Thermodynamical conservation of energy?

[Gavroy]

Homework Statement

There is a tower and a heavy box in it, which weighs 20.000 kg. This box falls down from 70m and after falling 40m(free fall), she is slowed down by magnets on the surface of the box, which interact after falling 40m with copper plates on the tower, which weigh 2.000kg. Then 2 m high, the velocity of the box is 2,77 m/s. Now the question is: What is the change in temperature for the copper plates? Of course friction is neglected!
m1=20.000kg
h1=70m
h2=2m
v=2,77m/s
c(Copper)=385 J/(kg*K)
m2= 2.000kg

The Attempt at a Solution

Now I thought about solving this by using the law of conservation of energy, since the potential energy at the beginning is equal to the potential energy at the end+ the kinetic energy the box has+the heat that is absorbed by the copper plates:
$$m1 g h1=1/2 m v²+m2 g h2+ m2 c T$$

But in this case, it would not matter, that the slow down process, does not start until the box has covered these 40m and this information would be redundant. So I think my approach is wrong, but I have no idea, what I am actually doing wrong. Can you help me, please?

 

[nickjer]

You sound right to me. Conservation of energy should work in this problem. Maybe the 40m was thrown in there to confuse people. Or maybe I am too tired and I am misreading something :)

The only reason the height at which the mag field is turned on would make any difference is in the power (the rate at which the energy is lost). Which doesn't seem to be needed for this problem.

 

[Gavroy]

thanks for your reply! I will try it this way now.
and otherwise, maybe someone has an idea, why these 40m are important, because our teacher has never given us an information, that is not needed to solve the problem.

 

[Mindscrape]

Hmm, I don't know if I quite understand the full situation going on here. It depends on how the box is being slowed down. Is it being slowed down purely due to a magnetic interaction, that there is a magnet on the ground for example, then all forces are conservative and the 40m height doesn't matter. If, on the other hand, the box slows down due to electromagnetic induction, this is how the tower roller coasters brake for example, then that is a non-conservative force akin to friction. I think you can say that all the energy goes into ohmic heating, and you're back on track with accounting for all energy in your energy conservation. However, in the electromagnetic induction case, the heat energy term doesn't come in effect until it is 30m from the ground, and you definitely want to factor that aspect in.

 

[Gavroy]

Yes, I think you are right, it must be induction, cause there is no other magnet.
But how can I calculate the heat in this case? Can you help me?

 

[Mindscrape]

If you know the energy at the start of the 30m, and the energy at 2m, you can use conservation of energy just how you outlined it before, at least given that the only extra energy we need to account for is heat. The way you were doing it would be right in this case if you first look at the energy to get to that midpoint

start = mid
U = Um + KEm
mid = end
Um + KEm = Ue+KEe+Q
=>U=Ue+KEe+Q

 

[Gavroy]

But this is equal to that what I have written, isn't it?

 

[Mindscrape]

Yeah, it looks good to me given some assumptions. I just brought up the electromagnetic induction concept because you seemed doubtful about what you were doing. I still don't know if that is a valid assumption to make, that almost all the energy lost is going to heat, so you that's why I placed my stamp of uncertainty on it all.