A block of ice at 0^ C falls from a height h and hits the ground perfectly inelastically. Assuming that all of the lost mechanical energy is absorbed by the ice, find the height h from which the ice must fall so that exactly one-quarter of its mass melts. (Take g = 10 ~m/s^2 and latent heat of fusion of ice L = 3.36 10^5 ~J/kg )

Step-by-step solution

Let the total mass of the ice block be m . The gravitational potential energy lost by the ice block when it falls from height h is: U = mgh The heat energy required to melt one-quarter of the mass of the ice is: Q = ( m 4 )L Since all the lost mechanical energy is absorbed by the ice as heat, we equate U and Q : mgh = mL 4 The total mass m cancels out from both sides: gh = L 4 Rearranging for h : h = L 4g Substitute the given values ( L = 3.36 10^5 ~J/kg and g = 10 ~m/s^2 ): h = 3.36 10^5 4 10 h = 336000 40 h = 840