Solving Transfer of Energy: Find Height Dropped for Bowling Ball

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To determine the height from which the bowling ball was dropped, the potential energy (PE) of the ball is calculated using the formula PE = mgh, where m is the mass (11 kg) and g is the acceleration due to gravity (9.8 m/s²). The energy required to melt 5 g of ice is also needed, which can be calculated using the enthalpy of fusion for ice, approximately 333.55 kJ/kg. The discussion emphasizes the need to equate the potential energy of the bowling ball to the energy required to melt the specified amount of ice. Participants are seeking guidance on how to proceed with the calculations after establishing the potential energy. Understanding both energy transformations is crucial for solving the problem.
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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
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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