M2 centre of mass question Watch

sulexk
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Three uniform rods AB, BC and AC are of length 3m, 4m and 5m have masses 5kg, 4kg and 3kg respectively. They are joined to make a framework. Calculate the distance of the Centre of mass of the framework (a) from AB (b) from BC.

This question is different from the others in that each bar has a different mass per unit length. How do I tackle this one?

I have tried using 5/3 kg cm^-1 and 4/4 kg cm^-1 and 3/5kgcm^-1, But it does not work.

I did use the standard lengths and it worked- simply using the lengths- but how can I ignore the masses?

thank you
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Thrug
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Try sketching the diagram,

then take moments about AB and BC.

Remember the rods are uniform so the weights are in the middle of each rod.
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sulexk
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I donot understand how to take moments like that in this case due to the mass per unit length difference?
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Thrug
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(Original post by sulexk)
I donot understand how to take moments like that in this case due to the mass per unit length difference?
Ok imagine a uniform horizontal rod, 3m length of 5kg.

Lets take moments about A which is the left hand side of the rod. As it is uniform the 5g will act directly in the middle. This is 1.5m away from A, so its 1.5*5.

As all the rods are uniform their masses act in the middle of the rods. So when you work out the distances you just times it by the different masses.

I am not sure why you can do it when they have the same mass but can't do it when the masses are different.
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sulexk
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(Original post by Thrug)
Ok imagine a uniform horizontal rod, 3m length of 5kg.

Lets take moments about A which is the left hand side of the rod. As it is uniform the 5g will act directly in the middle. This is 1.5m away from A, so its 1.5*5.

As all the rods are uniform their masses act in the middle of the rods. So when you work out the distances you just times it by the different masses.

I am not sure why you can do it when they have the same mass but can't do it when the masses are different.

So we use the lengths to calculate where the centre of mass is. and then use the masses in calculating the moments.

But because usually we have rods with the same mass per unit length we donot need to do this?
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Thrug
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(Original post by sulexk)
So we use the lengths to calculate where the centre of mass is. and then use the masses in calculating the moments.

But because usually we have rods with the same mass per unit length we donot need to do this?
Well I don't know how you were working it out before but it should always be how far is centre of mass (at right angles) * mass of rod.

Post the question and show your working.
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sulexk
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Well I use the table separate masses || Total mass

But in this case what would I do?


When I use the masses I obtain the correct answer but why do I get the right answer?
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