- #31
- 42,794
- 10,493
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
SUMMARY
The discussion focuses on solving a dynamics problem involving two blocks (A and B) connected by pulleys and strings, with the mass of the pulleys and strings considered negligible. The initial incorrect calculations for the accelerations of blocks A and B were identified, with the correct values being acceleration of block A = 10/13 g (forward) and acceleration of block B = 5/13 g (downward). Key mistakes included misunderstanding the tension in the strings and the relationship between the blocks' accelerations, which required the application of constraint motion equations.
PREREQUISITES- Understanding of Newton's Second Law (F=ma)
- Knowledge of tension forces in pulley systems
- Familiarity with constraint motion equations
- Basic principles of kinematics
- Study the derivation of constraint motion equations in pulley systems.
- Learn how to apply Newton's Second Law to multiple connected bodies.
- Explore the concept of mechanical advantage in pulley systems.
- Investigate the relationship between acceleration and position in dynamic systems.
Students and educators in physics, particularly those focusing on mechanics, as well as engineers and anyone involved in solving dynamics problems related to pulleys and connected systems.
- #32
Lnewqban
Homework Helper
Gold Member
- 4,138
- 2,350
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
- 42,794
- 10,493
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
.