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

Answer:

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

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

$Q=m(126\times(327.3-29.5))+m\times2.1\times10^{-4}$

We need to calculate the minimum speed of a lead bullet

Kinetic energy converted to heat energy

$Q=\dfrac{1}{2}mv^2$

Put the value into the formula

$m(126\times(327.3-29.5))+m\times2.1\times10^{-4}=\dfrac{1}{2}mv^2$

$v^2=2(126\times(327.3-29.5)+2.1\times10^{-4})$

$v=\sqrt{2(126\times(327.3-29.5)+2.1\times10^{-4})}$

$v=273.9\ m/s$

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