Solving Transfer of Energy: Find Height Dropped for Bowling Ball

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Renzokuken
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1. Homework Statement
An 11 kg bowling ball at 0 degrees C is dropped into a tub containing a mixture of ice and water. A short time later, when a new equilibrium has been established, there are 5.0 g less ice.
From what height was the ball dropped? Assume that no water or ice splashes out.




Homework Equations


PE=mgh

3. The Attempt at a Solution
PE=mgh=11*9.8*h=107.8h
I don't know what to do after this.
 
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You should find out how much energy it would take to melt 5 g of ice.
 
Is there a formula to find how much energy it takes for 5g of ice to melt?
 
You need to use the enthalpy of fusion. For water it is 6.0095 kJ/mol, or 333.55 kJ/kg