Determining Speed of a Chain: Calculating for a Point Particle System

[fball558]

speed of chain??

Homework Statement

A chain of metal links with total mass M = 6 kg is coiled up in a tight ball on a low-friction table. You pull on a link at one end of the chain with a constant force F = 69 N. Eventually the chain straightens out to its full length L = 1.0 m, and you keep pulling until you have pulled your end of the chain a total distance d = 3.6 m.

Consider the point particle system:
What is the speed of the chain at this instant?

Homework Equations

sqrt((2FA)/M) where F is force (69 n)
A is change in center of mass aka center of mass final - center of mass inital (this is where I am having some troubles)
M is mass (6 kg)

The Attempt at a Solution

i not sure what A is for this equation. i tried 3 different ways as followes and i am wrong all 3 times

first
i figured that it would be 3.6 becuae it moved this far when i do the formula i get
9.09945

then i figured 3.6 + 1.0 (from length of chain) use formula using 4.6
and get 10.28591

finally i did half of length plus the 3.6 distance to get 4.1
did formula and got 9.7101

all these are wrong and I am out of ideas if you have one let me know
thanks

 

[Doc Al]

Draw yourself a before and after diagram. If the chain starts out balled up at x = 0, what are the coordinates of the ends of the chain after pulling it the stated distance?

 

[fball558]

I really don't need to know the end points of the chain do i?
the A in the equation is for the center of mass. you compare its
final position to its inital.
so its inital is 0.
final would be 4.1
here is how i get that.
the ball stretched out will start at 0 then go to 1. the center (A) would be at .5. then you move (A) a distance of 3.6 which means the (A) would be at 4.1.
the left side would be at 3.6 and the right side would be at 4.6
but when i did the equation with 4.1 it said the answer was wrong.

 

[BAnders1]

Keep in mind that the force is not acting on a constant mass (the entire chain is not moving at the start).

 

[Doc Al]

I really don't need to know the end points of the chain do i?

Understanding where the end points of the chain are will help you determine where the center of mass is.

the A in the equation is for the center of mass. you compare its
final position to its inital.
so its inital is 0.
final would be 4.1
here is how i get that.
the ball stretched out will start at 0 then go to 1. the center (A) would be at .5. then you move (A) a distance of 3.6 which means the (A) would be at 4.1.

This is incorrect. Think this way: You grab one end of the chain (when it's at x=0) and you pull that end a distance of 3.6 m. So where is that end of the chain? Where's the other end? Where's the center of mass?

 

[fball558]

thanks guys. i was reading the problem as if the chain straightens the 1 m first then you move it the 3.6 so actually moving it 4.6. just need to learn how to read haha
thanks again for all the help.