# Statics machine equilibrium: support reaction- I have too many unknowns

1. Aug 28, 2011

### musicmar

1. The problem statement, all variables and given/known data
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)

3. 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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Last edited: Aug 29, 2011
2. Aug 29, 2011