Question

# A 48.5-kg block of ice at 0 °C is sliding on a horizontal surface. The initial...

A 48.5-kg block of ice at 0 °C is sliding on a horizontal surface. The initial speed of the ice is 8.24 m/s and the final speed is 4.08 m/s. Assume that the part of the block that melts has a very small mass and that all the heat generated by kinetic friction goes into the block of ice, and determine the mass of ice that melts into water at 0 °C.

Mass of ice = 48.5 kg

initial speed =8.24 m/s

final speed = 4.08 m/s

As question mentions very small mass melts, for final Kinetic energy calculation we can take the same mass, m = 48.5 Kg

Initial KE = 0.5 * mvi2 = 0.5*48.5*8.24^2 = 1646.5168 J

Final KE =  0.5 * mvf2 = 0.5*48.5*4.08^2 = 403.6752 J

Loss of KE = heat generated = 1646.5168 - 403.6752 = 1242.84 J

Let mass of ice that melts be m Kg

So m*334000 = 1242.84

=> m = 0.003721 Kg = 3.721 gram

So mass of ice that melts = 3.721grams

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