# Static Equilibrium

#### makeAwish

1. Homework Statement
Blocks A and B weigh 400 and 200 kN, respectively. They rest on a 30degrees inclined plane and are attached to a post hinged at O by cords parallel to the plane, as shown in Fig. E06-1.3. The post is held perpendicular to the plane by force P. Assume that all surfaces are smooth, determine the value of P.

2. Homework Equations

$$\sum F = 0$$

$$\sum M = 0$$

3. The Attempt at a Solution

I think my free-body diagram has too many forces. I not sure which one is considered as internal or external.

For block B,
my forces are tension 1, weight of B, normal contact force by a on b.

For block A,
my forces are tension 2, weight of A, normal contact force by grd on a, and normal contact force by B on A.

For the post,
my forces are tensions 1 and 2, force P, and a reaction force by grd on post at point O.

Then i take my x axis as along the slope.

And i find sum of Fx = 0, sum of Fy = 0 and sum of torque abt pt O = 0

But i can't really solve it. And i'm very unsure about my free body diagram. Are the normal forces internal forces cos they hold the system together? ( But if so, why for some diagrams, like those end supports, with pins or rollers, there is reaction force and it is an external force? Or reaction force and normal force are diff? )

I'm quite confused..

Can help me pls? Thanks!!

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#### Doc Al

Mentor
I think my free-body diagram has too many forces. I not sure which one is considered as internal or external.
That's not really a free body diagram. To solve the problem, draw (or imagine drawing) a separate free body diagram for each object: block A, block B, and the post. A free body diagram does not show internal forces.

For block B,
my forces are tension 1, weight of B, normal contact force by a on b.

For block A,
my forces are tension 2, weight of A, normal contact force by grd on a, and normal contact force by B on A.

For the post,
my forces are tensions 1 and 2, force P, and a reaction force by grd on post at point O.
OK.

Then i take my x axis as along the slope.

And i find sum of Fx = 0, sum of Fy = 0 and sum of torque abt pt O = 0
Apply those conditions for equilibrium to each object separately. Applying it to blocks A and B will give you the tensions in the cords. Then analyze the post to find the applied force P.

#### PhanthomJay

Homework Helper
Gold Member
Your free body diagrams are correct. When you draw a FBD, the forces internal to the SYSTEM are external to the body isolated in the FBD. In this problem, you need only look in the x direction, parallel to the slope. What are the 2 forces in the x direction acting on Block A? and on Block B? Their sum for each block must be 0.

#### makeAwish

That's not really a free body diagram. To solve the problem, draw (or imagine drawing) a separate free body diagram for each object: block A, block B, and the post. A free body diagram does not show internal forces.
Internal forces would be the normal forces? the reaction force by grd on post at point O is it an external force?

Apply those conditions for equilibrium to each object separately. Applying it to blocks A and B will give you the tensions in the cords. Then analyze the post to find the applied force P.
We can apply the equations to each object as well?
Hmm. How do we see if we should apply the equations to the block or apply by xy directions?

#### makeAwish

Hmm. Anyway, the reaction force by grd on post at point O should be pointing perpendicularly to the slope (i.e into the post) or at an angle to the slope?

#### Doc Al

Mentor
Internal forces would be the normal forces? the reaction force by grd on post at point O is it an external force?
Whether a specific force is internal or external depends on how you define your system. For example, if you consider blocks A and B to be a single system, then the normal force between them would be an internal force. But if you consider them to be separate systems, then the normal force would be an external force.

We can apply the equations to each object as well?
Of course! ∑F = 0 for every object.
Hmm. How do we see if we should apply the equations to the block or apply by xy directions?
Not sure I understand your question. But to find P, you want to analyze forces on the post. (In fact, all you need to do is analyze torques about point O.) But to do that, you need the tensions in the cords. To find those tensions, analyze forces on blocks A and B.

Hmm. Anyway, the reaction force by grd on post at point O should be pointing perpendicularly to the slope (i.e into the post) or at an angle to the slope?
You don't need to worry about the reaction force at point O to solve this problem. (But if you want to find it, apply ∑F = 0 to the post.)

#### makeAwish

So in this qns, when i analyse the post, i consider the forces acting on the post.
If i add in the reaction force by grd on post, i will have another unknown, and i can't solve right? Means when i analyse the post, i shld consider my system as post and ground?

#### makeAwish

Not sure I understand your question. But to find P, you want to analyze forces on the post. (In fact, all you need to do is analyze torques about point O.) But to do that, you need the tensions in the cords. To find those tensions, analyze forces on blocks A and B.
Ok i think i get it. Thanks! :)

You don't need to worry about the reaction force at point O to solve this problem. (But if you want to find it, apply ∑F = 0 to the post.)
Hmm, say i want to find it, :X
is the direction of the reaction force at point O, perpendicularly to the slope (i.e into the post) or at an angle from the post?

#### Doc Al

Mentor
If you want to find the reaction force at point O, figure it out by analyzing the forces on the post and applying ∑F = 0. You can start out by assuming a horizontal and vertical component for the support force, then solve for each.

Ok, thanks! :)

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