So confused on this physics problem....please help!?

Question

Ok, here's the problem...

"Calculate the height from which a block of ice at 0degrees celsius must be dropped for it to completely melt upon impact. Assume that there is no air resistance and that all the energy goes into melting the ice (Hint: equate the joules of gravitational potential energy to the product of the mass of ice and its heat of fusion (335,000 J/kg)).

My problem is that I have no clue what formulas/equations to use for this. I realize that the equation for Potential Energy is PE = mgh. And the equation for Quantity of heat is Q = cmDT. But how would I apply them to this problem?

Answer 1

Instead of using Q = cmDT, I will use Q = mL. This formula will represent the heat required for ice to melt. L is the latent heat, or heat of fusion, which was already given in the question.

(1) - Set P.E. formula equal to new formula I just gave you:

mgh = mL

(2) - "m" is on both sides, so it cancels out:

gh = L

(3) - Isolate h, since we're solving for height:

h = L/g

(4) - Plug in the given values:

h = 335000/9.80

(5) - Divide!

h = 34183.67 m


*As you can see from step 2, the height doesn't depend on the mass of ice.

**By the way, don't forget to vote my last answer as the best answer. Remember the question about the steel nail being pounded into the wood, and you had to find the change in temperature. I gave you a really good answer, and I explained everything step by step.

***I forgot to explain exactly why I used that new formula, Q = mL. You were trying to use Q = cmDT. The reason "DT" is in this formula is because there has to be some change in temperature. We know that ice melts at 0 degrees celsius. The problem says that the ice is already at 0 degrees celsius. That means that no further temperature change is required; the ice is ALREADY at melting temperature. When a phase change occurs (solid to liquid, liquid to gas, etc.), you can't use Q = cmDT ALONE. First, you need Q = cmDT to find the heat required to get a certain mass of ice to the proper temperature. THEN, Q = mL is the additional heat required to actually CHANGE that certain mass of ice into a different phase. If the ice had a different starting temperature, like 4 degrees for example, this is what would happen:

Q = cmDT + mL

This shows that the temperature must FIRST BE CHANGED to 0 degrees celsius, because that's the temperature ice melts at. THEN, additional heat is addes to actually melt the ice.

Answer 2

Since it says all the energy is used in melting the ice, then the Potential Energy is equal to the quantity of heat reqiured in melting the ice. There is no temperature change so,
Q=latent heat of fusion x mass of ice=mgh
therefore,
latent heat of fusion=gh
335000=10 x h
h= 33500 metres

Answer 3

come on, i think even einstein couldnt solve that problem, just give it a brake