Engineering, Statics -- A pulley is free to move on the cable

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Discussion Overview

The discussion revolves around a statics problem involving a pulley system where Pulley B is free to move on a cable. Participants are tasked with determining the location of point B as a function of distance d and expressing the force F required for equilibrium in terms of parameters P, d, and h. The conversation includes attempts at free body diagrams (FBDs) and the relationships between various angles and forces in the system.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about how to start the problem and considers creating a free body diagram (FBD) of the weight hanging on the cable.
  • Another participant suggests that creating an FBD is a good starting point and notes that h and d define the angle of the cable.
  • There is a discussion about the relationship between angles theta and beta, with one participant questioning if they are equal and how this affects the force needed for equilibrium.
  • Some participants mention using tangent values and right-angle triangles to relate the angles and distances in the problem.
  • One participant attempts to derive equations for the forces in the system, expressing them in terms of angles and the weight P.
  • There is confusion about the relevance of angle theta in calculations, with some participants asserting that it is not necessary for the problem.
  • Participants correct each other on the naming of angles and the relationships between them, indicating a collaborative effort to clarify the problem.
  • One participant expresses a need to substitute known values for cos(α) but is unsure how to relate this to the problem's parameters.

Areas of Agreement / Disagreement

Participants generally agree on the need to create free body diagrams and explore the relationships between the angles and forces. However, there is disagreement regarding the relevance of angle theta and its relationship to beta, indicating that the discussion remains unresolved on these points.

Contextual Notes

Participants have not reached a consensus on how to express the location of point B as a function of d or how to substitute known values into their equations. The discussion includes various assumptions about the angles and their relationships, which have not been fully clarified.

TimmyJ1203
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Homework Statement


1. Pulley B is free to move on the cable ABC which is fastened at A and being pulled by force F through the pulley C. Neglecting friction:
a. Determine location of point B as a function of d.
b. Express the force F required to maintain equilibrium in terms of P, d, and h.

The Attempt at a Solution


I have no idea where to even start. I thought about creating an FBD of the weight hanging on the cable for part b, but I can't figure out how to tie that to h and d.
 

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A FBD of the weight is a good start. h and d define the angle of the cable which gives the angle of the force for the FBD of the weight.

Attempt a FBD and we can go from there.
 
billy_joule said:
A FBD of the weight is a good start. h and d define the angle of the cable which gives the angle of the force for the FBD of the weight.

Attempt a FBD and we can go from there.

OH, okay, I'll try this. There are four problems after this one that I did no problem.

Not sure why I didn't see that.. I'll work on it a bit. Thank you.
 
Okay, so I tried drawing a FBD of point B, but I'm still not sure how to equate the measurements.

My friend recently mentioned to me that the pulley may be hanging directly in the middle of the cable. If that's the case I can use the tangent value of alpha to put d/2 and h in it, but I'm still not sure how to write point B as a location.

In the picture i just uploaded is theta supposed to be equal to beta? If they're related, then I don't see how theta affects the amount of force needed to keep the system in equilibrium.
 

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TimmyJ1203 said:
Okay, so I tried drawing a FBD of point B, but I'm still not sure how to equate the measurements.

My friend recently mentioned to me that the pulley may be hanging directly in the middle of the cable. If that's the case I can use the tangent value of alpha to put d/2 and h in it, but I'm still not sure how to write point B as a location.

In the picture i just uploaded is theta supposed to be equal to beta? If they're related, then I don't see how theta affects the amount of force needed to keep the system in equilibrium.
At equilibrium B will be at d/2.
Theta is not equal to alpha, draw some right angle triangles to find their relationship. What do the angles of triangles add to?
Separate F and F dash into their horizontal and vertical components to find their magnitude in terms of P and theta **.(**EDIT: beta or alpha, not theta)
 
Last edited:
But is theta equal to beta? I just realized that I didn't include my updated drawing.
I named the angle, that is adjacent to theta, beta.
 

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No, theta is a fixed and not relevant to your calculations, I'm not sure why it's included on the diagram.
Beta is a function of h and d.
 
Last edited:
Sorry.. I used the word adjacent incorrectly. Here is what I drew so far.

I still don't understand how beta can be related to theta. I'm attempting to imagine the pulley setup, and it seems like no matter what angle theta is, the forces F and F' will be equal and unaffected.
 

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TimmyJ1203 said:
Sorry.. I used the word adjacent incorrectly. Here is what I drew so far.

I still don't understand how beta can be related to theta. I'm attempting to imagine the pulley setup, and it seems like no matter what angle theta is, the forces F and F' will be equal and unaffected.
You are correct - In post #5 I should have said alpha or beta, not theta. I've edited in a correction.
 
  • #10
Okay, so this is what I got so far:

F_x = F * sin(α)
F_y = F * cos(α)

F'_x = F * sin(α)
F'_y = F * cos(α)

P_x = 0
P_y = P

ΣF_x = Fsinα - Fsinα = 0
0 = 0

ΣF_y = Fcosα + cosα - P = 0
2Fcosα = P
F = P/(2cosα)

I know I'm somehow supposed to substitute cosα for known values but all I can think of to substitute it with is h/l. Lower case L being the unknown.
I'm still also not sure how to determine the location of point B as a function of d.
 

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