# Centre of gravity for multiple objects

• aab234
In summary, the conversation discusses calculating the distance of the centre of gravity from support A for a framework containing 4 crates at 52kg each. The individual's answer was 3.8m, but after further analysis and correction of a mathematical error, the correct answer is 5.25m. The conversation also emphasizes the importance of using diagrams in physics and relying on the balance-point rule rather than solely remembering equations.
aab234
Hi. This is my first post so apologies if I do anything wrong.

I have a homework question.

*calculate the distance of the centre of gravity from support A for a framework containing 4 crates at 52kg per crate.

I'll describe the diagram:

A is on the far left. 3m from A are 2 crates stacked on each other (so 104kg), 6m from A there is another crate, then another crate at 9m from A.
I'm disregarding support B at 12m from A.

My answer is that as the crates ate the same mass, we'll call them m.
I'll use x as the unknown distance I'm looking for. So:

3 (2m) + 6 (m) + 9 (m)

19m = 5mx
x = 3.8m

So the centre of gravity is 3.8m from point A.
Am I correct?

As I've seen pop up a few times on here I'm studying with ICS and they're...a little lacking in quality educational material so I've had to work it out on my own so if I'm shockingly incorrect a point in the right direction would be great.

Thanks.

Welcome to PF;

All masses are in a line? ... imagine they are sitting on a beam and don't worry about the supports for now.
The center of gravity is the position x where you would put a pivot and the beam would balance.

x=3.8m is 0.8m to the right of the 2 stacked crates ... a single crate 1.6m on the other side would balance it, but you have two crates much further away than that so the whole thing tips over clockwise.

If you sketch it out to scale and draw in a pivot at your value for x, you intuition should tell you the same. The same intuition should give you an idea of where the pivot should go, which will tell you if your maths comes out right.

You analyzed it pretty OK, but you have to do the math correctly. The left hand side of your equation should be 21m, and the right hand side should be 4mx (you only had 4 crates, not 5).

Incidentally, Welcome to Physics Forums!

Chet

Doh! Maybe I should learn to add up first. Sigh...

So let's try that again.
3 (2m) + 6 ( m ) + 9 ( m )
21m = 4mx
x = 5.25

I've drawn a diagram and 5.25 metres from A as a fulcrum looks like it world balance so I think this is right.

Thanks for the help guys. I'll return the favour one day, when I've learned to add up obviously. How embarrassing.

*Would balance.

Seems I can't spell either. Not my finest hour I have to say.

2am effect? - have another coffee ;)
I've drawn a diagram and 5.25 metres from A as a fulcrum looks like it world balance so I think this is right.
... diagrams are the backbone of physics :)

If you rely too much on remembering equations, you cna get tied up in simple mistakes like this.
If you remembered about the balance-point rule, that wouldn't happen. Also you would not need to memorize the equation. Just remember that the sum of the moments must be zero.

## 1. What is the definition of centre of gravity for multiple objects?

The centre of gravity for multiple objects is the point at which the entire weight of a system can be considered to act. It is the average location of the weight distribution of all the individual objects in the system.

## 2. How is the centre of gravity calculated for multiple objects?

The centre of gravity can be calculated by finding the weighted average of the individual objects' positions. This involves multiplying each object's weight by its distance from a reference point and then dividing the sum of these products by the total weight of the system.

## 3. Does the shape of the objects affect the centre of gravity for multiple objects?

Yes, the shape of the objects does affect the centre of gravity. Objects with more weight distributed toward the edges will have a higher centre of gravity compared to objects with weight more evenly distributed throughout their shape.

## 4. What is the importance of the centre of gravity for multiple objects in physics?

The centre of gravity is important in physics because it helps determine the stability and balance of a system. It is also used in the study of forces and motion, as the location of the centre of gravity can affect how an object behaves when subjected to external forces.

## 5. Can the centre of gravity for multiple objects change?

Yes, the centre of gravity can change if the weight distribution of the individual objects in the system changes. For example, if an object is added or removed from the system, the centre of gravity will shift accordingly. Additionally, changes in the position or orientation of the objects can also affect the centre of gravity.

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