# How Does Pulling a Chain Affect Its Thermal Energy?

• soccerguy
In summary, a chain of metal links with a mass of 7 kg is coiled up on a low-friction table. When pulled with a constant force of 52 N, the chain straightens out to a length of 0.8 m and is pulled a total distance of 3.2 m. The speed of the chain is 6.45 m/s and the change in energy is 166.4 joules. Due to the rapid straightening process, the chain's temperature increases but there is insufficient time for significant thermal transfer. The increase in thermal energy cannot be calculated without knowing the temperature and heat capacity. However, the kinetic energy of the chain can be calculated using its velocity and the total work done on the
soccerguy

## Homework Statement

A chain of metal links with total mass m = 7 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 = 52 N. Eventually the chain straightens out to its full length L = 0.8 m, and you keep pulling until you have pulled your end of the chain a total distance d = 3.2 m (diagram is not to scale).

(a) Consider the point particle system:
What is the speed of the chain at this instant?
v = 6.45 m/s>

(b) Consider the real system:
What is the change in energy of the chain?
166.4 joules

(c) In straightening out, the links of the chain bang against each other, and their temperature rises. Assume that the process is so fast that there is insufficient time for significant thermal transfer of energy from the chain to the table, and ignore the small amount of energy radiated away as sound produced in the collisions among the links.
Calculate the increase in thermal energy of the chain.
= J

## Homework Equations

v = sqrt(2 * F * xcm / M)
w = F * d

## The Attempt at a Solution

I calculated the velocity using the v formula with xcm being the change in the center of mass, so 2.8 in my case, and then part (b) by doing 52 * 3.2 since that's how far your hand moved. However, I have no clue how to do thermal energy without a temperature and heat capacity, and my book makes no mention.

Hello Soccerguy,

Welcome to Physics Forums!
soccerguy said:
I calculated the velocity using the v formula with xcm being the change in the center of mass, so 2.8 in my case, and then part (b) by doing 52 * 3.2 since that's how far your hand moved. However, I have no clue how to do thermal energy without a temperature and heat capacity, and my book makes no mention.
(i) What is the kinetic energy of the chain (based on its velocity)?
(ii) What is the total work done on the chain? (Hint: you've already solved this in part b)
(iii) What's the difference between the total work done, and the kinetic energy of the chain?

If not all the work done went into the chain's kinetic energy, and there wasn't a change in potential energy, the remainder must have become what kind of energy...?

Sweet thank you :)

## 1. What is thermal energy of a chain?

Thermal energy of a chain refers to the amount of heat energy that is present within a chain or a series of interconnected bodies.

## 2. How is thermal energy of a chain measured?

Thermal energy of a chain can be measured in units of joules (J) using various methods such as calorimetry or thermodynamics formulas.

## 3. What factors affect the thermal energy of a chain?

The thermal energy of a chain is affected by factors such as the length of the chain, the type of material the chain is made of, and the temperature at which the chain is exposed to.

## 4. What is the relationship between thermal energy and temperature of a chain?

The thermal energy of a chain is directly proportional to the temperature at which the chain is exposed to. As the temperature increases, so does the thermal energy of the chain.

## 5. Why is understanding thermal energy of a chain important?

Understanding thermal energy of a chain is important in various fields of science such as thermodynamics and materials science. It helps in predicting the behavior of materials and determining their properties under different temperatures.

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