# position vector

• Apr 28th 2007, 10:41 PM
position vector
Hey All,

How do you solve these two similar questions,

1) point masses 2g, 4g, 5g ang 1g are situated at points A, B, C and D with the position vector 3i -4j, -i + 5j, i +7j, and 5i + j respectively. find the position vector of the centre of mass for these four particles.

2) point masses 1g, 2g, and 5g are situated at the points A, B and C, with position vector 2i + j, i + 2j, and i - 3j respectively. find the position vector of the centre of mass for these three particles. If the 1g and 2g masses have their positions swapped, what is the consequent change in the x position of the centre of mass.

Thank you
• Apr 29th 2007, 12:03 AM
CaptainBlack
Quote:

Hey All,

How would you solve these two similar questions,

1) point masses 2g, 4g, 5g ang 1g are situated at points A, B, C and D with the position vector 3i -4j, -i + 5j, i +7j, and 5i + j respectively. find the position vector of the centre of mass for these four particles.

2) point masses 1g, 2g, and 5g are situated at the points A, B and C, with position vector 2i + j, i + 2j, and i - 3j respectively. find the position vector of the centre of mass for these three particles. If the 1g and 2g masses have their positions swapped, what is the consquent change in the x position of the centre of mass.

Thank you

The centre of mass of massess m_1, m_2, .., m_n situated at v_1, v_2, ..., v_n is:

V = [sum_{r=1 to n} m_r*v_r]/[sum_{r=1 to n} m_r]

RonL
• Apr 29th 2007, 05:06 AM

I'm still confused on what you have to do.
• Apr 29th 2007, 07:53 AM
CaptainBlack
Quote:

I'm still confused on what you have to do.

You take the weighted sum of the position vectors, with weights equal
to the masses of the particles at each position divided by the total mass.

For 1) this is:

[2*(3i -4j) + 4*(-i + 5j) + 5*(i +7j) + 1*(5i + j)]/[2 + 4 + 5 + 1]

...... = {[2*3 - 4*1 + 5*1 + 1*5]*i + [-2*4 + 4*5 + 5*7 +1]*j}/12

...... = i + 4 j

RonL
• May 1st 2007, 01:33 PM
so using ur method the answer to question 2)

point masses 1g, 2g, and 5g are situated at the points A, B and C, with position vector 2i + j, i + 2j, and i - 3j respectively. find the position vector of the centre of mass for these three particles.

=(9i -10j) / 8

is this correct?

and how do you answer this for the same question;

If the 1g and 2g masses have their positions swapped, what is the consequent change in the x position of the centre of mass.

Thanks
• May 1st 2007, 01:55 PM
CaptainBlack
Quote:

so using ur method the answer to question 2)

point masses 1g, 2g, and 5g are situated at the points A, B and C, with position vector 2i + j, i + 2j, and i - 3j respectively. find the position vector of the centre of mass for these three particles.

=(9i -10j) / 8

is this correct?

Yes

Quote:

and how do you answer this for the same question;

If the 1g and 2g masses have their positions swapped, what is the consequent change in the x position of the centre of mass.

Thanks
NewCofM = [2(2i+j) + 1(i+2j) + 5(i-3j)]/8 = (10i - 11j)/8

Therefore the change in position of the centre of mass is:

(10i - 11j)/8 - (9i -10j) / 8 = (i - j)/8

RonL