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
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
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
Yes
NewCofM = [2(2i+j) + 1(i+2j) + 5(i-3j)]/8 = (10i - 11j)/8and 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
Therefore the change in position of the centre of mass is:
(10i - 11j)/8 - (9i -10j) / 8 = (i - j)/8
RonL