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.

1) 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?
_________m/s

Answer 1

v = 1166.9 m / s

Step-by-step explanation:

The equation for caloric energy is

Q = m
`c_(e)` ΔT = m ce (
`T_(f)`-T₀)

Where m is the mass, ce is the specific heat and DT is the temperature variation

In this case the cannonball has kinetic energy

Em = K = ½ m v²

They indicate that mechanical energy is completely transformed into heat

Q = Em

m
`c_(e)` (
`T_(f)` - To) = ½ m v²

v = √ 2
`c_(e)` (
`T_(f)`-To)

Let's calculate

v = √ (2 450 (1811-298))

v = 1166.9 m / s