A historian claims that a cannonball fired at a castle wall would melt on impact

Question

A historian claims that a cannonball fired at a castle wall would melt on impact with the wall. Let's examine this claim. Assume that the kinetic energy of the cannonball is completely transformed into the internal energy of the cannonball on impact with no energy transferred to the wall. The cannonball is made of iron, which has a specific heat capacity of 450 J/kg-K and a melting point of 1811 K.

If the cannonball has an initial temperature of 300 K, how fast would the cannonball need to travel in order to reach its melting point on impact?

If the latent heat of fusion of iron is 2.72

Explanation / Answer

heat requred by the cannon ball to reach to melting point

Q1 = m*S*dT

dT = 1811-300 = 1511 K

KE of the moving ball = 0.5*m*v^2

here the KE is onverted to heat

0.5*m*v^2 = m*S*dT

v^2 = 2*S*dT

v = sqerrt(2*S*dT)

v = sqrt(2*450*1511)

v = 1.17*10^3 m/s <-------answer

+++++++++++++++++++++

heat requred by the ball to completely melt

Q2 = m*S*dT + m*Lf

KE of the ball = 0.5*m*v^2

here the KE is onverted to heat

0.5*m*v^2 = m*S*dT + m*Lf

v^2 = 2*S*dT + 2*Lf

v = sqerrt(2*S*dT + 2*Lf)

v = sqrt( (2*450*1511) + (2*2.72e5))

v = 1.38*10^3 m/s <-------answer

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