A 10-kg iron ball is dropped onto a pavement from a height of 100 m. Suppose half of the heat generated goes into warming the ball. Show that the temperature increase of the ball is 1.1oC. (In SI units, the specific heat capacity of iron is 450 kJ/kg*oC.) Why is the answer the same for an iron ball of any mass?
Thanks for your help.
# Physics - MathMate, Thursday, September 24, 2009 at 6:53am
The basic principle is the conservation of energy.
When a ball is brought higher up by h=100 m., energy is required to make this happen. The energy is stored as potential energy, Ep=mgh, m=mass, g=acceleration due to gravity.
When the ball falls from this height in a free fall, energy is transformed into kinetic (movement) energy, given by the equation Ek=(1/2)mv², where v=velocity of the ball.
When the ball hits the ground, the velocity is reduced, so is the kinetic energy according to the formula Ek. Since total energy is conserved, the difference goes into other forms, such as kinetic energy of the fragments of soil flying around (sum of (1/2)mv² of the soil fragments), and the rest (in this case half) goes into heat, given by
Eh=mHΔT, H=specific heat, m again the mass, and ΔT=change in temperature.
I recapitulate:
The basic principle is the conservation of energy, in different forms.
Hope this clears up a little more of the picture. Post any time for more explanations.
# Physics - Ceres, Thursday, September 24, 2009 at 12:10pm
I worked on this the rest of last night and some more this morning and this is what I got.
Ep = mgh
Ep = 10kg(9.8m/s2)(100m)
Ep = 9800kgm2
I then equated that to the kenetic energy and used that amount to find the velocity:
9,800kg(m2) = 1/2 mv2
square root of 1960 = v
Now that I'm thinking it through more, I'm not sure why I did the calculations above.
Next I plugged in the numbers to find the change in temperature. I got:
Eh = mH(chng in Temp)
Eh = 10kg(450kj/kg*oC)(chng in T)
But I do not know the Eh (I'm not sure what that stands for) nor am I supposed to use the 1.1oC for the change in temp.
I understand all of the concepts you talked about - conservation of energy, potential energy to kenetic energy, etc. But my brain is still missing something and I'm not sure what it is. I included the above equations because maybe they would help you to see where my thinking has gone wrong. Thanks again for your help.
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