Weight And Balance Problem For The CFI Written

[Flyparrothead]

These kinds of questions are driving me up a wall. The question is, how should the 250 lb weight be shifted to balance the plank on the fulcrum.

What is throwing me off is where the datum is. Do you calculate the W & B for the two weights and the plank, find the CG and then determine how you would move the weight?

 

[tonycondon]

(1) the datum is the common measurement point.
(2) yes.

 

[JeffDG]

First, calculate everything to the left of the fulcrum and find the moment.

Next, calculate the moment of the plank to the right of the fulcrum. Subtract that from the total moment on the left, and divide by the weight on the right. That will give you an arm on the right for the weight on the right.

 

[Capt. Geoffrey Thorpe]

These kinds of questions are driving me up a wall. The question is, how should the 250 lb weight be shifted to balance the plank on the fulcrum.

What is throwing me off is where the datum is. Do you calculate the W & B for the two weights and the plank, find the CG and then determine how you would move the weight?

For convenience, I would pick the fulcrum as the datum. Then, to balance, the moment around the fulcrum (datum) needs to be zero - right?

0 = -15*500 + 200*15 + 250*x

solve for x

 

[The Old Man]

Even simpler, The weight to the right weighs half the weight on the left. Therfore, it needs to be twice the distance from the fulcrum.

 

[JeffDG]

Even simpler, The weight to the right weighs half the weight on the left. Therfore, it needs to be twice the distance from the fulcrum.

But the plank is not balanced on its CG either and you need to balance that out.

 

[The Old Man]

But the plank is not balanced on its CG either and you need to balance that out.

Oops, I didn't see the plank weight. That complicates the simple solution. 2/3 of the plank is to the right of the fulcrum, Meaning you need less than twice the distance on the weights.

 

[mantakos]

The datum is wherever you want it to be.

If you put the datum on the left edge, you get a moment of:

500 * 15 + 250 * 50 + 200 * 45 = 29000​

and a CG of:

29000 / 950 = 30.526 (approximately)​

or about 30.526" right of the left edge, which is about .526 right of the fulcrum.

If you put the datum at the center of the plank, you get a moment of:

500 * -30 + 250 * 5 = -13750​

and a CG of

-13750 / 950 = -14.474 (approximately)​

or 14.474" left of the center of the plank (which is also about .526 right of the fulcrum).

If we put the datum at the fulcrum, then we have a moment of:

500 * -15 + 20 * 250 + 200 * 15 = 500​

and a CG of:

500/950 = .526"​

or .526" right of the fulcrum.

These all give you the same CG. It doesn't matter where you put the datum, you'll always calculate the same CG.

So the CG is about half an inch too far to the right. If we leave the datum at the fulcrum, and want to balance everything, then we need a moment of 0. Our moment is 500 too great, so we need to shift the weights to reduce our moment by 500 inch-lbs. We can do this by taking the 250lb weight and moving it 2" to the left. Or we can take the 500lb weight and move it 1 inch to the left. Or we can take the whole plank/weight combo and move it .526 (approximately) inches to the left.
-harry

 

[poadeleted20]

There's a formula for this they teach in the ATP knowledge test material. You want to move the cg 15 inches, right? Formula is:

Distance to move = GW x CGmove/Wmoved

GW = Gross weight
CGmove = distance you want the cg to move
Wmoved = weight being moved

For this case,
GW = 500 + 250 + 200 = 950 lb (two weights plus plank)
CGmove = 15 inches
Wmoved = 250

That means:

Dmove = 950 x 15/250

Solve it!

For more formulae for these problems, see http://www.ajdesigner.com/phpweightshift/weight_shift_weight_moved.php

 

[EdFred]

Move it 57 inches? I don't think that's quite right considering moving it 57 inches would put it off the end of the plank.

 

[poadeleted20]

Move it 57 inches? I don't think that's quite right considering moving it 57 inches would put it off the end of the plank.

Sorry -- I was assuming the system was in balance where the cg symbol was on the original diagram, and so we were just trying to move the cg 15 inches left. Should have looked more closely.

In this case, you'll just have to do it as a simple WxA=M problem, using the fulcrum (the desired balance point) as the datum and using the arm of the 250-lb weight as the unknown:

(250 x X) + (200 x 15) + (500 x -15) = 0
250X + 3000 - 7500 = 0
250X = 4500
X = 18

250 lb weight goes 18 right of the fulcrum.

But the formula I posted above is still good to remember for when you go for your ATP.