s

(+\downarrow )                           2 + 4{v}_{B} = 0

{v}_{B} = -0.5 m/s = 0.5 m/s \uparrow

Trending

Online
Courses

Private
Teachers

Hire Our
Professionals

Study
Materials

Writing & Translation

View All
Services