- #31
- 42,822
- 10,503
So what equation do you get by carrying out the differentiation in post #16?Adesh said:
What's my mistake in this problem in dynamics involving pulleys?
- Thread starter Adesh
- Start date
Click For Summary
Homework Help Overview
The discussion revolves around a dynamics problem involving pulleys and two blocks, A and B. The original poster seeks to determine the accelerations of both blocks, given the gravitational force acting on block B and the assumption that the masses of the pulleys and strings are negligible. The poster initially calculates the accelerations but finds them to be incorrect, prompting a request for clarification on the mistakes made in their reasoning.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants discuss the forces acting on each block, particularly the gravitational force on block B and the tension in the strings. There is an exploration of how to set up force equations for both blocks and the implications of the tension being distributed across the strings. Some participants question the assumption that the tension is simply half of the gravitational force on block B.
Discussion Status
Participants are actively engaging with the problem, offering insights into the relationships between the blocks' accelerations and the constraints imposed by the lengths of the strings. There is a recognition that the blocks do not share the same acceleration, and some guidance has been provided regarding the use of constraint equations and the significance of the second derivatives of the lengths of the strings.
Contextual Notes
There is an ongoing discussion about the correct interpretation of the forces and accelerations involved, with some participants suggesting that the original poster's calculations may be based on incorrect assumptions about the system's dynamics. The conversation includes references to the need for a deeper understanding of the relationships between the blocks and the constraints of the system.
- #32
Lnewqban
Homework Helper
Gold Member
- 4,145
- 2,356
Another way to look at this problem:Adesh said:
A moveable pulley can be considered as a second class lever with mechanical advantage of 2.
- #33
Adesh
- 735
- 191
Acceleration of the blocks.haruspex said:
- #34
Adesh
- 735
- 191
But there is something that is troubling me, ##(-l_1, 0)## is the current position of the block A and ##(0, -l_2)## is the current position of block B, but acceleration is not the second derivative of fixed positions (because in that case it will always come out to be zero). We should say, that at ##t=0## the positions of the blocks were so and so.haruspex said:
- #35
- 42,822
- 10,503
You did not define l1 etc. as merely initial positions. Why should they not mean positions at time t, i.e. define l1 = l1(t) etc.Adesh said:
Also, you don't need to use vector representations. Just define each displacement in the direction that suits it.
- #36
Adesh
- 735
- 191
Yes, this advice and way of solving it is helping me very much. Now, I’m able to solve almost all problems of pulleys and strings, credit goes to you.haruspex said:
I think these pulleys and strings problems are archetypical, textbooks on Newtonian Mechanics (like French’s Mechanics, Univeristy Physics) don’t actaully teach it exclusively.
Now, I’m into elevator problems
.