# What is the speed of the chain at this instant?

• fball558
In summary, a chain with a mass of 6 kg is coiled up on a low-friction table. When a constant force of 69 N is applied to one end, the chain straightens out to a length of 1.0 m and is pulled a total distance of 3.6 m. The speed of the chain is 8.4439 m/s and the change in energy is 248.4 joules. To solve for the change in thermal energy, the formula used was Ef = Ei + W + Q, where Q represents thermal energy. After solving for Q, the correct formula is to subtract the final kinetic energy from the change in energy, resulting in a thermal energy of 1.161
fball558

## 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.

before this question i have already answered these questions. might need the info to solve not sure though.

(a) Consider the point particle system:
What is the speed of the chain at this instant?
8.4439 m/s

Consider the real system:
What is the change in energy of the chain?
delta(E) = 248.4 joules

## The Attempt at a Solution

i solved conservation of energy like
Ef = Ei + W + Q
then
Ef = 248.4 + Q where Q = 0
then
final Ke + Ethermal = 248.4
solved for Ethermal = 248.4 / Ke or 248.4/(1/2mv^2) using v found above
i get 1.1613 J but that is wrong. where did i mess up??

Last edited:
solved for Ethermal = 248.4 / Ke or 248.4/(1/2mv^2) using v found above
i get 1.1613 J but that is wrong. where did i mess up??

Instead of dividing by Ke...You have to subtract by Ke.

haha i need to go back to basic math.
thanks sriceb01
and welcome to the forums.
this site is great!

## 1. What is meant by "speed of the chain at this instant?"

The speed of the chain at this instant refers to the instantaneous speed or velocity of the chain at a specific moment in time. It is the rate at which the chain is moving or changing position at that exact moment.

## 2. How is the speed of the chain at this instant calculated?

The speed of the chain at this instant can be calculated by dividing the change in position of the chain by the change in time. This is known as the average speed formula: speed = distance/time. However, to determine the speed at an exact instant, we would need to use calculus to find the derivative of the position function with respect to time.

## 3. Can the speed of the chain at this instant change?

Yes, the speed of the chain at this instant can change depending on the forces acting on the chain. If there are no external forces, the speed will remain constant. However, if there are forces such as friction or tension, the speed can change at any given instant.

## 4. What factors can affect the speed of the chain at this instant?

The speed of the chain at this instant can be affected by various factors such as the length and weight of the chain, the forces acting on the chain, and the medium in which the chain is moving (e.g. air, water, etc.). Additionally, factors like the shape and surface of the chain can also impact its speed.

## 5. Why is it important to know the speed of the chain at this instant?

Knowing the speed of the chain at this instant is important for understanding the dynamics of the system in which the chain is a part of. It can also help in predicting the behavior of the chain and identifying any potential issues or risks. Additionally, the speed of the chain at this instant may be needed for further calculations or experiments.

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