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Please help Due in 2 hours. Statics machine equilibrium: reactions- too many unknowns
The woman using the lat pulldown machine is holding the 80-lb weight stationary in the position shown. What are the reactions at the built-in support E and pin support F? (A and C are pinned connections)
First, I isolated the pulleys and rope to find the components of the tension at D.
Dx=80cos60=40 lb
Dy=-40√3 lb
Then I set up my three equilibrium equations:
∑ME=0= -(80 lb)(13/6 ft) - (40√3 lb)(17/3 ft) - (40 lb)(27/4 ft) + ME + Fy(25/6 ft)
ME= (680√3)/3 +1330/3 + (25/6)Fy
∑Fx= 0 = Ex + Fx + (40 lb)
∑Fy= 0 = Ey + Fy - (80 lb) - (40√3 lb)
Right now, I have 3 equations and 5 unknowns, Ex, Ey, ME, Fx, and Fy.
I'm probably supposed to break it up into two systems, first just the top portion. But I'm not really sure how to proceed from here.
Thank you!
Homework Statement
The woman using the lat pulldown machine is holding the 80-lb weight stationary in the position shown. What are the reactions at the built-in support E and pin support F? (A and C are pinned connections)
The Attempt at a Solution
First, I isolated the pulleys and rope to find the components of the tension at D.
Dx=80cos60=40 lb
Dy=-40√3 lb
Then I set up my three equilibrium equations:
∑ME=0= -(80 lb)(13/6 ft) - (40√3 lb)(17/3 ft) - (40 lb)(27/4 ft) + ME + Fy(25/6 ft)
ME= (680√3)/3 +1330/3 + (25/6)Fy
∑Fx= 0 = Ex + Fx + (40 lb)
∑Fy= 0 = Ey + Fy - (80 lb) - (40√3 lb)
Right now, I have 3 equations and 5 unknowns, Ex, Ey, ME, Fx, and Fy.
I'm probably supposed to break it up into two systems, first just the top portion. But I'm not really sure how to proceed from here.
Thank you!
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