Dynamics -- Velocity of a Block in a system of Pulleys

Click For Summary
The discussion focuses on solving a physics problem involving the velocity of block C in a system of pulleys, with given relative accelerations for blocks C and D. The user expresses frustration over deriving the correct equations to find the velocity after 6 seconds, specifically struggling with the relationship between the lengths of the cables and the accelerations of the blocks. They initially attempt to establish a cable length equation but are uncertain about how to apply it to find block B's acceleration. The user seeks assistance in simplifying the problem, believing it may be easier than it appears. Clarification on the relationship between the blocks and their accelerations is needed to progress.
UsernameNotFound
Messages
1
Reaction score
0
Hey guys, I have been a long time lurker here but this problem has eluded me for a few hours now and my frustration at not being able to figure out what it is I am missing prompted me to finally pull the trigger on making an account here. I hope the way I wrote everything out is clear to understand but if it is not I would be happy to do my best to elaborate further. Thank you!

1. Homework Statement

The system shown starts from rest and each component moves with a constant acceleration. The relative acceleration of block C with respect to collar B is 60mm/s^2 upward and the relative acceleration of block D with respect to block A is 110mm/s^2 downward. Determine the velocity of block C after 6s.
13252705286065231206.tp4?REQUEST=SHOWmedia&conId=13252704214052800&media=59-a.jpg


2. Homework Equations
Relative Acceleration: ac = ac/b + ab
v = v0 + a*t


The Attempt at a Solution


My first thought to solve this problem involved deriving an equation for the length of the cable that connects blocks A B and C that I could differentiate twice to get an acceleration equation and an equation for the length of the cable that connects blocks A B and D to do the same with. For the length of cable 1 I got 2SA + 2SB + SC = Constant taking my reference point to be the line that goes through the center of the 3 top pulleys. For the other cable I wasn't 100% certain what it should be though for what the question is asking I don't believe it is necessary to know. I can't seem to find any way to utilize this equation for the length of the cable to give me an acceleration for block B that I can use combined with the relative velocity equation to give me the acceleration for block C that I can use with the kinematic equation to find the velocity. My next thoughts for this problem was to find some way to use the given relative acceleration to simply obtain accelerations for the blocks directly however if this is possible then despite my best efforts I haven't found a way to do so. Any help at solving this would be GREATLY appreciated. I feel like it is easier than I am making it out to be which makes it all the more frustrating that I cannot solve it.[/B]
 
Physics news on Phys.org
Let ##\delta_A##, ##\delta_B##, and ##\delta_D## be the downward displacements of A, B, and D respectively. In order for the bottom string to remain constant in length, $$(\delta_D-\delta_A)+(\delta_D-\delta_B)=0$$
 

Similar threads

  • · Replies 12 ·
Replies
12
Views
2K
Replies
3
Views
501
  • · Replies 8 ·
Replies
8
Views
5K
  • · Replies 11 ·
Replies
11
Views
2K
Replies
15
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
4
Views
796
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K