How Does Dancer Movement Affect the Center of Gravity on a Dance Floor?

[lilaznjewel]

Homework Statement

Given: A flat dance floor of dimensions ℓx =
19 m by ℓy = 23 m and has a mass of M =
1600 kg. Use the bottom left corner of the
dance floor as the origin. Three dance couples,
each of mass m = 150 kg start in the top left,
top right, and bottom left corners.
What is the initial y coordinate of the cen-
ter of gravity of the dance floor and three
couples?
Answer in units of m.

The couple in the bottom left corner moves
ℓx = 10 m to the right. What is the new x
coordinate of the center of gravity?

Homework Equations

xcm =
m1x1 + m2x2/
m1 + m2

The Attempt at a Solution

for the first part I did 1600(y-11.5)+150(y-23)+150(y-0)+150(y-23)=0
and solved for y and I got 12.34
and I got it right

my problem is I did the exact same thing for the next part just you know used the X coordinates and moved (0,0) to (10,0)
1600(x-8)+150(x-0)+150(x-10)+150(x-19)=0
I came out with 8.366
but my online homework says that answer is incorrect I don't know why isn't it basically the same question but with a different number

 

[PhanthomJay]

Homework Statement

Given: A flat dance floor of dimensions ℓx =
19 m by ℓy = 23 m and has a mass of M =
1600 kg. Use the bottom left corner of the
dance floor as the origin. Three dance couples,
each of mass m = 150 kg start in the top left,
top right, and bottom left corners.
What is the initial y coordinate of the cen-
ter of gravity of the dance floor and three
couples?
Answer in units of m.

The couple in the bottom left corner moves
ℓx = 10 m to the right. What is the new x
coordinate of the center of gravity?

Homework Equations

xcm =
m1x1 + m2x2/
m1 + m2

The Attempt at a Solution

for the first part I did 1600(y-11.5)+150(y-23)+150(y-0)+150(y-23)=0
and solved for y and I got 12.34
and I got it right

my problem is I did the exact same thing for the next part just you know used the X coordinates and moved (0,0) to (10,0)
1600(x-8)why are you using 1600(x-8)? Shouldn't it be 1600(x-9.5)?[/color] +150(x-0)+150(x-10)+150(x-19)=0
I came out with 8.366
but my online homework says that answer is incorrect I don't know why isn't it basically the same question but with a different number

see correction above[/color]. Your method is OK, although it is a bit cumbersome.

 

[lilaznjewel]

omg I am so stupid. Thank you for pointing out my mistake!