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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.
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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.
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