Question

A piece of ice of mass 50kg is pushed with a velocity of 5m/s along a horizontal surface.as a result of friction between the piece of ice and the surface,the piece stops after travelling 25m,the ice melted in the process is_____________.

Answer 1

A piece of ice of mass 50kg is pushed with a velocity of 5m/s along a horizontal surface. as a result of friction between the piece of ice and the surface, the piece stops after travelling 25m, the ice melted in the process is ___________.

Kinetic energy, which ice has:

$$W = \frac {M v ^ {2}}{2}$$

Energy which need to melt peace of ice of mass $M_{M}$:

$$Q = \lambda M _ {M}$$

where $\lambda$ - specific heat of fusion.

All kinetic energy was used to melt ice using friction force:

$$\frac {M v ^ {2}}{2} = \lambda M _ {M} \rightarrow M _ {M} = \frac {M v ^ {2}}{2 \lambda}$$ $$M _ {M} = \frac {5 0 k g * (5 m / s) ^ {2}}{2 * 3 3 4 * 1 0 ^ {3} J / k g} = 1. 8 7 * 1 0 ^ {- 3} k g$$

Answer: $M_{M} = 1.87 * 10^{-3} kg$