(Center of Mass) How much the skater walked?

In summary, the two skaters, one of 65kg and the other of 40kg, pulled each other with a rope of 10 meters until they reached a final position where the center of mass remained at 3.8 meters from the first skater. This means that the 40kg skater walked a distance of 6.2 meters from their initial position.
  • #1
frank1
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=>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,
 
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  • #2
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?
 
  • #3
Hi frank! :smile:

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?
 
  • #4
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
 
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  • #5
frank1 said:
=>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?
 

1. What is the definition of "center of mass"?

The center of mass is the point where the entire mass of an object can be considered to be concentrated. It is the point around which the object's mass is evenly distributed in all directions.

2. How is the center of mass calculated?

The center of mass is calculated by finding the average position of all the individual mass elements that make up the object. This can be done by taking into account the mass, position, and distance from a reference point of each element.

3. How does the center of mass affect the movement of a skater?

The center of mass plays a crucial role in the stability and movement of a skater. If the skater's center of mass is not positioned correctly, it can result in a loss of balance and cause falls. The skater must constantly adjust their center of mass to maintain balance and execute different skating maneuvers.

4. Can the center of mass be outside of the body?

Yes, the center of mass can be located outside of an object's physical boundaries. This is common in objects with irregular shapes or objects that are connected to other objects. In the case of a skater, their center of mass can be located outside of their body when they extend their limbs or jump.

5. How does the distance the skater walks affect their center of mass?

The distance the skater walks does not directly affect their center of mass. However, as the skater moves, their center of mass will shift accordingly. For example, when a skater walks, their center of mass will move with them, but the overall position of the center of mass will remain the same unless there are changes in the skater's body position.

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