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

In summary, the question is asking for the speed of a chain that is pulled with a constant force of 69 N, starting at a coiled up position with a total mass of 6 kg. The chain straightens out to a length of 1.0 m and is pulled a total distance of 3.6 m. To find the speed, the equation sqrt((2FA)/M) can be used, where F is the force, A is the change in center of mass, and M is the mass. The center of mass can be found by determining the end points of the chain after it is pulled, which are at 3.6 m and 4.6 m.
  • #1
fball558
147
0
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
 
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  • #2


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?
 
  • #3


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.
 
  • #4


Keep in mind that the force is not acting on a constant mass (the entire chain is not moving at the start).
 
  • #5


fball558 said:
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?
 
  • #6


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.
 

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

What is the speed of a chain?

The speed of a chain refers to how quickly the chain moves from one point to another. It is typically measured in meters per second or kilometers per hour.

How is the speed of a chain calculated?

The speed of a chain can be calculated by dividing the distance traveled by the time it takes to travel that distance. For example, if a chain travels 10 meters in 2 seconds, its speed would be 5 meters per second.

What factors can affect the speed of a chain?

The speed of a chain can be affected by various factors such as the tension of the chain, the weight of the chain, the surface it is moving on, and any external forces acting on the chain.

Can the speed of a chain be increased?

Yes, the speed of a chain can be increased by reducing its weight, increasing its tension, or reducing friction between the chain and the surface it is moving on. However, there may be limitations based on the materials and design of the chain.

What is the significance of knowing the speed of a chain?

Knowing the speed of a chain can help in various applications such as transportation and manufacturing. It can also help in understanding the performance and limitations of different types of chains, and in optimizing their design for specific purposes.

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