# Change in energy for a balled up chain

1. Dec 9, 2011

### phoenix133231

1. The problem statement, all variables and given/known data
A 1.1 m, 4 kg chain is wrapped up in a ball. You grab one of the ends of the chain and apply a constant force of 59 N and it begins to unwrap. When you pull your end of the chain 3.9 m, the chain is completely loose.
a) Find the change in energy of the system, before unraveling to when it is completely loose.
b) Find the change in thermal energy of the system, if you know that the links of the chain are banging against each other while you unravel the chain.

2. Relevant equations
F = m*a
T = 1/2*m*v^2

3. The attempt at a solution
a) So, I begin by finding the velocity of the chain after it is unraveled, by first finding the acceleration. So, 59 N = (4kg)(a) which gives me 14.75 m/s^2.

Then, using the kinematics equation, v^2 = v_i^2 + 2ax, I find that the velocity is...
v = sqrt(2*14.75m/s^2*4.45m) which is approximately 11.5 m/s.

Finally, the kinetic energy is going to be .5(4kg)(11.5m/s)^2 = 264.5 J.

But my dilemma is... I don't know what the initial energy is... if there even is any. I stated that the energy of the chain, when it was wrapped in a ball, is 0 J, since it's not moving, it doesn't have kinetic energy, and there's no height difference, so there's no potential energy. Is my reasoning correct?

Thus, change in energy = 264.5 J - 0 = 264.5 J?

b) Again, the change in thermal energy would be 0 - 264.5 J = -264.5 J, since there's initially thermal energy but no thermal energy when it's moving and loose?

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