A 0.010 kg (10 gram) round ball of solid lead at 280 K initially moves at 400 m/s passing horizontally through atmospheric air. Aerodynamic drag reduces the speed to 300 m/s before the ball suddenly impacts an immovable and impenetrable solid wall. The frictional work (by the ball on the air) causes the air to increase in temperature. Assume that heat transfer from the air to the ball is one-third the value of the frictional work. On impact, the mass of the lead does not change, but the impact causes the ball to flatten, partially melt and stick to the wall. In the instant this happens there is very little time for significant heat transfer to occur. Find a) the diameter of the ball, b) the ball temperature just before impact, and c) the fraction of the lead that likely melted upon impact.
The molar mass of lead is 207 kg/kmol, the density of solid lead is 11300 kg/m3, the specific heat (change in specific internal energy per degree) is 0.13 kJ/kg-K and at the melting point of lead of 600.6 K. at std. atm. pressure it requires 23 kJ/kg of energy input to melt solid lead at the melting temperature into liquid.