Question about Absolute Dependent Motion Analysis

In summary: When I wrote the equations, I decided the datums were unchangeable so the depth of masses below top pulley seemed unrelated to me.In summary, the two suspended masses are below the top pulley with different depths. The depth of B below the top pulley is found using yα, which is multiplied by the accelerations of the masses to get the depths below the top pulley.
  • #1
Oklid
19
0

Homework Statement


[/B]
2cy5mht.png


Find accelerations of these masses and the pulley are weightless.

Homework Equations


[/B]
Sb+Sc=Length of the second rope (L2)

The Attempt at a Solution


[/B]
sdpxd1.png


Just like I did, I placed all variables from datum to the masses.

In the second system, I write the equation as Sb+Sc=Length of the second rope (L2)

In the first, I couldn't write the equation with Sa, Sb, Sc. Because I couldn't define (?) with these Sb and Sc.

I could have done some mistakes, sorry.
 

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  • #2
Oklid said:
Because I couldn't define (?) with these Sb and Sc
So define a length for the first rope.
What you need next is to express the heights (or depths) of the two suspended masses in terms of these variables.
 
  • #3
haruspex said:
So define a length for the first rope.
What you need next is to express the heights (or depths) of the two suspended masses in terms of these variables.

But I couldn't define a length with these variables Sc and Sb. Because they are a system their own. If there was a single block named as K instead of the second system and suspended to a with first rope. then first rope would be defined as Sa+Sc=L1.
 
  • #4
Oklid said:
But I couldn't define a length with these variables Sc and Sb.
I am not suggesting you do.
L1 works fine as the length of the first rope. In terms of that and the variables you have, how far below the pulley are the two suspended masses?
 
  • #5
haruspex said:
I am not suggesting you do.
L1 works fine as the length of the first rope. In terms of that and the variables you have, how far below the pulley are the two suspended masses?

I couldn't understand the question, sorry.

L1 works fine but again I can't define the L1 with these variables as Sa, Sb, Sc. When I define L1, It is L1 = Sa + (?).

But I solved it geometrically. I defined these accelerations aA, aB, aC.
Then I plused second system masses accelerations scalerly aB + aC. and as vectorial in the direction of -J.
With the help of Thales Theorem I found aA equal (aB+aC)/2.

Is this correct?
 
  • #6
Oklid said:
L1 = Sa + (?).
Or more usefully ?=L1-Sa, so the depth of B below the top pulley is L1-Sa+Sb, etc.
Oklid said:
aA equal (aB+aC)/2.
Yes,
 
  • #7
haruspex said:
Or more usefully ?=L1-Sa, so the depth of B below the top pulley is L1-Sa+Sb, etc.

Yes, the depth of B below the top pulley is L1-Sa+Sb but with this, how can I do associate variables to get acceleration from lenghts?
 
  • #8
Oklid said:
Yes, the depth of B below the top pulley is L1-Sa+Sb but with this, how can I do associate variables to get acceleration from lenghts?
Differentiate. Twice.
 
  • #9
haruspex said:
Differentiate. Twice.

I didn't mention that, I know it.

I said when we know the depth of B below top datum, How I use it in my equations?

B has different datum point?

Edit: L2= Sc+Sb
L1= Sa+(?)
L1-Sa=(?)
Edit: I mean, yes we know that the depth of B below the top pulley is L1-Sa+Sb, so How can I use it?
 
Last edited:
  • #10
Oklid said:
I didn't mention that, I know it.

I said when we know the depth of B below top datum, How I use it in my equations?

B has different datum point?

Edit: L2= Sc+Sb
L1= Sa+(?)
L1-Sa=(?)
Edit: I mean, yes we know that the depth of B below the top pulley is L1-Sa+Sb, so How can I use it?
I don't think I have grasped what your difficulty is.
Using yα for depths below the top pulley, you have
##y_b=L_1-S_a+S_b##
##y_c=L_1-S_a+S_c##
##A_a=-\ddot{S_a}##
##A_b=\ddot{y_b}=\ddot{S_b}-\ddot{S_a}##
##A_c=\ddot{y_c}=\ddot{S_c}-\ddot{S_a}##
##S_b+S_c=L_2##
##\ddot{S_b}+\ddot{S_c}=0##
Hence ##A_b+A_c=2A_a##, which you already found somehow.

Is your question where to go next? If so, you need to consider the tensions in the strings, the forces on the individual masses, and how these relate to their accelerations. You will not get more information out of the conservation of string lengths.
 
  • #11
haruspex said:
I don't think I have grasped what your difficulty is.
Using yα for depths below the top pulley, you have
##y_b=L_1-S_a+S_b##
##y_c=L_1-S_a+S_c##
##A_a=-\ddot{S_a}##
##A_b=\ddot{y_b}=\ddot{S_b}-\ddot{S_a}##
##A_c=\ddot{y_c}=\ddot{S_c}-\ddot{S_a}##
##S_b+S_c=L_2##
##\ddot{S_b}+\ddot{S_c}=0##
Hence ##A_b+A_c=2A_a##, which you already found somehow.

Is your question where to go next? If so, you need to consider the tensions in the strings, the forces on the individual masses, and how these relate to their accelerations. You will not get more information out of the conservation of string lengths.

I think I know what my difficulty is.

When I wrote the equations, I decided the datums were unchangeable so the depth of masses below top pulley seemed unrelated to me.
I think I should seek more.

Thanks for helping, sir!

Edit: Spelling.
 
Last edited:

1. What is Absolute Dependent Motion Analysis?

Absolute Dependent Motion Analysis is a scientific method used to study the movement of objects in relation to a fixed point or reference frame. It involves analyzing the position, velocity, and acceleration of an object as it moves through space.

2. How is Absolute Dependent Motion Analysis different from other motion analysis techniques?

Unlike other motion analysis techniques, Absolute Dependent Motion Analysis does not rely on an external reference point, such as the ground or another object. Instead, it uses a fixed reference frame, allowing for more accurate measurements and calculations.

3. What are the applications of Absolute Dependent Motion Analysis?

Absolute Dependent Motion Analysis is commonly used in fields such as physics, engineering, and biomechanics. It can be used to study the motion of objects in various scenarios, such as projectile motion, circular motion, and collisions.

4. What are the key components of Absolute Dependent Motion Analysis?

The key components of Absolute Dependent Motion Analysis include a fixed reference frame, measurements of position and time, and calculations of velocity and acceleration. These components are used to analyze the motion of an object and determine its trajectory and other properties.

5. How can Absolute Dependent Motion Analysis be applied in real-world situations?

Absolute Dependent Motion Analysis can be used in various real-world situations, such as analyzing the performance of athletes in sports, studying the movement of vehicles in traffic, and designing structures that can withstand different types of motion. It can also be used to predict and prevent accidents, improve efficiency, and optimize performance.

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