A lead bullet has a initial temperature 27C. Melting point of lead is 327C ,its latent heat of melting is 2x10^4J/kg and specific heat capacity 126J/(kgC). Assuming that all kinetic energy convert to heat energy find the velocity of bullet needed to melt lead.
As given in the question kinetic energy of the bullet convert to heat energy.
kinetic energy of bullet (`E_k` ) will be equal to the sum of heat required to get the bullet to melting point(`Q_m` ) and latent heat required for melting (`Q_l` )
`E_k = Q_m+Q_l`
Assume that bullet has a mass of m.
`E_k = 1/2xxmxxv^2`
`Q_m = mxx126xx(327-27) = mxx126xx300`
`Q_l = mxx2xx10^4 `
`1/2xxmxxv^2 = mxx126xx300+mxx2xx10^4 `
`v^2 = 2(126xx300+20000)`
`v^2 = 115600`
`v = 340m/s`
So the bullet need to strike the steel at a velocity of 340m/s.