Center of gravity of a dancer

In summary, the initial y coordinate of the center of gravity of the dance floor and three couples is 12.34 m. The new x coordinate of the center of gravity after the couple in the bottom left corner moves 10 m to the right is 9.5 m.
  • #1
lilaznjewel
13
0

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
 
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  • #2
lilaznjewel said:

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)? +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. Your method is OK, although it is a bit cumbersome.
 
  • #3
omg I am so stupid. Thank you for pointing out my mistake!
 

What is the center of gravity of a dancer?

The center of gravity of a dancer is the point in their body where the force of gravity acts upon them. It is the average location of all the mass in their body.

How does a dancer's center of gravity affect their balance?

The location of a dancer's center of gravity is crucial to their balance. If their center of gravity is not aligned with their supporting base, they may struggle to maintain their balance and execute certain movements.

Can a dancer change their center of gravity?

Yes, a dancer can change their center of gravity by shifting their weight or changing their body position. They can also train to improve their core strength and control, which can help them better manage their center of gravity.

Does the center of gravity affect a dancer's performance?

Yes, the center of gravity can greatly impact a dancer's performance. A well-controlled and properly aligned center of gravity can enhance their movements and make them appear more fluid and effortless.

How can a dancer use their center of gravity to their advantage?

A dancer can use their center of gravity to create different effects in their performance. By shifting their weight, they can create dynamic movements and enhance their balance and control. They can also use their center of gravity to create illusions and create the illusion of floating or defying gravity.

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