Static Equilibrium Homework: Find the Force on A and B

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In summary, the problem involves a uniform plank with a length of 4m and a mass of 120N resting on two stools, A and B, with stool A being 0.5m in and stool B being 1.0m in. An 80N weight is placed between the two stools, with 1.75m in on the left and 2.25m in on the right. The solution involves finding the force on stools A and B using the equations for moment of force. After calculating the moments of both stools, A is found to have a force of 88N and B has a force of 112N.
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Doomoo
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Homework Statement


"A uniform plank, length of 4M,has a mass of 120N and rests on top of two stools. One Stool, A, is 0.5M into the plank on the left side. The other stool, B, is 1.0M in on the right side.

An 80N weight is placed between the two stools. Find the Force upon stools A and B.
Thus meaning that the 80N weight is 1.75M in on the left hand side, and 2.25 M in on the right hand side.

Homework Equations


Moment of a force = Force * distance.


The Attempt at a Solution


First I find the moment of the force of both A and B.
A = (1.5M * 120N) + ( 1.25M * 80N) = 280 N m.
B = (1m * 120) + (1.25M * 80) = 220N

So, we now have a ratio of 280/500:220/500 = 0.56:0.44
0.56 * 200 = 112, and 0.44 * 200 = 88.
Therefore, A = 112N and B = 88N.

This seems all well and good, except according to my answer book it is the other way round. A should be 88 and B 112. I can't see where I've gone wrong.

I'm thankful for any help given, I get so annoyed when I can't figure out a question =/.
 
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  • #2
Hi Doomoo, welcome to PF.
Your approach to the problem is not correct.
Take a reference point, say the stool A.
First condition is ΣFY = O. Weights act in the downward direction and reaction on A and B act in the upward direction.
Then take the sum of the moments of the forces about A and equate it to zero.
The solve for A and B.
 
Last edited:
  • #3
Ahh, I see.
Thanks a lot!
 

1. What is static equilibrium?

Static equilibrium is a state in which an object is at rest and has no net force acting on it. This means that all forces acting on the object are balanced and cancel each other out.

2. How do you determine the force on objects A and B in static equilibrium?

To determine the force on objects A and B, you will need to use the principles of static equilibrium. This involves analyzing all the forces acting on the objects and setting them equal to zero. Then, you can solve for the unknown forces using equations such as Newton's Second Law or the sum of forces in the x and y directions.

3. What information is needed to solve a static equilibrium problem?

To solve a static equilibrium problem, you will need to know the forces acting on the objects, the directions and magnitudes of these forces, and the point at which the forces are applied. You may also need to know the mass and weight of the objects, as well as any other relevant physical properties.

4. What are some common misconceptions about static equilibrium?

One common misconception about static equilibrium is that it only applies to objects at rest. In reality, static equilibrium can also apply to objects in motion, as long as their velocity is constant. Another misconception is that the forces acting on an object must be equal in magnitude to be in static equilibrium. In fact, the forces must only be balanced and cancel each other out, regardless of their magnitudes.

5. How can I check if my solution for a static equilibrium problem is correct?

To check if your solution is correct, you can perform a quick check by ensuring that the sum of forces in the x and y directions is equal to zero. You can also plug your solution back into the equations and see if they still hold true. Additionally, you can compare your solution to other known solutions or use a computer program to verify your calculations.

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