A chain of metal links with total mass m = 6 kg is coiled up in a tight ball on

Question

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 = 3.0 m (diagram is not to scale).

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

(b) Consider the extended system:
What is the change in energy of the chain?
E =  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.
Ethermal =  J

Explanation / Answer

a)Thw work done in straightening of the chain by F will be:

Work done = Force x distance

distance in this case would be:

D = d - L/2 = 3 - 1/2 = 2.5 m

W = F x D = 69x 2.5 = 172.5 J

This Workdone gets converted to the KE of the system, so

1/2 m v^2 = W = 172.5 J

v = sqrt ( 2 x 172.5/ 6) = 7.57 m/s

Hence, v = 7.57m/s

b)The change in energy will be:

(Delta)E = F x d = 69 x 3 = 207 J

Hence, (delta)E = 207 J

c)From energy conservation

(Delta)E = W + Q

Q = (delta)E - W

Q = 207 - 172.5= 34.5 J

Hence, Q = 34.5 J

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