How Does Pulling a Chain Affect Its Thermal Energy?

[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 * x_cm / M)
w = F * d

The Attempt at a Solution

I calculated the velocity using the v formula with x_cm 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.

 

[collinsmark]

Hello Soccerguy,

Welcome to Physics Forums!

I calculated the velocity using the v formula with x_cm 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...?

 

[soccerguy]

Sweet thank you :)