(Center of Mass) How much the skater walked?

[frank1]

=>Two skaters, one of 65kg e another of 40kg, are in a ice stadium and are holding the extremities of a rope of 10meters of negligible mass. They pull each other until they stay close to each other. What distance the 40kg skater "walked"?

My attempt:
Well, there aren´t external forces acting here, so the center of mass doesn't move... that's the theory but I'm failing when I try to aply this concept.

If I try to find the center of mass I find this number for it: (x1*m1+x2*m2)/(m1+m2)=>(0*65+10*40)/(65+40) =>Center of Mass=3,8m

And now... what is the next step?

Thanks in advance,

 

[Villyer]

When you write multiplication, express it by an '*' as opposed to a '.', I was confused at first where the numbers .65 and 10.4 were coming from.
But your calculated 3.8m is correct.

You stated that the center of mass doesn't move. Since this is true, where must the two skaters be when they meet on the ice?

 

[Infinitum]

Hi frank!

You are right about the absence of external forces. So when the skaters pull each other, at which position would they both finally land up?? Do you now see how much the skaters have moved?

 

[frank1]

Thanks Villyer and Infinitum for the help :)

Well, i think I'm missing some concept here, because see how i understand it: the center of mass doesn't move. The center of mass in the initial situation is in the x=3.8, so in the new situation (skaters face-to-face) it will still be 3.8, but then i'll have two unknow variables, the distance from the skater one to the 3,8 and the distance from the skater of 40kg to the 3,8...

:S

 

[HallsofIvy]

=>Two skaters, one of 65kg e another of 40kg, are in a ice stadium and are holding the extremities of a rope of 10meters of negligible mass. They pull each other until they stay close to each other. What distance the 40kg skater "walked"?

My attempt:
Well, there aren´t external forces acting here, so the center of mass doesn't move... that's the theory but I'm failing when I try to aply this concept.

If I try to find the center of mass I find this number for it: (x1*m1+x2*m2)/(m1+m2)=>(0*65+10*40)/(65+40) =>Center of Mass=3,8m

And now... what is the next step?

Thanks in advance,

That's what you get for using a formula without understanding what it means! You got 3,8 m but what does that tell you?

The answer comes from understanding the meaning of "0" and "10". You multiply the mass of the first person by 0 and the mass of the second person by 10 because you have set up a "coordinate system" in which the first person is at 0 and the second person is at 10. That is, distances are measured from the first person. Your answer "3,8 m" is measured from the first person, the one of mass 64 kg. The person of mass 40 kg moved from "10 m" to "3,8 m". How far was that?