Copper has a specific heat of 387 J/kg°C. A copper bullet is moving at 950 m/s. If the bullet is suddenly stopped so that all of its kinetic energy is converted into heat, determine the temperature that the copper bullet reached before it was stopped. Take the initial temperature of the bullet to be 30 °C.

1196.02 °C

Explanation:

If the kinetic energy is converted into heat,

then,

Kinetic energy of the copper = heat energy of the copper

1/2m(v²) = cm(t₂-t₁)

where m = mass of copper, v =  velocity of copper, c = specific heat capacity of copper, t₂ = final temperature of copper, t₁ = initial temperature of copper.

Since the mass of copper remains the same,

1/2v² = c(t₂-t₁)

make t₂ the subject of the equation

t₂ = 1/2(v²/c)+t₁ Equation 1

Given: v = 950 m/s, c = 387 J/kg°C, t₁ 30 °C

Substitute into equation 1

t₂ = 1/2(950²/387)+30

t₂ = 1196.02 °C

Hence the temperature the bullet reach before it was stopped = 1196.02 °C

c. magnitude and direction