Answer to Question #182789 in Physics for Robert

Question

A piece of ice weighing 4 g and with a temperature of 0 ° C falls freely from a height of 30 m towards the Earth's surface. When it hits the ground, it leads to a completely inelastic collision between the mentioned piece of ice and the Earth. Assuming that all the mechanical energy is absorbed by the ice sample, determine what proportion of it has melted. The latent heat of melting of ice is 333 kJ / kg. (Answer:ΔU =1330.82 J) I dont know the procedure.

Answer 1

Find the (potential) energy that turned into heat during the collision:

$$E=Mgh.$$

Express heat in terms of melted mass m:

$$Q=m\lambda.$$

We were told that

$$E=Q,\\ Mgh=m\lambda,\\\space\\ m=\frac{Mgh}{\lambda}=3.53·10^{-6}\text{ kg}.$$

This is just

$$k=\frac mM100\%=0.088\%,$$

or $8.825·10^{-4}$ of the initial mass.