Posted by Ceres on Wednesday, September 23, 2009 at 4:07pm.
The question is:
"A block of ice at 0oC is dropped from a height that causes it to completely melt upon impact. Assume that there is no air resistance and that all the energy goes into melting the ice. Show that the height necessary for this to occur is at least 34 km."
I know that it takes 334J/g to turn ice to liquid (thanks to help that was given to me for another problem). Does this have anything to do with this problem? no mass is given for the ice, so I assume that there is no difference for one gram than there is for many gms of ice. What does the height have to do with the ice turning to water? The higher up it drops from the more force it has? Thanks.
* Physics - MathMate, Wednesday, September 23, 2009 at 7:11pm
"I know that it takes 334J/g to turn ice to liquid "
That's a good start.
The question assumes no air-resistance, which means that the potential energy at the high altitude instantly and completely transforms into heat energy and distributed evenly to the piece of ice to melt it. It further assumes that the value of g, acceleration due to gravity does not change with elevation (height).
Potential energy when an object of mass m is positioned at a height h from ground is mgh, where g is the acceleration due to gravity.
So equating heat energy with potential energy, consider a 1-kg block of ice:
334 joules/g *1000g = 1 kg*9.8*h
Find h.
* Physics - Ceres, Wednesday, September 23, 2009 at 9:12pm
I am trying to understand what you wrote. Where did the 1000g come from? And how do we know the mass of the ice is 1kg? There is no weight for the ice listed in the problem. I did solve for h and got 34.1. I also didn't realize that heat energy would be the same as potential energy, so thank you for pointing that out. Sorry to be a bother, but I really want to understand why the problem works as it does. Thanks!
oh if you want mathmate to answer this question, then just say to mathmate where you put tour subject.
Sara is right.
If you ask the follow-up where it was asked, I will see it faster there than a repost/new post. I do appreciate that you have noted it as a repost and included the relevant information.
In fact, the question has been responded an hour and a half ago before I see this repost.
For the answer, see
http://www.jiskha.com/display.cgi?id=1253736433
feel free to post follow-ups.
I can help explain the solution to the problem.
The 1000g is used because it converts the units from grams to kilograms. Since the equation is asking for the height necessary for completely melting the ice, we can assume a 1kg block of ice for simplicity.
In the problem, we are given that it takes 334J/g to turn ice to liquid. So, if we have a 1kg block of ice, the heat energy needed would be 334 Joules/g * 1000g = 334,000 Joules.
On the other hand, the potential energy when an object of mass m is positioned at a height h from the ground is given by mgh, where g is the acceleration due to gravity.
In this case, we have a 1kg block of ice and we want to find the height h. So the equation becomes:
334,000 Joules = 1kg * 9.8m/s^2 * h
Simplifying the equation, we can solve for h:
334,000 Joules = 9.8h
h = 334,000 Joules / 9.8
h ≈ 34,082 meters or 34.1 kilometers
Therefore, the height necessary for the ice to completely melt upon impact is at least 34.1 kilometers.
I hope that helps you understand the solution to the problem! Let me know if you have any further questions.