# Equilibrium of Coplanar Force Systems HW Problem

• noboost4you
In summary, the person is having trouble with a homework problem involving finding the tension in a cable and the reactions at a point. They mention using a moment equation involving a pulley and platform and finding the weight of the boy and platform in units of Newtons. After some confusion, they ask for suggestions and someone gives information on how to approach the problem using a free body diagram. The final answers are given as T = 143 N, Ax = 71.5 N to the left, and Ay = 464 N up.
noboost4you
I've been having trouble with the homework problem attached as an image.

I need to find the tension in the cable and the reactions at A (Ay and Ax). In previous homeworks, I've been able to find the reactions at similar points A by finding the moment about A around a few other points. Now that there is a pulley and platform involved, I'm drawing a blank.

In the book it says to find the Moment about the pulley the equilibrium equation is: (sum)Mo = T1(r) - T2(r) = 0 ... from which we get T1 = T2

This is an odd problem so the answer is in the back of the book and no matter what I do, I cannot get that answer.

I changed the mass of the boy and platform into units of Newtons as well.

Can anyone shed any light on this problem for me?

Thanks alot

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Anyone have any suggestions? Really scraping the bottom of the barrel here. Thanks

noboost4you said:
Anyone have any suggestions? Really scraping the bottom of the barrel here. Thanks

Too bad the attachment doesn't work.

The attachment/image seems to working fine.

The tension in the cable is simply a force, T. The tension applies a force on the platform via the pulley. The resultant force on the pulley introduces a moment on the platform about pivot at A. The weight of the boy and the mass of the platform also produce moments about the pivot at A.

For a distributed load (such as the platform weight), the moment arm is at the center of gravity.

Moment producing forces are normal to the respective moment arm.

I would love to say that that information was helpful, but it just made me more confused. Does it matter that the rope is at an angle?

noboost4you said:
I would love to say that that information was helpful, but it just made me more confused. Does it matter that the rope is at an angle?

Of course, it matters. Check your Static's book for more details, or post an attempt.

Are the answers 143.6 and 445 and 71.8?

haynewp said:
Are the answers 143.6 and 445 and 71.8?

No, but you're close.

T = 143 N, Ax = 71.5 N to the left, and Ay = 464 N up

I got it now, I had left out a cosine. Make a cut through the cable up at where it attaches to the top support. Then sum moments about point A using the vertical weights given in order to find the tension in the cable.

I'm not following "make a cut through the cable" part?

Thanks

It is just making a free body diagram with the cable detached from the support. That is how I found the force in the cable. There are 3 steps; sum moments about A with the cable cut to get the cable force (note the cable is conveniently perpendicular to the platform), then sum vertical forces, and then sum horizontal forces to get the reactions at A. This was the easiest way for me to get the answers but it may not match the procedure your book suggests.

## 1. What is the definition of equilibrium in a coplanar force system?

Equilibrium in a coplanar force system refers to a state in which all the forces acting on an object are balanced and cancel each other out, resulting in no net force or acceleration on the object.

## 2. How do I determine if a coplanar force system is in equilibrium?

To determine if a coplanar force system is in equilibrium, you can use the equations of static equilibrium, which state that the sum of all forces in the x-direction and the sum of all forces in the y-direction must equal zero. Additionally, the sum of all moments about any point must also equal zero.

## 3. What is the difference between a coplanar force system and a non-coplanar force system?

A coplanar force system is one in which all the forces are acting in the same plane, whereas a non-coplanar force system has forces acting in different planes. In a coplanar system, the equations of static equilibrium can be simplified because all forces are acting in the same direction.

## 4. How do I calculate the resultant force in a coplanar force system?

To calculate the resultant force in a coplanar force system, you can use the Pythagorean theorem to find the magnitude of the resultant force, and trigonometric functions to find its direction.

## 5. What are some real-life examples of coplanar force systems?

Coplanar force systems can be seen in many everyday situations, such as a person pushing a shopping cart, a book resting on a table, or a person climbing a ladder. In all of these situations, the forces acting on the objects are balanced, resulting in equilibrium.

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