How Can You Find Forces P, F, and T in a Static Equilibrium Problem?

[Handsome jack]

1. Homework Statement
Find forces P,F,and T

Homework Equations

Fx = 0
Fy = 0

The Attempt at a Solution

So far I only got force T from getting the moment from point b. Don't know how-to start getting force P and F since they're both at the same point. Any help will be much obliged thank you
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[Titan97]

Assuming the rods are inextensible, find the reaction between the velocities of the three ends.
For example, if a horozontal rod is given a velocity of say 5m/s at one end A along the direction of rod, then the other end will also have the same velocity. If it does not, the rod will extend.

 

[TSny]

Welcome to PF!

What do you mean by F_x = 0 and F_y = 0? Have you tried to use these?

 

[Handsome jack]

Welcome to PF!

What do you mean by F_x = 0 and F_y = 0? Have you tried to use these?

That means that all forces on x and y-axis must equal to 0 since it's on equilibrium

 

[TSny]

That means that all forces on x and y-axis must equal to 0 since it's on equilibrium

Do you mean that the sum of the x components of all of the forces must be zero? Similarly for the y components?

If so, have you tried using these facts?

 

[Titan97]

How can the system be at equilibrium? There is a net force acting along horizontal.

 

[TSny]

How can the system be at equilibrium? There is a net force acting along horizontal.

Looks like the force P might be acting down and to the left according to the second picture in post #1.

 

[Titan97]

If its not at equilibrium, then can't I say that the force along the rod at both ends should be equal? (Assuming the rod does not extend)

 

[Handsome jack]

Oh God sorry. Force P is down to the left. It's on equilibrium, just have to find what the other forces are that are F and p that contribute to the cancellation of the other forces

 

[TSny]

If its not at equilibrium, then can't I say that the force along the rod at both ends should be equal? (Assuming the rod does not extend)

No, I don't think so. A rod can sustain tension. There is no need for the force parallel to the rod at one end to equal the force parallel to the rod at the other end.

Also, if you were to consider a single rod in the system, you would need to take into account forces acting on the rod from the other rods. If the rod is in equilibrium then the net force (including internal forces) acting parallel to the rod at one end would be equal and opposite to the net parallel force at the other end (assuming we can neglect the weights of the rods.)

 

[TSny]

Force P is down to the left. It's on equilibrium, just have to find what the other forces are that are F and p that contribute to the cancellation of the other forces

How would you write out ΣF_x = 0 for this problem?

 

[Handsome jack]

tried using process of elimination to find P and F so far I got the answer not sure if it's correct

 

[TSny]

OK, your process looks correct. I'm too lazy today to get out my calculator and check all the numbers.

 

[Handsome jack]

OK, your process looks correct. I'm too lazy today to get out my calculator and check all the numbers.

Thanks

 

[TSny]

I put the equations into some software. It gives somewhat different answers than what you are getting. Could be round off errors. For example sin(33.69) = .5547 instead of .55.

Note that using the little triangles allows you to have exact expressions for the sines and cosines of the angles. For force P, the hypotenuse of the triangle is √10 so you can write the sine of the angle as 1/√10 and the cosine as 3/√10.

Force P then comes out to be 2400√10 . Likewise F can be expressed as a nice number times √13.