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Pulley Traction in Equilibrium

  • Thread starter Missnomer
  • Start date
  • #1
1
0

Homework Statement


Sum of downward forces exerted at A and B is 41lbs by the leg, what is the weight attached?
Kpvcb5E.jpg


Homework Equations


None, really...


The Attempt at a Solution


Tension (T) throughout the system must be constant and equal to the weight (W).
I first assumed that the leg was entirely pulled up by B since I thought the force passing A
is going down (wrong since this is in equilibrium) and claimed W = 41sin60, but it's not that simple.

Tension pulls both ways, so there is an upward force at A as well as B.
Since
[itex]ƩF_y = 0[/itex]
[itex]Tsin25 + Tsin60 - 41lb = 0[/itex]
[itex]T = W = 41 / (sin25 + sin60) = 31.0lb[/itex]

But using this value of T in checking horizontal forces, they don't balance out.
What am I missing here, or are my calculations correct and there just is a net horizontal force
on the leg that the leg has to resist?

Thanks in advance :).
 

Answers and Replies

  • #2
Andrew Mason
Science Advisor
Homework Helper
7,568
330

Homework Statement


Sum of downward forces exerted at A and B is 41lbs by the leg, what is the weight attached?
Kpvcb5E.jpg


Homework Equations


None, really...


The Attempt at a Solution


Tension (T) throughout the system must be constant and equal to the weight (W).
I first assumed that the leg was entirely pulled up by B since I thought the force passing A
is going down (wrong since this is in equilibrium) and claimed W = 41sin60, but it's not that simple.

Tension pulls both ways, so there is an upward force at A as well as B.
Since
[itex]ƩF_y = 0[/itex]
[itex]Tsin25 + Tsin60 - 41lb = 0[/itex]
[itex]T = W = 41 / (sin25 + sin60) = 31.0lb[/itex]

But using this value of T in checking horizontal forces, they don't balance out.
What am I missing here, or are my calculations correct and there just is a net horizontal force
on the leg that the leg has to resist?

Thanks in advance :).
The horizontal forces balance if you take into account the friction between the patient and the bed.

AM
 

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