# Force Equilibrium Problem

• Dlong
In summary, the conversation revolves around a statics problem involving an object resting on a rotating disc and being pushed into a stationary wall. The question is about the reaction force of the wall and the factors needed to solve the problem, such as friction force and the location of the center of rotation. The suggested approach is to use the formula F = ma to calculate the reaction force.

#### Dlong

Hello,

I am a first time poster and I need some help with a basic statics problem. I drew a free body diagram to help illustrate. An object with a mass 'M' is resting on a rotating disc that is spinning with constant velocity 'V'. The mass is continuously being pushed into a static wall due to the rotating disc beneath it. The mass is stationary because it is being stopped by the wall. Thus, the static wall forces the object to slide across the surface the disc as the disc rotates.

The question is, what is the reaction force of the wall? Given the mass of the object and the velocity of the disc, what else do I need to know in order to solve this problem? Friction force? If so, which way is it pointing? I was hoping someone can point me in the right direction. I have attached the image of the FBD in the thread. Let me know if you need any additional information.

Any help is much appreciated,

David

#### Attachments

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Your diagram is rather unclear. Where is the center of rotation located?

"The mass is continuously being pushed into a static wall due to the rotating disc beneath it."

This may be true.

"The mass is stationary because it is being stopped by the wall."

This may be true.

"Thus, the static wall forces the object to slide across the surface the disc as the disc rotates."

How do you figure this conclusion? Are the wall and the object attracted magnetically? Are you sure that a more reasonable explanation might be possible?

If you want to calculate the reaction of the object, always remember that F = ma.

How would friction determine the reaction of the object on the stationary wall?

## What is a force equilibrium problem?

A force equilibrium problem is a type of physics problem that involves determining the forces acting on an object in order for it to remain in a state of equilibrium, or a state where the net force on the object is equal to zero.

## What are the key principles involved in solving a force equilibrium problem?

The key principles involved in solving a force equilibrium problem are Newton's First Law of Motion (the law of inertia), which states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force, and Newton's Second Law of Motion, which states that the net force on an object is equal to its mass multiplied by its acceleration.

## What are the steps to solving a force equilibrium problem?

The steps to solving a force equilibrium problem are: 1) Draw a free-body diagram of the object, showing all the forces acting on it and their directions; 2) Write out the equations for Newton's Second Law of Motion for each axis (x and y) based on the free-body diagram; 3) Solve the equations simultaneously to find the magnitude and direction of each force; 4) Check that the net force on the object is equal to zero to confirm that the object is in a state of equilibrium.

## What are some common mistakes when solving a force equilibrium problem?

Some common mistakes when solving a force equilibrium problem include: not properly identifying and labeling all the forces acting on the object, using incorrect signs or directions for the forces, and not taking into account the possibility of rotational equilibrium if the object is not only moving in a linear direction.

## What are some real-world applications of force equilibrium problems?

Force equilibrium problems have many real-world applications, including in engineering, architecture, and design. For example, they can be used to determine the forces acting on a bridge or building to ensure structural stability, or to determine the forces needed to maintain the balance of a structure, such as a crane or a see-saw. They are also used in sports, such as in analyzing the forces involved in a gymnast's routine or a diver's dive.