Question

An iron nail is driven into a block of ice by a single blow of a hammer. The hammerhead has a mass of 0.5 kg and an initial speed of 0.8 m/s. Nail and hammer are at rest after the blow. How much ice melts? Assume

Answer 1

`m = 4.790* 10^(-4)\,g`

Step-by-step explanation:

By means of the First Law of Thermodynamics, which is a generalization of the Principle of Energy Conservation, the kinetic energy of the hammer is dissipated by the hammer in the form of heat, which melts the ice. That is to say:

`K_(in) - Q_(out) = 0`

`Q_(in) = K_(in)`

`Q_(in) = (1)/(2)\cdot (0.5\,kg)\cdot (0.8\,(m)/(s) )^(2)`

`Q_(in) = 0.16\,J`

Let consider that ice melts a 0 °C and 1 atm, so that heat is entirely latent. Hence:

`Q_(in) = m\cdot L_(f)`

The melt mass of ice by a single blow is:

`m = (Q_(in))/(L_(f))`

`m = (0.16\,J)/(334\,(J)/(g) )`

`m = 4.790* 10^(-4)\,g`