Moments-calculate centre of mass

In summary: Between what two points do you think there is a distance of x-3? :confused: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 … :smile:and then decide what two points you want to measure the distance between. :smile:
  • #1
tweety1234
112
0

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..

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

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

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  • #2
tweety1234 said:
[tex] 56N \times 1m + 42N \times 4m = 98N (xm-3m) [/tex]

Hi tweety1234! :smile:

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

it should be … ? :wink:
 
  • #3
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
Redbelly98 said:
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?
 
  • #5
should it be x-4 instead? Cause there's 1 meter in between x and A
 
  • #6
tweety1234 said:
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 … ? :smile:
 
  • #7
tiny-tim said:
Hi tweety1234! :smile:

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

it should be … ? :wink:

x represents the distance from point A , were the weight of the plank lies. so should it not be x-3 ?
 
  • #8
tiny-tim said:
No, there's 1 metre in between the woman and A.

x is … ? :smile:

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

thank you!
 
  • #9
tweety1234 said:
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?
 
  • #10
tweety1234 said:
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.
 
  • #11
Redbelly98 said:
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?
 
  • #12
tweety1234 said:
... my moments equation is..

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

I'm going to have to wait until your attachment is approved, and I can look at the diagram, before commenting further.
 
  • #13
tweety1234 said:
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! :smile: seems to have missed) …

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

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. :smile:
 

1. What is the definition of centre of mass?

The centre of mass is the point at which the mass of an object is evenly distributed in all directions. It is the average position of all the mass in an object.

2. How is the centre of mass calculated?

The centre of mass is calculated by taking the sum of the product of each mass element and its position, divided by the total mass of the object. This can be represented by the formula: xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn), where xcm is the centre of mass, m is the mass, and x is the position in the x-axis.

3. Why is it important to calculate the centre of mass?

The centre of mass is important because it helps determine the stability and motion of an object. It is also used to analyze the energy and momentum of a system, and can help in designing structures and machines to ensure balance and safety.

4. Can the centre of mass be outside of an object?

Yes, the centre of mass can be outside of an object. This is often the case for irregularly shaped objects or objects with unequal distribution of mass. In such cases, the centre of mass may be located at a point outside of the physical boundaries of the object.

5. How does the distribution of mass affect the centre of mass?

The distribution of mass affects the centre of mass by shifting its position. Objects with a higher concentration of mass in one area will have a centre of mass closer to that area. On the other hand, objects with a more uniform distribution of mass will have a centre of mass closer to the geometric centre of the object.

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