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 298 K, how fast would the cannonball need to travel in order to reach its melting point on impact?

Answer 1

Answer:

   v = 1,167 10³ m / s

Explanation:

The equation for heat is

             Q = m ce ΔT

Let's replace

              Q = m 450 (1811-298)

              Q = m 6.81 105

This is the energy of the ball, using energy conservation

              Q = Me = K = ½ m v²

              m 6.81 10⁵ = ½ m v²

               v = √ (2 6.81 105)

               v = 1,167 10³ m / s

This speed is greater than the speed of sound, so the process is unlikely to occur