Treating Cables with Pulleys & Blocks - Leonel

[leonel]

Can any of you help me in how to treat the cables in the arrangement pulleys and blocks attached ?.

thanks, Leonel

 

[Chen]

Is cable E fixed to the ground on one end, by that little parallelogram block?

 

[HallsofIvy]

Assuming that the cable is of fixed length and fastened at its end, then the length of the cable, E, is the distance from that fixed point to block B and so its length is increasing at 18 in/sec just like the blocks motion. Also, it is clear that, since the two pulleys can be taken to be right up against blocks A and B, C and D are of equal length at all times and so have the same rate of change.
Specifically, C+ D+ E= fixed length so dC/dt+ dD/dt+ dE/dt= 0. dC/dt= dD/dt and
dE/dt= 18: 2dC/dt= -18 or dC/dt= dD/dt= -9 in/sec.

Since the distance between blocks A and B are decreasing in length by 9 in/sec, A's speed relative to B is 9 in/ sec: yes, A's speed relative to the stationary base is 27 in/second.

 

[leonel]

That's correct, Chen !

 

[leonel]

HalsofIvy, thanks a lot for your response ! My thoughts have been the same of yours..

But, the problem is that the book responses are: cable D Velocity is assumed to be + 36 in/s while the Vcd is - 18 in/s. therefore, that makes Vc = + 18 in/s. What results in a complete difference...Maybe some typing problems (2 mistakes ??!) in the book "Vector Mechanics for engineers" Beer and Johnston" fifth ed. Ex.11.42.