Complex Equilibrium Problem

[CoogsDownFall]

Homework Statement

A uniform 300-kg, 6.0 M long, freely pivoted at P, as shown in the figure. The beam is supported in a horizontal position by a light strut, 5.0 M long, which is freely pivoted at Q and is loosely pinned to the beam at R. A load of mass is suspended from the end of the beam at S. A maximum compression of 23,000 N in the strut is permitted, due to safety. The Maximum mass M of the load is closest to Pic

Homework Equations

$∑Fx=0$
$∑Fy=0$
$∑Ftorque=0$
$Torque = r * F$
$F = m * a$

The Attempt at a Solution

I started with first trying to find the forces of both the X and Y axis and then the force of the torque and setting this equal to 23,000 N. What is really messing me up is the beam that is at an angle. So for the forces acting on Y I set Fy = m * (9.8). I know there are forces acting on the X-axis, I am just struggling to be able to find them. Then for the Torque value I have Torque = m * (9.8) * (3.0). I figured because the large beam was cut in half that is the new radius. Any help would be great!

 

[haruspex]

I see no figure. Please supply a figure or more detailed description. E.g. where are P, Q, R and S in relation to the beam and to each other?

 

[CoogsDownFall]

There is a link to it if you click the word "pic"

 

[haruspex]

There is a link to it if you click the word "pic"

OK - doesn't stand out that well on my screen.
Yes, torque is the way to go, but which point are you taking torque about? What forces have a torque about that point? For each of those, what is the distance from its line of action to the point?

 

[HalfLostAndSearching]

As a scientist, it is important to approach this problem systematically and logically. Here are some steps that may help:

1. Draw a free body diagram of the system, clearly labeling all the forces acting on the beam, strut, and load. This will help you visualize the problem and identify any unknown forces.

2. Use the equations of equilibrium to set up a system of equations. Since the system is in equilibrium, the sum of forces in the x-direction, y-direction, and torque must be equal to zero. This will give you three equations to solve for the three unknown forces.

3. Start with the simplest equations first. For example, in the x-direction, there are only two forces acting: the force from the strut and the force from the load. Since the beam is in equilibrium, these two forces must be equal and opposite.

4. Next, move on to the y-direction. Here, you will have three forces: the force from the strut, the force from the load, and the weight of the beam itself. Again, these forces must balance out in order for the beam to remain in equilibrium.

5. Finally, consider the torque equation. This will involve finding the distances between the pivot points and the forces acting on the beam. Remember that torque is equal to the force multiplied by the distance from the pivot point. You may need to use trigonometry to find the distances in this case.

6. Once you have set up your system of equations, solve for the unknown forces. Make sure to use the correct units and pay attention to the direction of the forces.

7. Once you have found the forces, you can calculate the maximum mass that the beam can support. This will be equal to the force from the load divided by the acceleration due to gravity.

8. Check your answer and make sure it makes sense. For example, does the maximum mass calculated fall within the permitted compression limit of the strut? Does it seem reasonable given the dimensions and materials of the system?

Overall, solving this type of complex equilibrium problem requires careful attention to detail and a solid understanding of the equations of equilibrium. By following a systematic approach, you should be able to arrive at the correct answer.