# How Do You Determine Fx and Fy in a Rigid-Body Equilibrium Problem?

• physicsCU
In summary, the problem involves finding the tension on a cable and the force on a beam by balancing torque and force. Part A requires accounting for all forces and finding the tension in the cable. In Part B and C, the x-component and y-component of the force exerted by the wall on the beam must be found, respectively. These components can be expressed in terms of the tension, angle, mass, and gravitational acceleration.
physicsCU
OK, I am having trouble with parts B and C.

Here is the problem:

A worker sits on a beam attached to a wall at one end, supported by a cable on the other which is itself attached to the wall. Find the tension on the cable and the force on the beam by balancing torque and force.

A uniform steel beam of length L and mass m1 is attached via a hinge to the side of a building. The beam is supported by a steel cable attached to the end of the beam at an angle theta, as shown. Through the hinge, the wall exerts an unknown force, F , on the beam. A workman of mass m2 sits eating lunch a distance d from the building.

Part A. Find T, the tension in the cable. Remember to account for all the forces in the problem.

Part B. Find Fx, the x-component of the force exerted by the wall on the beam (F), using the axis shown. Remember to pay attention to the direction that the wall exerts the force.

Part C. Find Fy, the y-component of force that the wall exerts on the beam (F), using the axis shown. Remember to pay attention to the direction that the wall exerts the force.
Express your answer in terms of T, theta, m1, m2, and g.

I really have no idea where to go on B or C. But on B, I think the Fx is the normal force from the wall. So I try to use torque_net = 0. But I get d*m2*g - (something). I don't know what that something is.

And C, I have no idea.

Any help is appreciated. Thanks!

physicsCU said:
Part B. Find Fx, the x-component of the force exerted by the wall on the beam (F), using the axis shown. Remember to pay attention to the direction that the wall exerts the force.
Consider the horizontal forces acting on the beam. (What are they?) They must add to zero.
Part C. Find Fy, the y-component of force that the wall exerts on the beam (F), using the axis shown. Remember to pay attention to the direction that the wall exerts the force.
Express your answer in terms of T, theta, m1, m2, and g.
Taking the end of the beam as your axis, consider all the forces acting on the beam that create torque about that axis. (What are they?) The net torque must be zero.

Take axis at the beam attached the wall.
(Tsin[theta])(l )=m[1]gl/2 +m[2]gd
T=(m[1]g/2sin[theta])+m[2]gd/l sin[theta]

F[x]=Tcos[theta]=(m[1]g+m[2]gl)0.5cot[theta]
F[y]=m[1]g+m[2]g-Tsin[theta])=0.5m[1]g-m[2]g(1-d/l)

## What is a rigid-body equilibrium problem?

A rigid-body equilibrium problem is a type of physics problem that involves analyzing the forces acting on a rigid object that is in a state of equilibrium, meaning that it is not moving or rotating. This type of problem is commonly used to analyze the stability of structures and objects.

## What are the conditions for a rigid body to be in equilibrium?

For a rigid body to be in equilibrium, there must be no net force acting on the object in any direction and no net torque causing the object to rotate. This means that the forces acting on the object must be balanced and the sum of the torques must be equal to zero.

## How do you solve a rigid-body equilibrium problem?

To solve a rigid-body equilibrium problem, you must first draw a free-body diagram of the object, showing all the external forces acting on it. Then, you can use the equations of equilibrium, which state that the sum of the forces in each direction must be equal to zero, and the sum of the torques must be equal to zero. By setting up and solving these equations, you can determine the unknown forces or angles in the problem.

## What are the common types of forces in a rigid-body equilibrium problem?

The common types of forces encountered in a rigid-body equilibrium problem include weight, normal force, frictional force, tension, compression, and shear. These forces can be either external forces acting on the object or internal forces within the object itself.

## What are some real-life applications of rigid-body equilibrium problems?

Rigid-body equilibrium problems have many practical applications in engineering and architecture. For example, they can be used to determine the stability of bridges, buildings, and other structures. They are also important in designing machines and other mechanical systems to ensure that they are balanced and do not experience excessive forces or torques.

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