A 0.02 kg-lead bullet traveling 200 m/s strikes an armor plate and comes to a stop. If all of it's energy is converted to heat that it absorbs, what is the temperature change?
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To determine the temperature change, we need to utilize the concept of specific heat and the equation for calculating the change in temperature.
The equation for calculating the change in temperature using specific heat is:
ΔT = Q / (m * c)
Where:
ΔT is the change in temperature
Q is the heat absorbed or released
m is the mass of the object
c is the specific heat of the material
First, let's calculate the heat absorbed or released by the bullet. Since it comes to a stop, all of its kinetic energy is converted into heat. The kinetic energy (KE) is given by:
KE = (1/2) * m * v^2
Where:
m is the mass of the bullet
v is the velocity of the bullet
Substituting the given values, we have:
m = 0.02 kg
v = 200 m/s
KE = (1/2) * 0.02 kg * (200 m/s)^2
KE = 400 J
Now, let's calculate the temperature change. We need to know the specific heat of lead, which is approximately 130 J/(kg·°C).
Substituting the values into the equation:
ΔT = Q / (m * c)
ΔT = 400 J / (0.02 kg * 130 J/(kg·°C))
Calculating this, we find:
ΔT ≈ 12.31 °C
Therefore, the temperature change of the bullet when it comes to a stop and all its energy is converted into heat, would be approximately 12.31 degrees Celsius.