Moments-calculate centre of mass

[tweety1234]

Homework Statement

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.

Homework Equations

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)

http://www.mathhelpforum.com/math-help/attachments/advanced-applied-math/9167d1228774308-mechanics-help-untitled.jpg

 

[tiny-tim]

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

Hi tweety1234!

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

it should be … ?

 

[Redbelly98]

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.

 

[tweety1234]

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.

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 don't get the right answer?

 

[tweety1234]

should it be x-4 instead? Cause there's 1 meter in between x and A

 

[tiny-tim]

should it be x-4 instead? Cause there's 1 meter in between x and A

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

x is … ?

 

[tweety1234]

Hi tweety1234!

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

it should be … ?

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

 

[tweety1234]

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

x is … ?

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

thank you!

 

[Redbelly98]

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

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

 

[Redbelly98]

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

thank you!

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

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

 

[tweety1234]

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

if i want to work out the distance won't i have to minus 3 meters?

 

[Redbelly98]

... my moments equation is..

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

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

 

[tiny-tim]

if i want to work out the distance won't i have to minus 3 meters?

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.