Slider block A moves to the left with a constant velocity of #6m/s#. Determine?

Made from my PC

A) velocity of block B
B) the velocity of point C with respect to point D?

1 Answer
Mar 7, 2018

See below.

Explanation:

Calling the pulleys from left to right 1,2,3 we have

#L = (x_1-x_A) + (y_1-y_2)+(y_3-y_2)+(y_3-y_2)#

where

#(x_1-x_A),(y_1-y_2),(y_3-y_2)# are rope segments composing #L#

Now

#dot L = 0 = (0-dot x_A)+(0- dot y_2)+(0-dot y_2)+(0- dot y_2)#

or

#dot x_A +3 dot y_2 = 0# and finally

#dot y_2 = - dot x_A/3 = -6/3 = -2# [m/s]

NOTE

According to the suggested numbering,

#x_1= y_1# pulley #1# center,
#y_2# pulley #2# center,
#y_3# pulley #3# center.

#x_1=y_1# and #y_3# are fixed and #y_2# moves

The same technique was used in

https://socratic.org/questions/find-the-reading-of-the-spring-balance-shown-in-fig-the-elevator-is-going-up-wit

Item B) is left as an exercise using the same technique.