Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Centre of mass question

Well a new term means a new set of mechanics questions and this one has me completely stumped, because it's nothing like anything I've seen before:

Particles of mass 2 kg, 3 kg and p kg are placed at points whose coordinates are (1,3), (4,6) and (7,-8) respectively. Given that the centre of mass of these particles lies on the x-axis, find p.

I've done centres of mass of laminae, centres of mass of wire shapes, centre of mass of hanging objects and centre of mass of laminae and wire shapes with weights on various ends, but I don't understand, is this a wire shape? And if so, perhaps a little jog of my memory would help me here

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Centre of mass question

Hi Au101;

This is highly experimental, last time I did one of these it was for the emperor Napoleon. I am getting p = 3.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Centre of mass question

Hehehe .

Well the answer book agrees with you .

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Centre of mass question

Vector of x's.

Vector of y's.

Vector of masses.

Dot product the x vector and the m vector and divide by the sum of the masses ( sum of the m  vector)

Dot product the y vector and the m vector and divide by the sum of the masses.

Solve the simultaneous set for x and 0 ( remember the point is on the x axis so y = 0 )

P = 3 and the COM is at ( 35 / 8 , 0 ).

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Centre of mass question

Ahhh thanks!:)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Centre of mass question

Hi;

Here is a nice page that might help.

http://cnx.org/content/m14119/latest/

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Centre of mass question

Hi again Bobbym, sorry it's been a while, thanks for the link, it's very nicely illustrated.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Centre of mass question

Hi Au101;

You have to look for it but it does this problem for 2 points. It is simple to apply it to 3 points

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.