Solving for Velocity on a Pulley System

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Homework Help Overview

The discussion revolves around a pulley system where participants are attempting to determine the velocities of different segments of rope connected to various pulleys. The problem involves understanding the relationships between the velocities of the ropes and the motion of the pulleys.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are inspecting the velocities of the ropes and attempting to apply the given equation for velocity on a pulley. There is confusion regarding the direction of the velocities and how to proceed with the calculations, particularly for pulleys B and D.

Discussion Status

Some participants have offered suggestions to label the ropes for clarity and to write equations for each pulley without solving them immediately. There is an ongoing exploration of the relationships between the velocities, but no consensus has been reached on the next steps.

Contextual Notes

There is mention of specific velocities being assigned to certain ropes, but some information appears to be missing, particularly regarding the velocity of pulley B. Participants are also navigating potential confusion in notation and terminology related to the ropes.

RoyalFlush100
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Homework Statement


In the picture below.

Homework Equations


Velocity on a pulley = (velocity on left rope + velocity right rope)/2
Pulley A and C have 0 velocity.

The Attempt at a Solution


By inspection the right sided rope on pulley A is 120 mm/s going up.
After that is when I get confused. Pulley B and D are in motion, so I don't see what else to do from here.
 

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RoyalFlush100 said:
left sided rope on pulley A is 120 mm/s going up.
Looks like down to me.
RoyalFlush100 said:
Velocity on a pulley = (velocity on left rope + velocity right rope)/2
So apply that to each pulley in turn, working from the left.
What does it tell you about the velocity of the second rope segment (the one on the right of pulley A)?
 
haruspex said:
Looks like down to me.

So apply that to each pulley in turn, working from the left.
What does it tell you about the velocity of the second rope segment (the one on the right of pulley A)?

Yeah, I meant the rope to the right.

But still, we don't know vB, meaning we'd have:
vB = (150+vBR)/2
Where vBR is the velocity on the right of pulley B.
By inspection vCL = -vBR

But from here, I'm not sure how to proceed since vB is not 0
 
RoyalFlush100 said:
Yeah, I meant the rope to the right.
Ok.
I feel your notation is going to get a bit confusing since you will have two names for the same rope.
I'll just label them and their velocities a to e across the top, and the segment left of the lowest pulley is f.
You already have a=-b.
Next, look at pulley C. What equation can you write for that? Then move on to pulley B.
You don't need to solve these equations, determining velocities, as you go along. Just get all the equations written first.
 

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