# Center of mass of concrete wall

In summary, the center of mass of a silo containing a 2000kg load of hay at 800kg/m^3 is located at 3.17m above the base.

## Homework Statement

A cylin drical con crete sil o is 4m in diameter and 30m high. it consists of a 6000kg concreet base and a 38000kg concrete cylindrical concreete walls. locate the center of mass of the silo (A) when it's empty and (B) when it is two thrids full of silage whose density is 800kg/m^3. neglect the thickness of the silo walls and base.

## The Attempt at a Solution

Part A

6000kg*y = 38000kg (.5(30m) - y)
y = 12.95 m
or
Center of mass is the y direction is 13m high and in the middle of the silo

Part B

Volume = 2m^2*PI*20m = 251.327 m^3

Mass = 251.327 m^3 * 800 kg / m^3

= 201062 kg

h of grain = 20m

201062kg*y = 38000kg*(20m -y)

6.29*y = 20m

y= 3.17m

the real question is part B i don't think that makes sense...

Always draw a picture!

201062kg*y = 38000kg*(20m -y)

This line is wrong.

Always draw a picture so that you don't get confused.

You'll see you have the (20m - y) in the wrong place.

And you've left out the base, for which you need to use Part A's answer.

tiny-tim said:
This line is wrong.

Always draw a picture so that you don't get confused.

You'll see you have the (20m - y) in the wrong place.

And you've left out the base, for which you need to use Part A's answer.

i have a picture, i usualy upload a paint picture for you guys, but didnt this time, and the x direction is obvious, for x direction, Center of mass is the y direction is 13m high and in the x direction it is in the middle of the silo (1/2 the diameter)

6000+(201062kg*(20*.5-y)) = 38000kg*(.5*30m - y)

y= 8.87m
i like that answer a lot

ycm = 8.87 m
xcm = 2m (or right in the middle however you look at it)

Last edited:
anyone verify this?

don't do a balancing equation - choose a baseline

6000+(201062kg*(20*.5-y)) = 38000kg*(.5*30m - y)

y= 8.87m

(oops! I just meant draw a picture for yourself … there's no need to draw one for the forum if the question is clearly worded. )

Your picture is very artistic, but you really need to spoil it (!) by marking the positions of the centres of gravity of the base the walls and the silage, with the weights of each next to them.

The advantage in this case is that you would have seen that the c. of g. of the silage is at 10m, and (from Part A) that of the rest is at 12.95m - so the overall c. of g. must be somewhere in between!

Have you been taught always to do a "balancing" equation about the expected position, y?

If so, I suppose you'd better carry on doing what the teacher says, only more carefully.

But if not, stop doing it, especially when you have more than two items to balance - there's too much risk of putting one on the wrong side - which is what you've done!

Choose whatever baseline which makes the calculation easiest - in this case, choose the level of the base, for two reasons:
(a) it makes one of the items zero, which always shortens the calculation!

(b) height above the base is the answer you want anyway.

For example, the calculation for Part A would be y = 38000*15/(38000 + 6000) = 12.95, as you said . Isn't that both easier and more intuitive?

Now try it for Part B!

38000*15 + 201062*10 / (3800+6000+201062)

10.53m

thankyou!

Last edited:
You're very welcome!

[size=-2](don't forget to mark thread "solved"!)[/size]​

## 1. What is the center of mass of a concrete wall?

The center of mass of a concrete wall is the point at which the weight of the wall is evenly distributed in all directions. It is also known as the centroid or balance point of the wall.

## 2. How is the center of mass calculated for a concrete wall?

The center of mass of a concrete wall is calculated by finding the average position of all the individual particles that make up the wall. This is done by dividing the total mass of the wall by the total volume and taking into account the distribution of density within the wall.

## 3. Why is the center of mass important for a concrete wall?

The center of mass is important for a concrete wall because it determines the stability and balance of the wall. If the center of mass is not located within the base of the wall, it can lead to tipping or collapse.

## 4. Can the center of mass of a concrete wall change?

Yes, the center of mass of a concrete wall can change if the wall is altered or if additional weight is added or removed from the wall. However, the center of mass will always be located within the base of the wall.

## 5. How can the center of mass of a concrete wall be used in construction?

The center of mass of a concrete wall can be used in construction to determine the placement of support structures and to ensure the stability of the wall. It can also be used to calculate the amount of force that the wall can withstand before tipping or collapsing.