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

In summary, the problem involves finding the reactions at the built-in support E and pin support F for a woman using a lat pulldown machine with an 80-lb weight. After isolating the pulleys and rope, three equilibrium equations are set up, but there are currently 5 unknowns. The next step may involve breaking it up into two systems. The deadline for the assignment is 45 minutes.
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Please help Due in 2 hours. Statics machine equilibrium: reactions- too many unknowns

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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Please help. Due in 45 minutes.
 

1. What is a statics machine equilibrium?

A statics machine equilibrium is a concept in physics that deals with the balance of forces and torques acting on a rigid body that is at rest. It is used to analyze and predict the motion of objects under the influence of external forces.

2. What is a support reaction in a statics machine equilibrium?

A support reaction is a force or torque that is exerted on a rigid body by a supporting structure or surface. It is necessary to maintain the equilibrium of the body and prevent it from moving or collapsing.

3. How do I determine the support reactions in a statics machine equilibrium?

To determine the support reactions, you need to draw a free body diagram of the rigid body and apply the equations of equilibrium, which state that the sum of all forces and torques acting on the body must equal zero. This will allow you to solve for the unknown support reactions.

4. What should I do if I have too many unknowns in a statics machine equilibrium problem?

If you have too many unknowns, you may need to revise your free body diagram to include additional forces or constraints that were not initially considered. You may also need to apply other principles, such as the principle of virtual work, to solve for the unknowns.

5. Why is it important to solve for the support reactions in a statics machine equilibrium?

Solving for the support reactions is important because it allows you to determine whether a structure or object is stable and can withstand the external forces acting on it. It is also crucial for designing and analyzing structures, such as bridges and buildings, to ensure they can support their intended load without failure.

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