Question

It is claimed that if a lead bullet goes fast enough, it can melt completely when it comes to a halt suddenly, and all its kinetic energy is converted into heat via friction. Find the minimum speed of a lead bullet (initial temperature = 29.5 °C) for such an event to happen.

Answer 1

The minimum speed of a lead bullet is 273.9 m/s

Step-by-step explanation:

Given that,

Initial temperature = 29.5°C

We need to calculate the heat

Using formula of heat

`Q= mc(T_(2)-T_(1))+mL`

Where,
`mc(T_(2)-T_(1))` = Energy needed to bring bullet from 29 to 327.3°

ml=Energy needed to melt bullet at this temperature

Put the value into the formula

`Q=m(126*(327.3-29.5))+m*2.1*10^(-4)`

We need to calculate the minimum speed of a lead bullet

Kinetic energy converted to heat energy

`Q=(1)/(2)mv^2`

Put the value into the formula

`m(126*(327.3-29.5))+m*2.1*10^(-4)=(1)/(2)mv^2`

`v^2=2(126*(327.3-29.5)+2.1*10^(-4))`

`v=\sqrt{2(126*(327.3-29.5)+2.1*10^(-4))}`

`v=273.9\ m/s`

Hence, The minimum speed of a lead bullet is 273.9 m/s