# Boom problem using rotational equilibrium methods

• qnney
In summary, the conversation is about a problem involving rotational equilibrium methods. The goal is to find the 3 unknowns: T, V, and H, using given variables and equations. The issue seems to be with the radii of the tension and load forces. After some discussion and clarification, the person is on the right track to solve the problem.
qnney
URGENT! Boom problem using rotational equilibrium methods

Hi!

Here is a picture of the problem I'm about to explain... http://i96.photobucket.com/albums/l168/synovial/boom.jpg

My professor did not give us numbers to use, just variables.

The goal of the problem is to find the 3 unknowns: T, V, and H. The given variables are the entire length of the boom (L--not pictured), mass of the boom, mass of the load, $$\Theta$$, x, and p.

The rope is connected to distance x from the end. The load hangs at distance p from the end. The boom's center of gravity is in the middle.

I know that I am supposed to find all of the forces in the X and Y directions, but I can't seem to calculate the torques correctly.

$$\Sigma$$Fx = 0
0 = H -Tcos$$\Theta$$

$$\Sigma$$Fy = 0
0 = V + Tsin$$\Theta$$-Wboom-Wload

$$\Sigma$$$$\tau$$Fa = 0
0 = $$\tau$$T perpindicular + $$\tau$$V + $$\tau$$H + $$\tau$$W boom + $$\tau$$W load

qnney--always start torque problems by picking a good pivot point! Where do you want yours to be? (HINT: Put it at the point where you have the most unknown forces acting).

Don't hesitate to ask more questions if you get stuck again!

I think a good place for the pivot point would be at the intersection of the V and H forces. Does this work?

That's what I used.

Ok, so far I think I've figured out:

Sum of the torques = 0
0 = -Tsin$$theta$$(L-p) + Wboom(L/2) + Wload (L-x)

Er... well, that's not consistent with the drawing you made OR with the description of the problem, but it's close.

The issue seems to be with your radii. The tension connects to the beam at a radius of (L-x) according to the text of the problem, and at (L-p-x) according to the picture. By both accounts, the load connects to the beam at a radius of (L-p)

It looks like you just got a bit mixed up, but otherwise, you seem to be on the right track.

Thanks so so much! I wasn't so sure if I was getting those right.

So now I think I can solve for T in this problem and then plug that value back into the $$\Sigma$$Fx and $$\Sigma$$Fy equations to get V and H.

:)

Looks like you're on the home stretch now!

Hey, no problemo!

## 1. What is the "Boom problem" in rotational equilibrium methods?

The "Boom problem" is a common physics problem that involves finding the forces acting on a horizontal beam (or "boom") that is supported by a pivot point at one end and a cable at the other end. The goal is to determine the tension in the cable and the reaction force at the pivot point in order to maintain rotational equilibrium.

## 2. How do you approach solving the "Boom problem" using rotational equilibrium methods?

The first step in solving the "Boom problem" is to draw a diagram of the system and label all the known and unknown forces. Then, apply the principle of rotational equilibrium, which states that the sum of all torques acting on an object must equal zero for it to be in rotational equilibrium. This allows you to set up and solve equations to find the unknown forces.

## 3. What are the key equations used in solving the "Boom problem" using rotational equilibrium methods?

The key equations used in solving the "Boom problem" are the sum of torques equation (Στ = 0) and the sum of forces equation (ΣF = 0). These equations are based on the principles of rotational equilibrium and Newton's laws of motion, and can be used to find the unknown forces in the system.

## 4. What are some common mistakes to avoid when solving the "Boom problem" using rotational equilibrium methods?

Some common mistakes to avoid when solving the "Boom problem" include not correctly identifying all the forces acting on the beam, not considering the direction of the forces, and not applying the equations correctly. It is also important to use consistent units and to double-check your calculations for accuracy.

## 5. How can the "Boom problem" using rotational equilibrium methods be applied in real-life situations?

The "Boom problem" using rotational equilibrium methods can be applied in various real-life situations, such as calculating the forces acting on a crane arm, a diving board, or a seesaw. It can also be used in engineering and construction to design stable structures and determine the necessary support and tension forces. Additionally, understanding rotational equilibrium can aid in understanding the stability and balance of objects in everyday life.

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