Answer to Question #90436 in Mechanics | Relativity for AWESOME

Question

An ice cube at 0 oC is dropped on a ground and it melts to water at 0 oC. If all the kinetic energy of ice went into melting it, from what height did it fall

Answer 1

Beginning potential energy of the ice cube: $E_p=m*g*h$

Where,

$m -$ weight of ice cube

$h -$ height of drop

$g -$ gravitational acceleration ($g=9.8 m/s^2$ for SI)

At the monet of the falling end kinetic energy: $E_k=m*v^2/2$

Where,

$v-$ speed in the moment of contact with groung

Using the energy conversation law:$E_k=E_p$

Using the heat of fusion formula: $Q=L*m$

Where,

$Q-$ nesessary heat for melting

$L-$ heat of fusion of ice ($L=334*10^3 J/kg$ for SI).

According to the task: $E_k=Q$ or $L*m=m*g*h$ $\implies$ $h=L/g$

Using numbers, $h=34.08*10^3 m$

Answer: $34.08*10^3 m$