If you drop a piece of ice on a hard surface, the energy of impact will melt some of the ice. The higher it drops, the more ice will melt upon impact. Show that to completely melt a block of ice that falls without air drag, it should ideally be dropped from a height of 34 km. [Hint: Equate the joules of gravitational potential energy to the product of the mass of ice and its heat of fusion (in SI units, 335,000 J/kg). Do you see why the answer doesn’t depend on mass?]

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter17: Energy In Thermal Processes: The First Law Of Thermodynamics
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If you drop a piece of ice on a hard surface, the energy of impact will melt some of the ice. The higher it drops, the more ice will melt upon impact. Show that to completely melt a block of ice that falls without air drag, it should ideally be dropped from a height of 34 km. [Hint: Equate the joules of gravitational potential energy to the product of the mass of ice and its heat of fusion (in SI units, 335,000 J/kg). Do you see why the answer doesn’t depend on mass?]

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