# Homework Help: Moments-calculate centre of mass

1. Dec 8, 2008

### tweety1234

1. The problem statement, all variables and given/known data
A woman and a man support a non-uniform plank, AB of mass 10kg and length 4m. The woman holds the plank 1m from A and the man holds the plank at B. The vertical reaction provided by the woman is 56N find;

A) the vertical reaction force provided my the man

b) The position at which at which the weight of the plank acts measured from A.

2. Relevant equations

3. The attempt at a solution

I worked out the vertical reaction produced by the man which is 42N, but I am really stuck on question 'b' ...

the answer in my book says the center of mass is 2.29m from A,

I have drawn a diagram, can anybody please check it and let me know what's wrong with it?

also my moments equation is..

$$56N \times 1m + 42N \times 4m = 98N (xm-3m)$$

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2. Dec 8, 2008

### tiny-tim

Hi tweety1234!

That's fine, except I don't understand where the (x-3) comes from …

it should be … ?

3. Dec 8, 2008

### Redbelly98

Staff Emeritus
I can't see your diagram yet, but your description of the problem seems clear enough to respond.

What is "x" in your moment equation?

You seem to be taking moments with respect to end A, which is good. It would make sense to let "x" simply be the distance from A to the center-of-gravity position. But you seem to be defining x as something else.

4. Dec 8, 2008

### tweety1234

sorry for my unclear post, yes xm is the distance from A to the center of gravity,

but if my equation is correct i still dont get the right answer?

5. Dec 8, 2008

### tweety1234

should it be x-4 instead? Cause theres 1 meter in between x and A

6. Dec 8, 2008

### tiny-tim

No, there's 1 metre in between the woman and A.

x is … ?

7. Dec 8, 2008

### tweety1234

x represents the distance from point A , were the weight of the plank lies. so should it not be x-3 ?

8. Dec 8, 2008

### tweety1234

Okay, now I am a bit confused. Can you show me what the equation should look like ?

thank you!

9. Dec 8, 2008

### Redbelly98

Staff Emeritus
If it's x, how can it also be x-3?

10. Dec 8, 2008

### Redbelly98

Staff Emeritus
You have a force (the weight) acting at a distance x.

Since torque = force times distance, it really is pretty simple.

11. Dec 8, 2008

### tweety1234

if i want to work out the distance wont i have to minus 3 meters?

12. Dec 8, 2008

### Redbelly98

Staff Emeritus
I'm going to have to wait until your attachment is approved, and I can look at the diagram, before commenting further.

13. Dec 8, 2008

### tiny-tim

tweety1234, just look at your own diagram (which Redbelly … hi Redbelly98! seems to have missed) …

between what two points do you think there is a distance of x-3?

General hint: whenever you draw a diagram, give letters to all the points on it, so that you can talk about them later …

in this case, call the woman's position W, and the centre of mass C …

and then decide what two points you want to measure the distance between.